from:"Kristofer Munsterhjelm"


On 08/31/2013 02:24 PM, Vidar Wahlberg wrote:

This may be a bit outside what is usually discussed here, but I'll give
it a shot and if someone know of some resources I should check up on
then please let me know.

I've not followed this list for a long time, but my impression is that
the main focus is on the technical or mathematical properties, and less
on the sociological issues.


I focus more on mathematics than on the sociological aspects, and I 
suppose at least part of the reason is that anybody can do mathematics. 
The old joke goes that a mathematician is a device for turning coffee 
into theorems. It may not be entirely true, but there is a point: if you 
like solving puzzles, there are plenty to be solved with nothing more 
than a computer and your mind.


In contrast, the sociological issues are much more fuzzy, particularly 
when you get into the matter of actually participating to change the 
system. I have tried to argue social things too here, but there are many 
opinions of what's desired and say, how the voters act in different 
situations.


Lately I've started to lean in a more empirical direction in that 
respect. It's possible to argue that voters act in this or that manner, 
and it's possible to do so in many different ways that all sound 
reasonable on the face of it, so we'd need some kind of tiebreaker. And 
that tiebreaker would ultimately be the reality of the matter. But I 
don't have the resources to poll people in the real world, design and 
run experiments, and so on, so I rely on the reports of others (like 
BL's polling results on comparison to an objective standard vs 
comparison to other candidates).



For instance, when voting for persons then candidates with high
popularity and charisma are likely to win more votes than less
charismatic candidates, despite the less charismatic candidates being
far more suited for the task (more knowledge, experience, talent, etc.).
In the Norwegian system where we got multiple parties, but two blocks
(left and right), we also see that some people vote for their second
preference rather than the first, because the first is in the wrong
block or intend to cooperate with another party which the voter dislike
the most.


That's both a mathematical and a sociological thing, I think. I 
considered it in a game theoretical/mathematical sense in a previous 
post where I asked how one could solve the need for tactics in a 
parliamentary system with coalitions.


A voter might face a somewhat close race between a left- and a 
right-wing bloc, where the right-wing bloc looks like it's winning. Then 
if the voter is left-wing, he might vote strategically for the right 
bloc member that's closest to the center. But if everybody did this, 
then the right-wing bloc would win even if the strategically voting 
left-wingers could have made the left-wing bloc win by voting honestly.


I recall that one of the other list members suggested Asset voting to 
solve this problem: to let the negotiations happen among the candidates 
since the voting system can't possibly infer, based just on the votes, 
which coalitions are realistic.



If it is within the scope of this list, what are your thoughts on the
subject?
Alternatively:
Assuming the perfect election system where voting any different than
your real preference would only hurt your preference, how would you
design a form of government that is elected by the people, but is
resistant to sociological issues that can't be prevented by the election
method (such as the examples mentioned above)?


It's possible that the best democracy might not have voting at all. 
Gohlke's initial idea did not have much voting in it: groups of three 
people would meet, agree upon which to represent all three, and then the 
winner would join two other winners, and so on up until you had a 
council, no voting method needed.


Systems based on policy juries might not need elections either, nor more 
direct systems based on sortition. You have Aristotle's argument that 
elections are, in themselves, aristocratic because they favor the people 
who have the means by which to be well known in the first place; and you 
could probably make similar arguments in the vein that elections select 
for the wrong things: charisma, being a good salesman, making it appear 
as if the people is being heard despite the inner system's inflexibility 
and own stasis, and so on.


I once considered a hybrid system that *would* use elections, but in a 
quite different way: first you'd select a significant number of people 
at random, and then these would elect from among their number. It does 
away with continuity both for ill (problem with consistency of plans) 
and good (no monolithic party machines).


My point in all of this is that we don't know if the ideal democratic 
system would contain no election methods at all, only one throughout, or 
very many different ones (e.g. some kind of emergent competition for 
politicians system, where, like

Re: [EM] Biproportional representation (was Re: Preferential voting system where a candidate may win multiple seats)


On 07/29/2013 07:22 PM, Vidar Wahlberg wrote:

On Mon, Jul 29, 2013 at 01:36:49PM +0200, Kristofer Munsterhjelm wrote:

On 07/28/2013 04:37 PM, Vidar Wahlberg wrote:

Upper apportionment:
- Party seats are apportioned using unmodified Sainte-Laguë based on
   national votes. If desirable the first divisor may be modified, or a
   election threshold may be set to prevent fragmentation, but I've not
   done this.


Apportionment according to divisor methods can be done in two ways:
either explicitly (like Sainte-Laguë) or by a round-and-adjust
method (like Webster). If I understand you correctly, your
biproportional program uses the Webster method, i.e. you pick x so
that
SUM k=1...n round(support[k] * x)
equals the desired number of seats.

I don't know how to turn a given explicit divisor method into a
given rounding method, so how would you implement modified
Sainte-Laguë this way?


I may misunderstand you here, but in the upper apportionment I used
unmodified Sainte-Laguë. That is, exactly how it's done in counties
today (excluding leveling seat), just on the national vote count and
with 169 seats.
As of modifying Sainte-Laguë that would only mean modifying the first
divisor, which would have very little impact when 169 seats are to be
apportioned. Although, I did try this and that resulted in Miljøpartiet
de Grønne not winning a seat.


Oh, I see. I thought you meant that the iteration procedure itself used 
unmodified Sainte-Laguë but could be altered to use modified 
Sainte-Laguë if so desired.


If you're talking about the upper apportionment (i.e. the setting of the 
targets), then I understand you. Any method could be used to set the 
targets. For that matter, one could set the target to something not 
produced by a divisor method at all, although then it's not certain that 
the iterative process will find a solution.


I'm not sure what you mean by exactly how it's done in counties today, 
though. If you mean that the apportionment of seats to counties (i.e. 
how many seats each district gets in the district target) is done by 
unmodified Sainte-Laguë, that's right. But the apportionment of seats to 
parties within each county (e.g. how many seats AP should get in Oslo 
according to the current system) is done by modified Sainte-Laguë.



Since my last mail I've implemented preferential election (redo upper
apportionment until all parties have at least n seats, each rerun
excluding the party with least votes, transfering them to the next
preference). I chose to use n seats instead of x percent as I only
entered data for the 10 largest parties and thus would have to hard code
the total amount of votes to get a correct vote percentage, but I
digress.


I note that this would also support what I call CPO-SL because it, too, 
returns as output which parties are to be excluded. So one would just 
run CPO-SL on the national ballots, find out which parties to exclude, 
do that, and then count support by first preference votes of the 
uneliminated parties.


It would not be the same thing as running CPO-SL on each county to find 
more balanced councils there, though. Making a biproportional version of 
CPO-SL would be an interesting puzzle: I think that one would use 
something like minimax to balance the district concerns and the national 
concerns, but that is in any case a digression.



- District seats are determined externally and thus not apportioned in
   this implementation.


A similar trick could be used to implement a threshold if desired.
It would be complicated, though, something like:

1. Do a county-by-county count.
2. Parties below the threshold have their number of seats fixed to
the number of seats they got directly.
3. Fixing these parties' number of seats, determine the number of
seats for the other parties by national Sainte-Laguë: each party
gets a seat as in Sainte-Laguë, but when a party below the threshold
have got all their seats according to 2., remove that party from the
count.
4. Use the result as the target for the number of party seats.

I'd still rather use an absolute but lower threshold, though; or
none at all, like you're doing.


Regretably I'm not quite following you here. To try to explain the
method in short:
In upper apportionment you decide how many seats each party gets, this
is the final result and will not be changed (but where they receive the
seats is yet to be decided). Seats in districts/counties are determined
externally. Here is the only place we use Sainte-Laguë. If we want some
sort of threshold or preferential election, it must be done here.


Yes, that's what I'm saying. If the upper apportionment can be given 
outside the system itself, you can set it however you want. Say you want 
a threshold where all parties that get less than 4% national support 
only get as many seats as they would have got on a county-by-county 
basis (as is the case today).


Then you would use another method, not national Sainte-Laguë, to 
determine how many seats each

[EM] Possibly making Sainte-Lague even more STV-like

Here's a short post (since I don't have as much time as I would like) 
with an idea of how to make Sainte-Lague even more like STV. I started 
thinking about it as part of my thinking that perhaps pairwise 
multiwinner methods will always be too complex; and so I tried to 
include some Condorcet compliance here as well.


Start with the original Sainte-Lague count. For each party, call the 
difference between how many voters voted for them, and how many voters 
they'd need to get the number of seats they currently did, the excess. 
Then, as in STV, start redistributing the excess. Move a few voters at a 
time (I don't know how many you can safely move in a batch) from their 
first preference to their second.


(Note that for parties that got no seats and can get no seats through 
redistribution, this has the same effect as elimination: their seat 
count is 0 and so they can get that number of seats with no voters at all.)


Now the question is in what order to redistribute. I can think of three 
ways. The first is in reverse Condorcet order: you redistribute the 
voters for Condorcet losers first. The second is from parties with few 
seats; and the third is whoever has the greatest excess at any point.


The method stops when no more redistribution can be done. This is also a 
vague idea, but I guess something like maximal excess is minimal could 
work... though I then would have to use more rigorous mathematics to 
show that the method actually optimizes that.


The point of doing it in reverse Condorcet order would be to reduce to 
Condorcet in the single seat case. Consider an LCR situation with 
Condorcet social ordering CLR and where L gets the initial seat. Then 
all the R-votes are redistributed to C since R can't win anyway, so L 
loses its seat. At this point no further redistribution in this 
direction can alter anything (we can only distribute from L to C, not 
vice versa), so we'd like to finish there.


The few-seats order of doing it has an intuitive IRVish appeal: small 
parties are disqualified/redistributed first, then larger ones.


Finally, the greatest excess at any point may have some desirabla 
steady-state properties, and may get closer to optimizing maximin 
excess. I am not sure of this, though - it just sounds like something 
that would. I also think that one would elect C in the example above: R 
would have greatest excess (all the R-voters since they didn't get 
anything). Enough R-voters are distributed to C to make C win. Then L 
has the greatest excess and is redistributed to C as well, and it ends 
when they all have equal excess.



Could this idea be developed into a method that would be better than 
ordinary Sainte-Lague, yet also not as complex as my pairwise methods? 
Perhaps. But I have little time and so don't know yet. I thought I would 
just let you all know of the idea!


And it probably would not be cloneproof, (weakly) monotone or summable. 
But I don't know of any method that follows STV's algorithmic template 
that is.


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Re: [EM] Sociological issues of elections


On 09/02/2013 09:23 PM, Vidar Wahlberg wrote:


I once considered a hybrid system that *would* use elections, but in
a quite different way: first you'd select a significant number of
people at random, and then these would elect from among their
number. It does away with continuity both for ill (problem with
consistency of plans) and good (no monolithic party machines).


This reminds me a bit about how comments on slashdot.org are rated by
the readers. Perhaps you're familiar with this system?
They claim it works fairly well for their needs, but will it work for
electing a government? Even if you select a subset of the population,
those are susceptible to fearmongering, glorifying and generally create
a distorted image of the various candidates/parties to influence the
voter in a certain direction.


That's not quite what I meant. By among their number I meant that the 
people who were selected would elect a subset of their own. So you might 
pick, say, 500 for the initial level. Among these, the different people 
give reasons for why they should govern. Then the 500 elect 150 of their 
own to become the actual legislature.


I thought of that kind of system as a way of countering the most common 
objection against a randomly picked assembly: that the average person 
would rule, and he would be average in both the good and bad sense. So 
the electoral stage is supposed to remove the lower quality members of 
the random group. Since the initial group is picked at random, there's 
no direct way for a party to gain access to government: the chance that 
any given randomly picked person would be a party member is extremely low.


One could argue that the flipside of this kind of system is that it 
destroys the kind of continuity of planning that the parties provide. 
But in a sense, that continuity is also always subject to being changed 
by the changes in support.


I guess what you thought I was thinking of was a method where you pick a 
smaller sample that then run the traditional election (that is, choose 
parties etc). The benefit of that system would be that each member of 
the small sample would have a greater incentive to investigate the 
issues, but it's not the system I was thinking of, and to the extent 
that voting is also a participatory thing, the general population would 
not like having their choice taken away from them.


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Re: [EM] Wikipedia article needs editing

2013-08-28 Thread Kristofer Munsterhjelm


On 08/28/2013 11:12 PM, Richard Fobes wrote:

The Wikipedia article titled Electoral reform in the United States
contains a heading Electoral Reform Proposals and then under that
heading is a section titled Instant-runoff voting.  Obviously this
needs to be broadened to Election-method reform with IRV being just
one kind of election-method reform.

Does anyone have time to do this edit?  (I don't.)


I have quite a few real world issues to deal with right now, but I could 
give some ideas that come to mind if others would like to edit it.


One could mention Condorcet, particularly Schulze, as being used in 
different private organizations (usually of the technical variety), as a 
more concrete type of electoral reform: the voting method is seen as a 
tool, and the organizations reach for the tool known to them.
Then one could give a reference to Toby Nixon - or maybe not, since he 
wasn't reelected.
Finally, there would definitely be room for a mention of the CES and of 
Approval voting advocacy organizations (and possibly also CRV).


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Re: [EM] Top 2+1 Approval primaries

2013-07-25 Thread Kristofer Munsterhjelm


On 07/24/2013 08:54 PM, Jameson Quinn wrote:


Certainly you could propose complex systems that could be better than
this proposal in some ways. For instance, you could use a proportional
representation system such as Bucklin Transferrable Voting (BTV) for the
first round. But this proposal is a simple balance of the requirements:
nonpartisan voting, a balance of candidates and parties in the general
election, yet focused attention on a few strong candidates.


What do you think of a sequential PAV style primary? It seems to be 
simple enough:


1. Pick the winner.
2. Deweight all votes who approved of this winner by 1/3.
3. Pick the highest scoring candidate that's not the winner.

Would this be better than just picking the two Approval winners? It's 
not setwise PR, but setwise PR can, as you say, get very complex very fast.


The three-seats completion would either be:

1, 2, 3. As above.
4. Based on the original ballots, deweight those that approved of one of 
the winners by 1/3; of two of the winners by 1/5.
5. Pick the highest scoring candidate not already picked, based on the 
deweighted ballots,


or

1, 2, 3. As above
4. Start from the original ballots.
5. If the two picked candidates are from the same party, remove all 
candidates of this party from the ballots.

6. Pick the highest scoring candidate that has not already been picked.


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Re: [EM] Fwd: The list might like this...

2013-07-22 Thread Kristofer Munsterhjelm


On 07/22/2013 07:20 PM, Jameson Quinn wrote:

An interesting article from DLW  on modelling two-party voting as a
battle between two networks. (The comments are depressingly stupid, though.)


Maybe that could be used to argue in favor of Michael Allan's party 
that will dissolve itself. The general line would go to the effect of 
hey, connected nodes: you're what the party needs to succeed. So 
shouldn't you get some influence too? You can by using delegative 
structures, which is what we'd like to use.


Regarding the comments, I get the impression that the commenters know 
that something is wrong. But they don't know *why* something is rotten 
with the state of politics, so they try to find a simple explanation on 
their own. And the simplest explanations (in the sense of being easy to 
imagine) are conspiracy or that all blame can be placed on the current 
party in power.


I know that line of reasoning is potentially logically rude (in Suber's 
sense), so I'll be really careful with it. Still, it fits with the 
impression I get.



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Re: [EM] Fwd: The list might like this...

2013-07-22 Thread Kristofer Munsterhjelm


On 07/22/2013 07:20 PM, Jameson Quinn wrote:

An interesting article from DLW  on modelling two-party voting as a
battle between two networks. (The comments are depressingly stupid, though.)


Maybe that could be used to argue in favor of Michael Allan's party 
that will dissolve itself. The general line would go to the effect of 
hey, connected nodes: you're what the party needs to succeed. So 
shouldn't you get some influence too? You can by using delegative 
structures, which is what we'd like to use.


Regarding the comments, I get the impression that the commenters know 
that something is wrong. But they don't know *why* something is rotten 
with the state of politics, so they try to find a simple explanation. 
And the simplest explanations (in the sense of being easy to imagine) 
are conspiracy or that all blame can be placed on the current party in 
power.


I know that line of reasoning is potentially logically rude (in Suber's 
sense), so I'll be really careful with it. Still, it fits with the 
impression I get.



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Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-07-20 Thread Kristofer Munsterhjelm


On 07/19/2013 11:50 PM, Juho Laatu wrote:

On 19.7.2013, at 10.18, Kristofer Munsterhjelm wrote:



In such cases, I would also suggest a few of the seats of the
parliament be given by a centrist- or minmax-based method (e.g.
Condorcet, CPO-SL with few seats, or possibly even minmax approval
or something like it). The idea would be that there shouldn't be
any kingmakers, but if there's a near-tie, that tie is broken by a
moderate group.


In proportional systems one should distribute most of the seats
directly to different parties without seeking for compromise
candidates. I mean that also extreme parties should get their
proportional share of the seats. Only in the allocaton of the very
last seats (=last seats at national level) one can take the second
preferences of the voters into account. The second preferences often
point to compromise oriented candidates (by definition). The idea of
favouring compromise candidates thus means taking the second
preferences of the voters into account when allocating the very last
seats.

Sometimes the voters may prefer giving the last seat to a compromise
party (with only a small fraction of quota of first preference votes
supporting this decision) to giving it to one of the main parties
(that might have close to 0.5 quota of first preference votes left
supporting their candidate). The CPO approach is a good way to
estimate which allocation of seats would get wide support among the
electorate.


I was more thinking of doing so as a way of heading off the kingmaker 
objection. The objection goes something like: we need to have a 
threshold, because otherwise a very small party might be in position to 
make or break a coalition and so would get undue power. A threshold is 
an absolute way of avoiding this unless the party is at least to some 
extent large enough, but one could also avoid it by giving the 
tiebreaker spot to a centrist or broad appeal group. If complexity is 
not an issue, having a centrist tiebreaker group might even be 
preferable, since a threshold is indiscriminate about where it gives 
that tiebreaker power: a medium sized party could still become kingmaker 
were it lucky enough, given a threshold.


Now that I think about it, that might be a way to improve the inequality 
between proportional representation and coalition voting power. This 
could be done in one of two ways.


One could just state it as a constraint problem: given n adjustable 
seats, allocate so as to minimize the difference between coalition power 
and representation according to some metric. Like biproportional 
apportionment, this can be done by either departing from perfect 
representation of from perfect coalition power proportionality, and 
probably would meet somewhere in the middle.


The other option is to use parties or candidates with centrist positions 
or broad appeal as tiebreakers by themselves. If these are elected 
separately[1] to the main body of PR representatives, this would be more 
understandable to the voter, I think. The designer could say we used to 
have a 2% threshold to keep radicals from getting undue power; now we 
give 2% of the seats to a moderating body instead, which is more 
consistent and doesn't necessarily deprive the minor parties of a voice.


The former option is pretty straightforward in the explanatory sense (if 
difficult to actually implement because of the computational cost). But 
the second might require some more thought.


I often find it useful to consider extremes to determine the underlying 
logic. The extreme of the second option would be to give the entire 
parliament to a compromise group. In effect, that's what a single-winner 
rule does. If we consider a single-winner election as a council with 
only one seat and put it into the logic of the second option, then the 
single-winner election should give a candidate with broad support 
because the alternatives give a less accurate result. If one gives the 
single seat to a wing candidate, then the other voters are left 
unrepresented.


So what happens as we increase the number of seats? On the one hand, the 
quantization error due to the limited number of seats goes down. This is 
what permits PR in the first place. On the other, to the degree that the 
various members of the council are going to engage in coalition games, 
power starts to move from the center of the opinion space given by those 
members.


So, ideally speaking, PR opposes the tendency for the leadership of the 
central group to impose its views on the rest of the group (which when 
taken to its extreme can lead to the kind of corruption and inefficiency 
associated with one-party states). This it does by giving the different 
groups a voice and by making negotiation public. It is not perfect, 
because negotiation can still be concealed through backroom deals, but 
it's better than having no public negotiation at all.


And similarly, again ideally speaking, giving tiebreaker powers to a 
broad group counters

Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-07-19 Thread Kristofer Munsterhjelm

On 07/19/2013 07:45 AM, Juho Laatu wrote:

On 18.7.2013, at 23.36, Kristofer Munsterhjelm wrote:

(And now that I think about it: if it's desired, it should be
possible to make n-proportional apportionment methods for n2 --
e.g. a method that tries to balance regional representation,
national representation, and representation of minorities according
to their share of the population. The greater n is, though, the
less intuitive the results will be.)

I think any number of such (voted or static) proportionalities
could be used. To me the biggest problem is that the rounding
errors will increase, and as a result we will get also some strange
results. That means some less intuitive results as you say, but
maybe also more intuitive/fair in the sense that all groups will be
fairly represented.

With monoporopotional representation (ordinary PR), it's fairly easy to
explain to people what is going on: you get representatives
proportionally to what the voters say they want, in each district. With
biproportional representation between districts and nationwide results,
the proportionality becomes less obvious. A voter may say: Why did
party A get the seat, when it had fewer votes than party B, C, D and E,
and there were only 4 seats?. The response to this is: so that there
will be better proportional representation when you count the nation as
a whole. But then the voter may say: why did *we* get the strange
result? Why not the district over there?. And because of the
simultaneous constraints, it would be much harder to explain that,
because you might need to refer to the entire nationwide result to do it.

In short, multiple constraints might mean that the results over here
depends on what happens over there in a way that's not easy to
understand. And the more constraints you add, the harder it could get.

With voted and static proportionalities I refer to e.g.
percentage of votes to women vs. percentage of women in the society.

In real life having political and regional proportionality may be
enough for most countries, but I can see that in countries where the
balance betheen different groups of the society is critical, also
other proportionalities can be useful. This would allow e.g.
different ethnic groups to work within one (ideological) party
instead of being split in separate ethnic parties.

Yes. Also, if part of the point of representative democracy is that the
groups should take their conflict to parliament rather than resorting to
physical violence, accurate representation of ethnic groups might be
important where there has been struggle between those groups. Hylland
used an example of Bosnia-Herzegovina:
http://web.archive.org/web/20061005063631/http://www.oekonomi.uio.no/seminar/torsdag-v02/hylland-notes.doc
In his example, the two axes are geographical representation and
ethnic representation.

In such cases, I would also suggest a few of the seats of the parliament
be given by a centrist- or minmax-based method (e.g. Condorcet, CPO-SL
with few seats, or possibly even minmax approval or something like it).
The idea would be that there shouldn't be any kingmakers, but if there's
a near-tie, that tie is broken by a moderate group.

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Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-07-18 Thread Kristofer Munsterhjelm


On 07/18/2013 08:13 PM, Vidar Wahlberg wrote:


Thoughts are welcome, and sorry for the amount of mails, I'm having a
lot of spare time at the moment.


Could you try implementing Balinski's primal-dual method? It's somewhat 
explained in the Wikipedia article on biproportional apportionment, 
https://en.wikipedia.org/wiki/Biproportional_apportionment . Olli Salmi 
(who used to post to this list) wrote a document about it at 
http://www.uusikaupunki.fi/~olsalmi/vaalit/Biproportional_Elections.html .


If we're going to compare different methods, I also think we'd need some 
way of measuring the quality or proportionality of the result. The 
Sainte-Laguë index can be used in an ordinal manner on both axes, so you 
could say according to the SLI, the nationwide result produced by 
algorithm X is more proportional than the one produced by algorithm Y. 
However, unlike say, the Gallagher index, it's much harder to say *how 
much* more proportional X is than Y, since the index isn't bounded.


In 2011, the department of Mathematics at KTH held a workshop on 
electoral methods. One of the talks dealt with biproportional 
representation, and the slides can be found here: 
http://www.math.kth.se/wem/Zachariasen.pdf . They used the Gallagher 
index (which is optimized by quota-obeying methods) and determined that 
the Balinski method produced the most proportional results. Though the 
Gallagher index is optimized by quota methods, not divisor methods, it 
may still be of interest.


(And now that I think about it: if it's desired, it should be possible 
to make n-proportional apportionment methods for n2 -- e.g. a method 
that tries to balance regional representation, national representation, 
and representation of minorities according to their share of the 
population. The greater n is, though, the less intuitive the results 
will be.)



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Re: [EM] EM list problems?

2013-07-11 Thread Kristofer Munsterhjelm


On 07/11/2013 10:54 PM, Juho Laatu wrote:

This message (that was sent by me) was not properly delivered to me.
Did someone else have similar probelms or was it only me?

http://lists.electorama.com/pipermail/election-methods-electorama.com/2013-July/032170.html


I got it.


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Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-07-07 Thread Kristofer Munsterhjelm


On 07/07/2013 10:27 PM, Juho Laatu wrote:

On 7.7.2013, at 16.16, Vidar Wahlberg wrote:



Alternatively, instead of running Sainte-Laguë in each county, you
could run SL on the national result (distributing all 169 seats),
something which would produce a representation percentage very
close to the actual result, and then distribute the seats to the
parties in the different counties (keeping the same amount of seats
in each county).



I think this makes sense if you do not like the leveling seat style
of building proportionality at national level. The last seats will be
distributed pretty much in the same way anyway, but in this approach
all seats are in principle seen as equal. The algorithm may either
aim at some ideal allocation, or be a practical algorithm that just
finds a good enough result.


There's a balance between national proportionality and local 
proportionality. So if we're trying to get national proportionality 
while respecting local proportionality, it would make sense to alter the 
local distribution as little as possible while still getting a 
nationally accurate result. That's what biproportional 
apportionment/representation does.


My other suggestion was to have regional MPs, i.e. hierarchical MMP. But 
this raises the question of where the regional MPs should reside. I 
suppose national MMP systems have to deal with that issue as well: how 
do they do it? Where do top-up seats MPs in say, New Zealand, reside?


There's also a combination of these two, which I think Schulze 
suggested. If I remember correctly, it's basically MMP with overhang 
handled by deweighting party votes, thus fixing the decoy list problem 
in ordinary candidate + party list MMP.



If we want full proportinality, then proportionality should thus be
counted at national level. Another reason why national level votes
should be used to count the number of seats for each party is that
one should guarantee that it makes sense to vote for the small paries
also in the smallest counties. If there is no such prcedure or
leveling seats or some other national level leveling algorithms in
place, it would not make sense to vote for small parties in the small
counties. this would reduce the support of the smallest parties
already before the votes are counted.

This kind of balancing mechanisms will lead to electing a
representative of the small party at least in some county, or maybe
in this voter's own county, even if the number of votes would not be
sufficient to win any of the seats, if seats would be allocated
independently in each county.


I'd also like to note that if one were to use a method that tends 
towards Condorcet when there are few seats, e.g. my CPO-SL 
(Sainte-Laguë) method I described in A more Condorcet-like party list 
PR method, then the local seats will be even less proportional as a 
whole. This is related to that SNTV can work in multi-member elections, 
but pick the top N ranked candidates according to a Condorcet method's 
social ordering would not.


So if one wants to moderate the local councils with a method that tends 
towards Condorcet when there are few seats, then it becomes more 
important still to have a compensating mechanism to bring the local 
results more in line with the national result. Otherwise, the centrists 
would enjoy a great advantage at the cost of national level proportionality.


And yes, when one adjusts local outcomes to get greater national 
proportionality, that means that someone who shouldn't have won on the 
local level nevertheless does win. Hopefully the difference won't be as 
great as to make the voters complain! Perhaps this is part of the point 
of leveling seats: they start off not being owned by anyone, so giving 
them out to party members may not seem as much a way of overruling the 
local result as if one started with all seats filled and *then* adjusted.



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[EM] A more Condorcet-like party list PR method

2013-07-06 Thread Kristofer Munsterhjelm

Among other things, in Wahlberg's thread, there was a discussion about 
ways of making Sainte-Laguë party list PR accommodate ranked ballots.


The simplest method found was:

1. Allocate seats according to Sainte-Laguë or Webster with respect to 
first preference votes.

2. If any party got zero seats:
2.1. Remove the party with the least votes from all ballots.
2.2. Go to 1.

This will work most of the time, but it has two potential problems.

The first is that when there are only a few seats, it will reduce to 
Plurality (i.e. it doesn't take compromise parties into account).


The second is that the order of elimination may matter. If you have an 
L-C-R situation among parties, and none of them can get a seat by first 
preferences alone, then the compromise C (which may get a seat were L 
and R eliminated) may be eliminated early and so make the outcome worse 
for the L-C-R voters.



After some thinking, I think I've found a hack that should fix the 
second problem. I'm unsure how much it fixes the first, but it reduces 
to Condorcet in the single-seat case.


It's also probably too complex to be used, but that's another matter :-)


So, the method. It works like CPO-STV or Schulze STV: you define a 
function f({x}, {y}) for subsets {x} and {y}. This function produces a 
score of a virtual contest between the two subsets, and then these 
contests become the entries in a pairwise matrix that is run through a 
Condorcet method.


For this method, the subsets are sets of parties. To determine the score 
for f({x}, {y}), do this:


1. Eliminate all parties not in either {x} or {y}.
2. Do a restricted Sainte-Laguë allocation for {x}. A restricted 
allocation goes like Sainte-Laguë, but no party not in {x} can get any 
seats, and every party in {x} must get at least one seat. Implement 
thresholds as needed here.
2.1. If the allocation is contradictory (e.g. more parties than seats, 
or there is a threshold and a party below it has been given seats), then 
treat the allocation as one where no seats were given to any party.
3. Once done, for each party, add the number of voters that voted for 
that party, minus that party's quotient, to a common sum. Call this sum 
{x}'s proportionality score.
4. Do a restricted Sainte-Laguë allocation for {y} and similarly 
calculate {y}'s proportionality score.
5. f({x}, {y}) is equal to {x}'s proportionality score in this contest. 
f({y}, {x}) is equal to {y}'s proportionality score in this contest.


And here's a last-seat compromise example, adapted from the LCR example 
I gave earlier:

100: X
100: Y
 46: L  C  R
 44: R  C  L
 10: C  R  L

3 seats.
Let's determine f({XYR}, {XYC}):
The union of these subsets is {XYRC}, so L is eliminated. We now have:
100: X
100: Y
44: R
56: C

Restricted Sainte-Laguë allocation for {XYR}:
By the one-seat rule, we give one seat to each.
This gives a quotient of 100/3 for X and Y, and
44/3 for R.

The proportionality score is thus:
  100 - 100/3   (X-voters)
+ 100 - 100/3   (Y-voters)
+ 44 - 44/3 (R-voters)
+ 0 (C-voters)
= 488/3

Now, do {XYC}.
Restricted Sainte-Laguë allocation for {XYC}:
By the one-seat rule, we give one seat to each.
This gives a quotient of 100/3 for X and Y, and
56/3 for C.

The proportionality score is thus:
  100 - 100/3   (X-voters)
+ 100 - 100/3   (Y-voters)
+ 0 (R-voters)
+ 56 - 56/3 (C-voters)
= 512/3

So {XYC} wins, as it should.

And an example where the seats aren't all forced by the one-seat rule,
f({XL}, {XC}), again 3 seats:
The union of these subsets is {XLC}, so we have
100: X
 46: L
 54: C

Restricted Sainte-Laguë allocation for {XL}:
By the one-seat rule, one seat has to go to X and one
has to go to L. Now the quotients are 100/3 for X,
46/3 for L, and 54 for C. Since the allocation is
restricted to {XL}, C can't get any seats. Of the
remaining parties, X has the greatest quotient
and gets the second seat.

The final quotients are 100/5 for X, 46/3 for L, and
54 for C.

The proportionality score is thus:
  100 - 100/5   (X-voters)
+  46 - 46/3(L-voters)
+   0   (C-voters)
= 332/3

By the same reasoning, for {XC}, X gets two seats and C gets
one. This gives a proportionality score of 116, which is
348/3 and thus {XC} wins this

Re: [EM] A more Condorcet-like party list PR method

2013-07-06 Thread Kristofer Munsterhjelm


On 07/06/2013 02:26 PM, Kristofer Munsterhjelm wrote:


The method should be weakly summable (i.e. when the number of parties
are kept constant). For each cell in the matrix, do the elimination
first, then store the counts for each party. These counts can be summed
up between districts, so if n is the number of parties, you have (2^n)^2
cells, each of which stores n numbers in the worst case. And since n is
a constant, so is 2^n.


Replying to myself with an oops, here. By weakly summable, I usually 
mean summable with the number of seats held constant, number of 
candidates permitted to vary. If by candidates we mean parties, the 
Condorcet-like party list method fails this. Instead, it has a peculiar 
form of kinda-summability: with the number of candidates (parties) held 
constant but seats left to vary, it is summable.



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Re: [EM] Post-mortem on wikimedia's recent approval-with-abstention election

2013-07-05 Thread Kristofer Munsterhjelm


On 07/05/2013 12:29 AM, Jameson Quinn wrote:

https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections_2013/Post_mortem

I think it would be worthwhile to bring some expertise to the section at
the end. But let's keep it on-topic and try to keep from getting too
deep into the election theory weeds.


I don't have a user on Wikipedia, but I'll comment here about my first 
impressions.


It seems there are three main issues being raised here:

- That Schulze is not a multiwinner method but the Wikipedia election is 
a multiwinner election[1],

- that Schulze is really complicated and the results are hard to parse,
and
- that it is not intuitive that unranked means bottom rank.

-

That the Schulze method is not multiwinner is very true, but nor is the 
average approval method. Both of these methods can elect a long string 
of clones if the voters behave in a particularly partisan manner. 
However, there are really no very simple set-proportional (i.e. Droop 
proportional or analogous) voting methods. The simplest one is STV (or 
possibly Benham's recent method), but if you want Condorcet logic, it 
gets very hairy very quickly.



Complexity is a significant downside to Schulze, and there seems to be 
two two objections on the Wikimedia page. First, that who wins (and his 
margin) is not obvious; second, that the actual matrix is hard to parse. 
Now, there are ways to make Schulze continuous (so that it would say, 
for instance, Chen, 31.5%)[2], but this would make the method itself 
extremely complex. So I don't think we can have a more justified way 
of showing the quality of the winners without paying for it with 
significant complexity.


If the objection that who wins is not obvious instead regards the 
method, then we're not so quite out of luck. Other Condorcet methods may 
seem more intuitive: I think the Ranked Pairs method is moreso, for 
instance. On the one hand, this is a distraction. Whether or not the 
algorithm itself goes through intuitive-seeming steps doesn't matter 
from a game theory/social choice point of view - the results matter. On 
the other hand, I understand how some would prefer a more 
intuitive-sounding method: it grants some confidence that the method 
won't sneak up on them, do weird things with their ballots, and 
subsequently provide a very wrong result. So if the method seems opaque, 
well, then perhaps a less opaque method would be better.


As for the Condorcet matrix, one shouldn't have to parse it directly. 
There is a lot of information there, and it's not really relevant to 
examinations of the result, I think. But I further suppose that the 
matrix could be made more visual by coloring victories in different 
shades of green and losses in different shades of red - as long as that 
doesn't produce more confusion than insight[3].



Finally, it may or may not be obvious that unranked means worse than 
the rest. Here we have the same does unranked mean disapproval or just 
no opinion? question that I mentioned when talking about the Plurality 
criterion. Either can be defended, but I think at its extreme, average 
(i.e. unranked means no opinion) has a dangerous edge case where only a 
few supporters rank/rate a certain candidate and he then wins. So, at 
least to me, it seems that pointing the Approval-style interpretation 
of the ranked ballot in Schulze would suffice. Make it clear what the 
ballot *means* and then link to reasons why it's defined that way for 
the voters that would like more details.




[1] Oddly, on the 2011 page about this, Rob Richie said: The Schulze 
method is a very defensible voting method to use when electing one 
person  Huh. There was no signature, though, so we can't be sure it 
really was him.


[2] E.g. http://arxiv.org/abs/0912.2190 and http://arxiv.org/abs/0912.2195 .

[3] Here's an example of a gradient-colored matrix: 
http://www.koth.org/lcgi-bin/hugetable.pl?hill



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Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-07-05 Thread Kristofer Munsterhjelm


On 07/04/2013 08:39 PM, Vidar Wahlberg wrote:

On Thu, Jul 04, 2013 at 07:18:18PM +0300, Juho Laatu wrote:

That doesn't sound so different from leveling seats. In the
Norwegian system, you give each county an extra seat, but this
seat is assigned based on the difference betweeen the seats so
far allocated (on county by county basis) and the national
apportionment. I'm not sure how the algorithm decides which
county gets which party's seats, but it's not a simple
biproportional thing.


Yes, the end result is probably very similar. The fact that each
leveling seat is tied to one county further reduces the difference
(since there are no countyless seats).


About the Norwegian leveling seat algorithm: The leveling seats goes
to the party (with at least 4% of the national votes) with the
highest quotient. Once a party in a county has received a leveling
seat, that county may not receive any more leveling seats. The
quotient is calculated as following: (party_county_votes /
(party_county_seats * 2 + 1) / (county_votes / county_seats)
county_seats does not include the leveling seat. Since each county
receives 1 leveling seat the result would be fairly close to just
increasing the amount of seats in the county by one, but smaller
parties who haven't received any seats at all in the county (but got
at least 4% of the national votes) have a slight advantage with the
leveling seat algorithm as the algorithm use 1 instead of 1.4 as the
first divisor.


I still am not quite sure how it works, because your quotient 
description only refers to the county count, not the national count, and 
I would expect the leveling seats to make use of both.


But I think I see the general outline: the discrepancy is calculated in 
terms of national seats that ought to have been achieved, per party, 
minus the number of seats actually achieved, and then the spare seats 
are given to parties to bring the two counts more in line with each 
other, in such a way that the parties that were closest to getting an 
extra seat anyway (if that's what the quotient does) will get them.


If so, it's not that different from the biproportional representation 
algorithm, but it still feels less intuitive than it. Hm, again I would 
have to think about it further...



As for the election threshold, I completely agree with Juho, also
minorities should be represented in the parliament. I've never
really understood the argument that an increase in parties
represented in the parliament will lead to chaos. How the election
threshold work in Norway, that's not really what's preventing other
parties to be represented (that we're using 1.4 as the first divisor
in Sainte-Laguë is what's making it difficult for smaller parties to
get a foothold).


I think the argument goes that because the system is based on parties, 
the various parties will act like unified blocs. Therefore, the actual 
power in parliament will be closer to Banzhaf's power indices than the 
fraction of the seats held by any given party.


As an extreme, say you have two coalitions: a left-wing and a right-wing 
coalition. They're evenly matched (say 84 seats each). Then the last 
seat is held by a party with low support (party X).


To attain majority, these combinations are theoretically possible:

Left-wing bloc + party X
Left-wing bloc + right-wing bloc
Right-wing bloc + party X

Each of the three groups can in theory ally with either of the other 
two. This means that, as far as attaining a majority goes, the single 
party-X seat has the same power as either of the two coalitions. And 
that is obviously not desirable. The argument then is that if you add in 
lots of very small parties, any of them might become a kingmaker and so 
get extremely disproportional amounts of power.


I'm not sure I agree with it, but I can *understand* the argument. The 
worries could be alleviated by somehow making party discipline less 
strict so that it's harder for the parties to rule over their MPs, but I 
don't know how to do that. Another option is to make minority rule the 
default so that the coalitions shift according to the law or policy 
being considered. But some would consider that more chaotic in another 
manner.



I favour systems that are so simple that regular voters can easily
understand how they work.


Even though I'm a fan of Ranked Pairs  Condorcet methods, I too
share this sentiment. Another argument could be that voters probably
would be wary of drastically changing the existing voting system. In
the Norwegian voting system, changing it by removing election
threshold, increase seats in each county by 1 and remove leveling
seats, and possibly reduce the first Sainte-Laguë divisor slightly,
say 1.3, while making it possible for voters to rank parties, could
greatly help prevent the fear of wasting ones vote. Using the
counting method mentioned earlier (exclude party with fewest votes,
rerun Sainte-Laguë until all remaining parties got at least 1 seat),
it's arguably easier to

Re: [EM] Burlington dumps IRV; Immunity from Majority Complaints (IMC) criterion

2013-07-05 Thread Kristofer Munsterhjelm


On 07/05/2013 02:47 PM, sepp...@alumni.caltech.edu wrote:


Only one voting method satisfies IMC: Maximize Affirmed Majorities (MAM).


Can other methods satisfy IMC too, or does IMC imply MAM?



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Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-07-04 Thread Kristofer Munsterhjelm


On 07/04/2013 08:55 AM, Juho Laatu wrote:


In principle ability to vote for persons helps populist candidates.
My best understanding is that in Finland, that uses open lists, well
known candidates (from sports, TV etc.) probably have slightly better
chances to win a seat when compared to countries using closed lists,
but that difference is not big. Also closed lists can be populated
with well known figures to get populist votes (in addition to
nominating experienced politicians).

Also campaining could in principle be more populist in open lists,
but I don't see big difference here either. In FInland the level of
populism differs more between parties than between the candidates of
a single party.

All in all, I believe the risk of excessive populism is not big in
ranked methods either.


Both closed list and open (and ranked) methods have their failure modes. 
Closed list fails when the party leadership becomes unaccountable and 
insulates itself, and then the voter is forced to either vote my way or 
the highway - i.e. to accept the leadership's ranking or to not vote 
for the party. Person-based methods fail when it produces an incentive 
to be excessively populist.


In a way, that's a mirror of the general balancing act of democracy. If 
it is too representative as opposed to direct, then the powerholders 
might just run away with the power and mockingly say to the voters that 
they have no choice but to vote for one of the powerholders. If it's too 
direct, then it can amplify too much and oscillate around various 
policies if not degenerating entirely to populism.


I suspect that the solution to this particular problem lies not in 
getting the balance right, but somehow setting up the right feedback 
system so that public discussion and opinion convergence can move beyond 
populism. That said, I think I favor ranked multiwinner methods if I 
have to choose: the populist objection seems to be employed to 
exaggerate the negative results of giving the people more choice.



The leveling seat algorithm is... peculiar.


You said that you don't like methods that lead towards a two/three
party system. In other words the method should allow also small
parties to survive. I note that typically small districts are one key
reason why small parties do not get any seats. If you e.g. have a
district with 3 seats, it is obvious that only two/three largest
parties can win there. The leveling seats (that are allocated based
on support at national level) could fix that problem, but I
understood that n Norway they don't apply to the smallest parties.
Therefore the 5% threshold probably effectively reduces the chances
of the smallest parties to get their proportional share (at national
level) of the seats. It does not make sense to the voters to vote for
parties that most likely will not get any seats in their district
anyway.

I don't know what the situation in Norway actually is today. My
comments here are thus just general comments on how multi-winner
election methods usually work.


The Norwegian threshold is at 4%. If parties get sufficient local 
support, they still get seats; the 4% only regards leveling seats.


As a concrete example, in the 2009 parliamentary election, the Liberal 
Party (Venstre) achieved a support result of 3.9%, just below the 
threshold of 4%. In the previous election, their support reached 5.9%. 
As a consequence of going below the threshold, the party lost 8 of its 
10 MPs.



I'd like to get rid of both leveling seats and election threshold.


If you want to achieve exact proportionality (also for small parties)
I think it is important that proportionality will be counted at
national level. Also in ranked methods it is not enough if each
district does its best alone since the small number of seats per
district will distort proportionality at national level. From this
point of view the leveing seats (or any construction that aims at
providing proportionality at national level) is good, and thresholds
are bad.

- - -

I note that you can achieve national level proportionality in list
based methods also without leveling seats. In Finland there was a
proposal that was alrady once accepted by the parliament but then
cancelled by the current government. This proposal counted the
proportionality first at national level, and then allocated a
predetermined number of seats to each district so that at the same
time also the calculated national proportionality numbers were met.
This means that the last seats in some districts were slightly
forced to correct parties, to meeth the national proportionality
target. All methods that try to reach multiple targets, like
political proportionality and geographic proportionality at the same
time will have some rounding errors. In the Finnish proposal those
rounding errors were thus solved by slight distortion in who and
which party wins the last seat in each district, instead of using
e.g. leveling seats to capture the rounding errors.


That doesn't

Re: [EM] Quotaless STV-PR suggestion

2013-07-03 Thread Kristofer Munsterhjelm


On 07/02/2013 07:09 PM, Chris Benham wrote:


I am sure this meets Droop Proportionality for Solid Coalitions.


Does that mean that the method reduces to largest remainders Droop when 
the voters vote for all candidates of a single party each?


That would be interesting because there's no explicit quota in the 
system anywhere -- but I suppose it wouldn't be unprecedented, since 
Schulze STV doesn't have an explicit quota anywhere either.



At least some versions of STV-PR have the problem that adding or
removing a few ballots that vote for nobody (say just plump for some
X that is ignored or voted no higher than equal-bottom on all the
other ballots)  can change at
least one of the winners by changing the size of the quota. It is
much simpler than Meek to explain and operate, but seems (from some
examples I've seen) to give Meek-like results.


Yes, it does seem to be simpler than Meek.


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Re: [EM] Discourse

2013-07-01 Thread Kristofer Munsterhjelm


On 07/01/2013 07:27 PM, Benjamin Grant wrote:

Did my arrival somehow bring less civility and/or tolerance, or was this
always a rough-and-tumble place before I even got here?

I would hate to think that I brought the level of conversation down,
politeness-wise.


If you're counting my recent response to DLW in that, let me say that it 
is not typical of me. I try to generally be more civil than that. So at 
least as concerns me, I think you were just unlucky.


On another note, I've been thinking about writing a reply to your 
fairness/quality ideas, but I haven't had the time to do it yet. I'll 
try to get around to it, eventually :-)



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Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-06-30 Thread Kristofer Munsterhjelm


On 06/30/2013 03:02 AM, Chris Benham wrote:

**
Kristofer Munsterhjelm**wrote (29 June 2013):

The combined method would go like this:

1. Run the ballots through RP (or Schulze, etc). Reverse the outcome
ordering (or the ballots; these systems are reversal symmetric so it
doesn't matter). Call the result the elimination order.
2. Distribute seats using Sainte-Laguë.
3. Call parties that receive no seats unrepresented. If there are
unrepresented parties, remove the unrepresented party that is listed
first in the elimination order.
4. Go to 2 until no party is unrepresented.

This should help preserve parties that are popular as second preferences
but not as first preferences, because the elimination order will remove
parties that hide the second preferences before it removes the party
that is being hidden, thus letting the second-preference party grow in
support before it is at risk of being eliminated.

Note that this doesn't solve the small-council problem. If we have:

46: L  C  R
44: R  C  L
10: C  R  L

1 seat,

then the first seat goes to L just like in Plurality. The elimination
order never enters the picture.



Kristopher,
I don't see this. Your elimination order is obviously L, R,C.  R and C
are unrepresented so we eliminate R.
Then we have
46: L
54: C
Then we redistribute the seat to C and then eliminate L and confirm the
final redistribution.


Ah, right. I erred there; good call.


But I'm not on board with the spirit of this method, because it seems to
give a say to voters who are efficiently represented a say in which
party/candidate will represent other voters.


Well, in one sense the problem is that the parties that have no seats 
are fragmented. So replacing each of the fragmented parties with a 
larger party that is closer to the center would help with that.


I can see your objection, though, because there is an element of 
majority rule. If the majority prefers left-wing to right-wing, and 
there are right-wing voters who are unrepresented and vote for 
right-wing parties from most extreme to least, then those voters would 
prefer to get a party as right-wing as possible into the assembly, but 
the elimination order will preferentially preserve left-wing parties.


Would you suggest that the elimination ordering only be calculated based 
on the votes of those who currently don't get any representation?


I suppose that could work, although that may also introduce some path 
dependence. But it doesn't handle the example very well anymore:


46: L  C  R
44: R  C  L
10: C  R  L

As you noted, R and C are unrepresented. So the RP ordering among the R- 
and C-voters is R  C  L (by Majority), hence the elimination ordering 
is L  C  R.


Now we have two options. Either we can eliminate L - which will give the 
right result but override all the L-voters - or we can eliminate of the 
unrepresented, the one first in the elimination ranking, which is C. If 
we go by the second path, then we have


46: L
54: R

so L is eliminated anyway and R wins, which seems to be a more IRV-like 
outcome.


The problem here seems to be that the L-voters *become* unrepresented. 
What we really have are competing desires, and a sequential elimination 
process will favor those desires in a particular order. If I'm right, 
then we have a situation kind of like solving simultaneous equations. 
Thus it could be solved by an iterative method - in this case, noticing 
L would be eliminated anyway and thus eliminating L ahead of time to 
make C win - or by something that doesn't use eliminations at all, such 
as some analog of Schulze STV.


But either suggestion will make the method a lot more complex. It seems 
that PR methods get really complex really quickly as one places 
additional demands on them.



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Re: [EM] calculating the N matrix in Schulze STV

2013-06-29 Thread Kristofer Munsterhjelm


On 06/29/2013 09:38 AM, Alexander Kjäll wrote:

Hi

I'm trying to implement the Schulze STV method and are currently working
through the paper schulze2.pdf.

On page 38 there is an example (section 6.3) where this result was
arrived at:

N[{a,b,c},d] = 169;

and Ñ[{a,b,c}, {a,b,d}] = 169;

And i can't seem to figure out how to arrive at the number 169.

It's not a sum of any of the voting groups (as those are all divisible
by three, and 169 is not), and since all voters cast linear order
preferences of candidates the weight p of the votes should all be 1 (as
far as i understood it).

Could someone here maybe help me by explaining what step I'm not
understanding correctly, I'm guessing it has something to do with
Proportional Completion but I'm not really seeing that.


It hasn't to do with proportional completion. Instead, let's define the 
process for calculating N[{x,y,z}, w] as follows:


Let each candidate in the set (here {x, y, z}) have an assigned vote 
count.


If a given set of ballots ranks a subset of {x, y, z} before w, it can 
contribute to the vote count of that subset, in any proportion. Say the 
given ballot set is 100: x  y  z  w. Then it can contribute any 
combination of positive reals to the vote count of x, y, and z, as long 
as the sum of the combination is 100.


The ballots' values are distributed to the vote counts so that the vote 
count with the minimal value is the highest. The value of this (minimal) 
count is then the value of N[{x,y,z},w].


And to give an example of this, consider the example on page 38, where 
we're trying to determine N[{a,b,c},d]. After processing, we find out that:


value   rankprefer these of {A,B,C} to D
60  ABCDE   A B C
45  ACEBD   A B C
30  ADBEC   A
15  AEDCB   A
12  BAEDC   A B
48  BCDEA   B C
39  BDACE   B
21  BECAD   A B C
27  CADBE   A C
 9  CBAED   A B C
51  CDEAB   A C
33  CEBDA   B C
42  DACEB   none
18  DBECA   none
 6  DCBAE   none
54  DEABC   none
57  EABCD   A B C
36  EBDAC   B
24  ECADB   A C
 3  EDCBA   none

or
value   can be distributed among
60  A B C
45  A B C
30  A
15  A
12  A B
48  B C
39  B
21  A B C
27  A C
 9  A B C
51  A C
33  B C
57  A B C
36  B
24  A C

So now to distribute. There's probably an algorithm that ensures that 
the minimal value is maximal, but I don't know it. I know it's possible 
to do with linear programming, but that's probably overkill. For this 
particular example, it suffices to first add in all one-candidate 
combinations, then all two-candidate combinations in such a way as to 
maximize the minimum at each step, then all three-candidate combinations 
in a similar manner. That gives a reordered list of


30  A
15  A
39  B
36  B
12  A B
24  A C
27  A C
51  A C
33  B C
48  B C
 9  A B C
60  A B C
45  A B C
21  A B C
57  A B C

or
 45 A
 75 B
 12 A B
102 A C
 81 B C
192 A B C

and adding them in, we get

after step  allocation to   sum of values added
A   B   C   this step
--- -   --
 1  450   0  45
 2  45   75   0  75
 3  57   75   0  12
 4  79.5 75  79.5   102
 5  79.5117.75  117.75   81
 6  169 169 169 192,

giving us a maximum minimal value of 169, which was what was wanted.

I am not at all sure that algorithm will work in the general case, 
though, so I suggest you look at Schulze's source code to find out how 
it is done there. But this example should show how you get at 
N[{x,y,z},w]: by distributing votes between the candidates ranked before 
the comparison candidate on each ballot so that the candidate that 
ends up with least votes has the most.



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Re: [EM] calculating the N matrix in Schulze STV

2013-06-29 Thread Kristofer Munsterhjelm


On 06/29/2013 11:32 AM, Markus Schulze wrote:

Hallo,

N[{a,b,c},d] = 169 or Ñ[{a,b,c}, {a,b,d}] = 169 means
that W=169 is the largest value such that the electorate
can be divided into 4 disjoint parts T1,T2,T3,T4 such that

(1) Every voter in T1 prefers candidate a to candidate d;
and T1 consists of at least W voters.

(2) Every voter in T2 prefers candidate b to candidate d;
and T2 consists of at least W voters.

(3) Every voter in T3 prefers candidate c to candidate d;
and T3 consists of at least W voters.


What algorithm do you use to distribute the voters in this manner? The 
same voter may increase any of the subset of candidates he prefers to d, 
so it doesn't seem straightforward to determine which candidate's group 
a given voter should be placed into.



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Re: [EM] Preferential voting system where a candidate may win multiple seats

2013-06-29 Thread Kristofer Munsterhjelm


On 06/29/2013 01:27 AM, Vidar Wahlberg wrote:

On Fri, Jun 28, 2013 at 03:04:13PM +0200, Vidar Wahlberg wrote:

This gave me an idea.
We seem to agree that it's notably the exclusion part that may end up
excluding a party that is preferred by many, but just isn't their first
preference.
I'm sticking to quota election because I don't fully grasp how to apply
other methods (Sainte-Laguë, for instance) to determine when to start
excluding parties.
1. Give seats to parties exceeding the quota (seats = votes / quota)
2. Create an ordered list using Ranked Pairs/Beatpath, exclude the least
preferred party and redistribute its votes. Repeat.


Chris, Kristofer.
Spending the rest of the day on this, I think I finally understood what
you meant with best formula for apportioning seats in List PR. Or at
least I eventually came up with a very simple method, even though it
does not meet my concerns about excluding a second preference party that
is far more popular than a party that have some more first preference
voters.
For larger parties who are very likely to get a seat there's neither any
reason to create an ordered list, as those parties who do receive one or
more seats will never have any votes transfered.

Basically, this is what I do:
1. Distribute seats using Sainte-Laguë.
2. If any parties received no seats, exclude the party with least votes
and redistribute votes to 2nd preference.
3. Repeat 1-2 until all non-excluded parties got at least 1 seat.

Although as noted a party that is a popular as second preference (but
less popular as first preference) will easily be excluded, even though
more voters would prefer this party over another party.


I think that when the number of seats is large enough, you could combine 
the two methods. That is, by combining them, you handle the problem 
arising from voters not having an influence, but the problem arising 
from the method not becoming Condorcet-like when there are few seats 
remains.


The combined method would go like this:

1. Run the ballots through RP (or Schulze, etc). Reverse the outcome 
ordering (or the ballots; these systems are reversal symmetric so it 
doesn't matter). Call the result the elimination order.

2. Distribute seats using Sainte-Laguë.
3. Call parties that receive no seats unrepresented. If there are 
unrepresented parties, remove the unrepresented party that is listed 
first in the elimination order.

4. Go to 2 until no party is unrepresented.

This should help preserve parties that are popular as second preferences 
but not as first preferences, because the elimination order will remove 
parties that hide the second preferences before it removes the party 
that is being hidden, thus letting the second-preference party grow in 
support before it is at risk of being eliminated.


Note that this doesn't solve the small-council problem. If we have:

46: L  C  R
44: R  C  L
10: C  R  L

1 seat,

then the first seat goes to L just like in Plurality. The elimination 
order never enters the picture.


For a similar reason, it is not perfect: if the second preference party 
has widespread support but is hidden behind many parties that get one 
seat each, then the council will fill up with the smaller parties and 
the second preference party never gets a shot. But in a sense, that is 
proportional: every voter is represented. The question is how much 
second preferences should override first preferences. I think that an 
answer to that, and implementation thereof, would also fix the L-C-R 
problem, because they're two aspects of the same thing.


(And good luck explaining the purpose of the elimination order, and why 
it should be determined by Condorcet, to the average voter!)



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Re: [EM] Warren needs to double check his work.


On 06/25/2013 07:15 PM, David L Wetzell wrote:

KM2:So you're saying that nothing short of actually trying the
experiment in public elections will change your mind?
Then I believe I am done here. I can't change your position, so all I
can do is to argue to others that your position is flawed.

dlw2: Yes, our diffs are epistemic.  The thought experiments commonly
used here are not persuasive to me, since I'm trying to hold onto a
realistic notion of voters that views voter-utilities or political
spectrumes as at best useful heuristics.


Congratulations. You have just said that your anti-evidence armor is 
*so* strong that nothing I could ever produce today would change your 
mind. No argument, no proof, whether it be from the US or outside it, 
from national or international organizations, from theory or practice. 
No piece of it can change your mind, not a one.


That sounds awfully like faith to me. And I know that arguing with a man 
of faith is a losing proposition. If you ever wonder why people act 
unprofessional and don't respond to your assertions, perhaps it's 
because there's no compromise to be found. Eventually, even a fool tires 
of arguing with a wall.


But I suppose I shouldn't be surprised. The way you make use of your 
general defenses is entirely consistent with your statement that nothing 
can convince you, because you seem to think that each defense is 
absolute and frees you from having to actually address an objection.


When you reply to any of my references to other nations by American 
exceptionalism, you never say how much evidence would be necessary to 
put the claim of extremely specific American exceptionalism into doubt. 
You just use it as a general defense, a way of brushing away every 
objection.


When you come with assertions that anybody not agreeing with you in 
Burlington is either a useful fool or one of Them, you never bother 
backing this up with an actual money trail, nor do you reconcile it with 
reports that it was the IRV campaign who got the most out-of-town money, 
let alone account for the extreme specificity (violation of Occam's 
razor) required to claim that we, on a mailing list somewhere, are being 
manipulated by some Shadowy Others. You just use it as a general defense.


And when I object that you can't just claim this and that and this too, 
and then be free of any counter, you reach for your meta-armor: Sunk 
cost immunity!. Like some diplomat holding up a wallet, you seem to 
think that it is absolute: that it can make any requests for evidence 
evaporate, no matter how particular the claim being tested is. You never 
specify when the sunk cost might be met, and you never say how 
tangential a claim has to be before it is no longer protected by sunk 
cost immunity. Apparently any claim (American exceptionalism, very 
specific economies of scale, conspiracy) will be protected as long as it 
can be somehow linked up with a pro-IRV position.


Why not just claim that US voters get an instinctual satisfaction in 
watching the IRV process run to completion, and so that no other method 
can provide what IRV provides? You'd be done with it once and for all. 
Then when someone else asks for evidence, just pull out your wallet 
again. Ridiculous? Yes, but that's because it doesn't match your 
intuition. The logic is the same: anything pro-IRV is protected by sunk 
cost immunity.


Instead of specific counters, you use general defenses. I liked you 
better when you bothered to look into the facts and then said that 
perhaps Brazil isn't applicable to my point because it is a 
dominant-party system. But nowadays it doesn't appear you have the time 
for that. It doesn't appear you have time to check my data, either, or 
you'd find out that Olson's results about IRV and Condorcet error 
resistance aren't contingent on there being many candidates. But it's so 
easy to just use another general defense, another catch-all armor plate: 
in this case the it doesn't matter when there are few candidates 
response that has served you so well against advanced methods in the past.


But I should thank you for making clear what you had previously only 
shown in an indirect, sneaky manner: that there is nothing that can 
change your mind. Then I know there is no point in continuing the 
discussion, except perhaps as to show others just how much you stack the 
deck.


So enjoy your anti-evidence armor, and thanks for telling me what you 
otherwise only implied. Your persistent special pleading and refusal to 
follow the same rules and courtesy of discourse as everybody else just 
angers me. In so doing, you only drive me further from the IRV campaign. 
And so I am tempted to recommend you continue your logic and thus 
repel even more people. But nobody should have to face this sniping, 
this special pleading, this armored presumption of being invincible. So 
I am not going to recommend that.


---

All who'd feel like arguing with DLW, remember what he said about no

Re: [EM] Two notes and a possibly interesting method from a friend


On 06/27/2013 06:58 PM, Benjamin Grant wrote:

Hi, first a quick note: I haven’t been commenting because real life
stuff, work, etc has been keeping me busy, but I fully intend to go back
and answer any posts sent to me via the list(s).  If just that my time
and focus comes in bursts and droughts. ;)

Second note, I continue to thank all who are being helpful to me in the
journey.

Now, I asked my friend, who hasn’t read up on election stuff to come up
with a good method – I was wondering what someone intelligent would come
up with, with no prior exposure to election science.

Note: the thought experiment I asked of him had many basic constraints,
for example, the requirement that a voter be able to go and vote on a
single day within ten minutes, and that there would be ten candidates,
among others.

This is the method he suggested:

·Present the people with the ballot of 10 candidates and ask them to
pick their top three and their bottom three.

·Every time a candidate is picked in a person's top three, the candidate
gets a +1. Every time a candidate is picked in a person's bottom three,
the candidate gets a -2. The four candidates the person did not pick for
either get +0.  (Sidebar: For N number of candidates, you have MOD(N/3)
positives, MOD(N/3) negatives, and the rest are left neutral.)

·At the end of the night, we add up the scores and the candidate with
the highest score wins--even if the score is negative.

It’s very interesting, and I in my newness to this all don’t immediately
the warts, but since every method has them, I assume this one does too?


That's a weighted positional system. Every weighted positional system 
except Plurality fails the Majority criterion.


Here's an example. Say we have ten candidates, so that the first three 
in a ranking is supported, the next four are neutral, and the last three 
are penalized. I'll mark the divisions with a |. Then:


74: A  B  C  | D  E  F  G  | H  I  J
26: H  I  G  | J  D  E  F  | C  A  B

There are 100 voters in total, so A must win by the Majority criterion. 
In fact, A has greater than 2/3 majority support. But let's count the 
score for A and G.


A gets +1 point from 74 voters and -2 points from 26 voters for a total 
of 22 points.
G gets 0 points from 74 voters and +1 points from 26 voters for a total 
of 26 points.


So A doesn't have the greatest score and thus can't win, contrary to the 
Majority criterion.


I don't know how to generalize the method for n candidates because I 
don't know what MOD(N/3) means. If it means the remainder after dividing 
N by 3, then that doesn't match: 10/3 gives a remainder of 1, which 
suggests you should have one positive and one negative, not three of 
each. But I imagine it would in any case have a problem when n=2.


It would probably also have clone problems. Say H is cloned in the 
example above. I'm going to clone H only once (into H and h) and keep 
the limits where they are, since I don't know how to generalize the 
number of positives. Still, you can probably adapt it to fit the general 
system.


74: A  B  C  | D  E  F  G  H  | h  I  J
26: H  h  I  | G  J  D  E  F  | C  A  B

The problem here is that it pushes G off the positives list and so G no 
longer wins. Even if you increase the number of positives, one just has 
to add more clones to make the same example work.


If MOD(N/3) is just the integer division of N/3, then with 11 candidates 
you'd still only have 3 positives and 3 negatives, so the clone problem 
above works. And if MOD(N/3) is integer division, then for N=2, you'd 
get 0 positive places and 0 negative places, so there would be no way of 
assigning points to any candidate.



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Re: [EM] Absolutely new here


On 06/16/2013 06:18 PM, Abd ul-Rahman Lomax wrote:

At 02:02 AM 6/16/2013, Kristofer Munsterhjelm wrote:


It would work, but the rating variant is better. In the context of
ranking, Bucklin fails Condorcet, for instance.


Straight Bucklin does fail Condorcet, of course, as do straight Range
and Approval. However, we can tell from the fact that Range fails
Condorcet that there is a problem with the Condorcet Criterion, one of
the simplest and most intuitively correct of the voting systems criteria.


Your first claim is right, of course. It is also right that I'd never 
want to have Range used as a straight ranked system. Depending on how 
you implement it, ranked Range becomes Borda, Plurality or 
Antiplurality, neither of which are very good.


I don't think your second claim follows, though. Condorcet might be a 
bad criterion to apply to a rated or grade-based method (because it 
doesn't take preference strength into account), but that it is a bad 
criterion in general doesn't necessarily apply. In the case of a ranked 
method, like say the original Bucklin, you don't *have* preference strength.



The problem also applies to the Majority Criterion. Those criteria do
not consider preference strength. Practical, small-scale, choice systems
do, routinely. They do it through deliberative process and repeated
elections, vote-for-one, seeking a majority. And then, a process that
can even review a majority choice and reverse it, where preference
strength justifies it.

Thus a deterministic single-poll method that optimizes social utility,
and that collects information allowing that, *must* violate the criteria.

And that's a problem, because this is a fundamental principle of
democracy: no binding choice is made without the consent of a majority
of those voting on the issue. Some are aware of the tyranny of the
majority, but solutions to *that* cannot be found in deciding *against*
the preference of the majority, *without their consent.* The result is
minority rule, not broader consensus.


And that's kind of the thing I'm talking about. Ranked ballot methods 
don't have preference strength data. In that case, ruling in favor of 
the majority is better than doing so in favor of the minority. Of 
course, it would be better to not have to make that choice in the first 
place, but my point is that if you consider Bucklin, the ranked method, 
then it has to make a choice one way or another. And between the choice 
of making assumptions that makes it fail Condorcet, and making 
assumptions that makes it pass, the latter is preferrable. That is also 
what ranked Bucklin does.


But my point is that while rated Bucklin (MAV) might be a good method, a 
ranked quantization of it might be worse than other ranked systems that 
exist: simply because in the rated version, the weirdness is less 
relevant since it doesn't have to make assumptions the ranked version does.



So there is a solution: repeated election. Over the years of considering
this problem, I've concluded that with the use of advanced voting
systems, such as Range methods, and good ballot analysis in a first
round, with a runoff where a majority decision is not clear, such that a
Condorcet winner in a primary will *always* make it into a runoff, in
addition to one or more social utility maximizers, it is possible to

1. Find a majority choice, almost always, in two ballots, with the
exceptions being harmless.
2. Satisfy the Majority and Condorcet criteria.
3. Optimize social utility.

These have been considered opposing goals. That is because

1. Voting systems study has neglected repeated ballot.
2. Voter turnout has been neglected.
3. The electorate has been assumed, where runoffs have even been
considered, to be the same electorate with the same opinions. Neither is
real.


And that would be a system that gets around the problem by not having to 
make an assumption. For instance, when MJ/MAV fails Condorcet, or when a 
Condorcet method picks a Condorcet winner, and you're right about the 
differences in voter turnout fixing things, then the runoff can 
distinguish a weak CW from a strong CW -- or a candidate that fails 
Condorcet for good reason from a candidate that is picked by MJ because 
of artifacts in MJ/MAV itself.



It also has some bullet-voting incentive. Say that you support
candidate A. You're reasonably sure it will get quite a number of
second-place votes. Then even though you might prefer B to A, it's
strategically an advantage to rank A first, because then the method
will detect a majority for A sooner.


This is somehow assumed to be bad. That incentive exists if there is
significant preference strength. Thus bullet voting is a measure of
preference strength, i.e., is useful in measuring social utility. There
is, however, another cause for bullet voting: voter ignorance (which is
natural and normal). A voter simply may not know enough about another
candidate to vote for the candidate. And this is probably the major
cause of bullet

Re: [EM] another concern - the opposite of the Spoiler Effect - Packing


On 06/28/2013 03:30 AM, Benjamin Grant wrote:

Something else came up while I was analyzing some voting methods.  If
you have a disproportionate number of political leaning in an election,
some voting systems go awry.

There may be a criterion for this, this is what I mean.

Let’s say that you have three total candidates.  one is conservative,
two are liberal, none are moderate.  If the majority of the electorate
is conservative, then it may make sense that a conservative gets
chosen.  However, in some systems – say one in which each voter gets one
positive vote and one negative vote to cast – having more candidates of
a particular “wing” can hurt you. Continuing this example, if we run
Gore/Nader/Bush, both Gore and Nader supporters give their negative
votes to Bush, casting their positive votes for their own candidate.


This is what clone independence is supposed to check. Usually clone 
independence is considered as one criterion, but when it's subdivided, 
it's usually into three:


- Vote-splitting, where cloning a winner makes him lose,
- Teaming, where cloning a loser makes him win,
- Crowding, where cloning a loser makes some other loser win,

with examples:

- Vote-splitting: cloning A changes the win from A to B,
- Teaming: cloning A changes the win from B to A,
- Crowding: cloning A changes the win from B to C.

Vote-splitting is the standard Plurality problem. It seems what you're 
talking about is teaming, which is the opposite of vote-splitting (in a 
sense). Crowding is more of a chaos happens thing.


The Wikipedia article on the clone independence criterion calls teaming 
clone positive and vote-splitting clone negative. See 
https://en.wikipedia.org/wiki/Independence_of_clones_criterion .



Is this a thing? Kind of the opposite of the spoiler effect – that
having many like-minded candidates actually increases the chance that
one of them might win, even if their opposition is more numerous?

Does this only happen with negative votes?  Or can it happen with other
methods?


The typical method where teaming works is Borda. In Borda you have n 
candidates and the first ranked gets (n-1) points, the next (n-2) points 
and so on down. No voter gets a negative score.


More generally, consider a weighted positional system where the first 
rank gets x_1 points, second rank x_2 points and so on. This system is 
equivalent to one where the first rank gets x_1 + Q points, the second 
rank gets x_2 + Q points and so on, for any constant Q. So it can't only 
happen with negative votes, because you could make Q large enough so 
that all the weights were positive, and it would be the same method.


Though that's probably not what you meant. Teaming can happen with 
methods that aren't weighted positional as well. On the Wikipedia 
example, there's an example of teaming happening in Copeland (the 
sports tournament method). More obviously, a method that just picks a 
random candidate as the winner exhibits teaming, because the more 
candidates you can add of your own stripe, the more likely the 
figurative roulette wheel is to stop at one of your own candidates.



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Re: [EM] Preferential voting system where a candidate may win multiple seats


On 06/27/2013 03:12 AM, Vidar Wahlberg wrote:

Greetings!

I'm new here, I'm not a mathematician and merely a layman on the subject
of voting methods so please grant me some leeway, but do feel free to
correct any misconceptions I may have.

Briefly about my goals:
I'm trying to find a better alternative to the voting system used in
Norway (party-list PR, counting votes using a modified Sainte-Laguë
method where first divisor is 1.4 instead of 1), where you still vote
for parties rather than persons and may rank parties in a preferred
order instead of only being able to vote for a single party. A party may
win multiple seats in each district.


From one Norwegian to another, greetings and welcome!


The short answer to why not vote directly for persons? would be that
in Norway there's more focus on the goals of a party rather than the
goal of its politicians, and some may argue that the extra abstraction
layer is a good thing, as well as I'd like an alternative that won't be
completely alien to the common people. I'm hoping that any discussion
that may arise won't focus on this aspect, though.


I think seeing an STV-like method in Norway would be interesting. Not 
because I particularly prefer appeals to a given person, but because I 
think it would give the voters greater power to keep the party 
leadership from silencing the wings. For instance, if the voters are 
significantly more opposed to data retention than the Labor Party 
leadership, they could preferably vote for Labor Party candidates also 
opposed to data retention without having to abandon voting for that 
party (if they think it has otherwise good ideas).


I don't have proof that it wouldn't degenerate into a raw populist 
competition, though, so I can certainly see your point. I just don't 
know of any examples of STV-like methods failing or leading to raw 
populism in the countries where they're used.



As of why I'm interested in this then that's because I'm arguing for a
preferential election rather than the one person one vote system which
I believe is leading us towards a two/three party system, and I need to
know (better) what options are out there.

So far I've not been able to find much information on preferential
voting system where you vote for a party rather than a person. If anyone
have more insight and can guide me to more literature I would appreciate
it.


The United States doesn't have list PR. Therefore, most of the 
discussion of these methods are in context of state population 
apportionment, i.e. how many seats to give each state in Congress. The 
problem is similar: you want to give seats in a body according to 
fractions that may not exactly round off. In party list PR, the 
fractions are based on relative party support. In apportionment, the 
fractions are based on relative state population.


The Range Voting web site has a page on apportionment here: 
http://rangevoting.org/Apportion.html . You can find some simulations of 
bias at http://www.rangevoting.org/BishopSim.html , and Warren also 
discusses a new divisor method at 
http://www.rangevoting.org/NewAppo.html . If I recall correctly, the new 
method was constructed by modeling the distribution that the fractions 
will have, and then calculating the divisor that will give the least 
bias given that distribution.



And here's the part where I hope you'll be gentle:
I tinkered a bit on my own. Where as I am a fan of Ranked Pairs and
Beatpath, I find those difficult to explain to someone with no insight
in voting systems, and neither could I figure out how to apply RP in a
way where a candidate can win multiple seats.


I think Ranked Pairs is best described by a logic that greater 
majorities are more important than lesser ones. So you go down the 
sorted list and you piece together the social ranking based on the 
pairwise victories. Sometimes, what you want to add conflicts with what 
you already have, but again greater majorities are more important than 
lesser ones, so in that case you just skip the piece of information that 
can't be integrated.


But it might still be too hard to explain. You'd have to lay the 
foundation first: that the problem of Plurality (etc) can be considered 
a problem of candidates obscuring each other; that a one-on-one 
comparison has no such obscuring going on; and thus that if we were to 
use one-on-one comparisons, that'd be better. Or use a sports analogy 
(since round-robin tournaments usually use Copeland with 3-1-0 or 2-1-0 
weights).


As for applying Condorcet in multiwinner methods, the usual approach is 
to consider all combinations of outcomes as virtual candidates. That's 
what Schulze STV does, but beware: the Schulze STV paper is not the most 
accessible or easy to understand. Without some kind of branch-and-bound 
magic, it would also be impractical in a 169-seat parliament :-)



The basics behind PR-STV on the other hand are fairly easy to explain,
and I did manage to implement a way of counting votes to

Re: [EM] Score Voting and Approval Voting not practically substantially different from Plurality?

2013-06-26 Thread Kristofer Munsterhjelm


On 06/26/2013 11:24 AM, Juho Laatu wrote:


On 25.6.2013, at 18.07, Benjamin Grant wrote:



Now there are some criteria that aren't important to me at all, that I
do not value what the try to protect - and those I factor out.



I think I don't have any criteria that I'd absolutely require.


How about unanimity? :-)


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Re: [EM] Warren needs to double check his work.


On 06/25/2013 12:25 AM, David L Wetzell wrote:

KM:Alright, then tell me what kind of evidence would change your mind as
to whether the scarcity of competitive candidates is an artifact of
Plurality or inherent to single-winner elections. (If no such evidence
can exist, then there's no point in discussing.)

dlw:Let's switch to IRV + American forms of PR(in more local elections)
and watch the feedback loop.   We should be able to observe over time
how the dynamics of elections shift, as voter-prefs get better
cultivated.  When folks get habituated to the new system then it'd be
easy to put multiple alts to IRV on various ballots, using IRV to choose
between them, and then we'd see from various experiments  whether
upgrading from IRV continues a feedback loop in improving the quantity
as well as quality of competitive candidates on the ballot.


So you're saying that nothing short of actually trying the experiment in 
public elections will change your mind? Then I believe I am done here. I 
can't change your position, so all I can do is to argue to others that 
your position is flawed.


Though, on another level, I could argue that IRV itself has already been 
tested in the US. Yes, I'm going to use the B-word. But you have already 
made it clear enough that you consider Burlington to be an anomaly: 
therefore, it appears only widespread center-squeezing will be enough to 
show the inferiority of IRV.


If anything, I'm reminded of a right-populist party over here. Their 
policies have been criticized many times. One of their replies is 
simply: we've never been in power, so you don't know that it would turn 
out that bad.



KM:And furthermore, tell me why we shouldn't just use what you call
multi-winner elections like runoffs and not have to take on faith that
no single-winner method can produce diversity.

dlw: We need both diversity and hierarchy.  This is why we need a mix of
election rules, some encouraging diversity/equality, others encouraging
hierarchy/order.  We need the latter because of the need for collective
action and coordination.


So long as there are parties, there will always be hierarchy. Fred 
Gohlke argues pretty well for this. He does that because he thinks party 
hierarchy is a bad thing. I'm not going to comment on whether it is, 
here, because it is besides the point. Instead, I'll only say: Why?


There are nations that only use what you call multi-winner rules. There 
are even nations on the American continent that do so. Yet they manage. 
Their lack of what you call single-winner elections for partisan 
positions do not seem to measurably harm them in comparison with similar 
nations that do use such election rules.



I classify multiple stage elections as hybrids between multi-winner and
single-winner elections.  I think they're costly but good systems.  If
we replaced all of our current fptp systems with a partisan primary in
the US with the FairVote upgrade on top two primary, it'd improve the
system.  But I'd rather not use one election rule for all elections.  I
think it'd be hard to get turnout up and fair in the first election,
even with four winners.


If Abd is right, then low turnout is a feature, not a bug.

And what do you mean by and fair in the first election?


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Re: [EM] Is it professional?


On 06/25/2013 12:38 AM, David L Wetzell wrote:

It's a good argument.

1. What if candidates/parties are inherently fuzzy and rankings are
tenuous?  It can be done, I just don't put a lot of faith in them.

A. If I'm wrong and IRV proves defunct then IRV can be used to upgrade IRV.
B. If I'm right then the switch to an upgrade might make it harder to
switch away from FPTP/Top2 Primary and the return won't be higher.

2. At issue is how much better wd BTR-IRV be.  Maybe voters will rank
and there'll be GIGO.  Not for all of them, but for enough of them.  I'm
not saying voters can't learn, I'm saying voters will need to learn and
there still might be epistemic limits to their learning of how to vote.
  It's not like buying groceries every week, something relatively stable
and done a lot of times.

3. We get IRV quicker and the US system must hew to the true center
sooner, with the cultural wars wedge issues that have been poisoning our
democracy more effectively reframed by outsiders who may not be able to
get elected but would be able to get their ideas into the public square
with a system like IRV.

We needed a system like IRV over forty years ago.  There'll be more
scope for experimentation and voter-learning down the road, right now
the gaming of the fptp system has accumulated so much dysfunction and
resistance to reform that it's best to push forward with whatever will
do the most good the soonest possible and that seems to be a modified
form of IRV.


The amusing thing about the GIGO argument is that it is not IRV that 
does best when dealing with noisy votes. That honor goes to Condorcet 
(as shown by Brian Olson's simulations). Even Approval does better than 
IRV as noise increases.


And still, the three-scenarios argument holds. If there is some kind of 
weird IRV-specific GIGO so that IRV is really good, then BTR-IRV is no 
worse, fuzzy epistemic limits or no.


Finally, specificity can hit both ways. Perhaps the specificity works to 
degrade DLW's unproven IRV/Approval hybrid, and what we need is a robust 
noise-handling method like Condorcet. Perhaps, perhaps. Without any 
evidence, anybody can play that game and it will get us nowhere.



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Re: [EM] Score Voting and Approval Voting not practically substantially different from Plurality?


On 06/25/2013 09:00 AM, Juho Laatu wrote:

On 25.6.2013, at 1.06, Kristofer Munsterhjelm wrote:


Remember that criterion compliances are absolute. So a method may
fail a criterion yet be perfectly acceptable in real elections.


I just want to support this viewpoint. It is not essential how many
criteria a mehod violates. It is more important how bad those
violations are, i.e. if the method likely have serious problems or
not. The best method might well be a method that violates multiple
criteria, but manages to spread the  (unavoidable) problems evenly so
that all of them stay insignificant.


In a sense, it's like certain kinds of mathematical tests. There are 
primality tests that return either this number is definitely a prime 
or this number might be prime or might be composite. If you get the 
former result, you know you're dealing with a prime, but if you get the 
second, you don't know whether you're dealing with a prime or a 
composite number.


Criterion compliances are similar. If something passes IIA, you don't 
have to worry about candidates being added or removed as long as the 
voters don't alter their votes when the candidates are being 
added/removed. Whatever the dynamics might be on the nomination side, 
IIA secures the method. On the other hand, if something fails IIA, then 
you have the might be scenario. The method might fail IIA in blatant 
ways, or it might fail it where it doesn't really matter. You don't know.


In my case, I do like the certainty that criterion compliance provides, 
but sometimes, it just isn't available.


There is, though, one situation where criterion compliances go both 
ways. The method might produce a result that goes so completely against 
common sense that opponents can use it to argue against the method, even 
if that result itself only would appear very rarely. Perception does 
matter; and it's reasonable that it does, because sometimes the bizarre 
failure is symptomatic of a method that behaves strangely under pressure 
in general. That is not true all the time, though.



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Re: [EM] Is it professional?


On 06/25/2013 09:17 AM, Juho Laatu wrote:

On 25.6.2013, at 1.25, Benjamin Grant wrote:


On Mon, Jun 24, 2013 at 6:19 PM, Kristofer Munsterhjelm
km_el...@lavabit.com mailto:km_el...@lavabit.com wrote:

Scenario 1: Voters don't rank now, but will rank when they see
it's worth it. Here IRV will eventually crash but BTR-IRV is,
well, better.

Scenario 2: Voters rank, contrary to your assumptions (but
suggested by international evidence). Again, BTR-IRV does better.

Scenario 3: Voters don't rank and never will. BTR-IRV is here no
worse than IRV.

Under what scenario does BTR-IRV *lose* against ordinary IRV?


I am quite interested in the answer to this as well, as I imagine that
whatever the answer is is a defining advantage, should any exist.


One can see this problem from two quite different points of view.

One approach is that BTR-IRV is simply an improved version of IRV that
it avoids some of the key problems of IRV. Therefore it could be
straight forward to get also BTR-IRV accepted if the society accepts IRV.

Another approach is to have a more political power oriented viewpoint.
IRV tends to favour major parties. If the incumbent strong parties (that
do have a lot to say on what route the politics take) may well count
their chances in each proposed method. This might lead to favouring
methods like IRV that still allow the largest parties to take a lion's
share of the victories.


Right. I've heard this argument from others: that IRV, favoring the 
large parties, will get greater support from them. But the problem with 
that argument is that on the face of it, it seems to apply just as well 
to Plurality. The ones who already have power, have power to some degree 
because of the imbalances in the power allocation system. Therefore, 
they'll be disinclined to switch the power allocation system or parts of 
it, for something that will distribute power away from them. Or to be 
more direct: the people who are in power because of Plurality would see 
no need to advocate IRV unless they would also be in power under IRV -- 
and if they already have power, why take the chance?


I think the argument would be better if adapted to a sort of internal 
discontent scenario. For simplicity's sake, say you have a 1984-like 
structure with three classes:


- The upper class wants to stay in power,
- The middle class wants to switch places with the upper class,
- The lower class wants to remove the class system itself.

Then you could appeal to parts of the middle by using a conservative 
reform like IRV. The argument would go: you're strong, but not strong 
enough. You would like some leveling, but not so much that you can't 
enjoy your share of the power. Well, how about this method? It slightly 
levels the playing field - enough for you to now compete with the 
powerholders, but not enough that those third-party dudes will compete 
with *you*.



A classical example is one where there are two major parties and a
smaller compromise party candidate between the lajor party candidates.
Should the mathod allow that compromise candidate win? Condorcet
compliant methods seem to think that the compromise candidate should
win. (I also note that different political systems may have different
needs. In some systems the strongest are expected to rule whil in others
compromises are the default mode of operation.)


Ideally, I'd want the compromise candidate to win if he's genuinely a 
compromise candidate, but not if he's a bland nobody's favorite that 
gets the second place by default. But handling that will require some 
sophistication. Runoffs may work.


Or perhaps given Condorcet, the voters will learn to punish bland 
candidates with last-place votes. That would be sort of like market 
adjustment: demand of compromise candidates increase due to Condorcet, 
then supply follows, giving multiple compromise candidates, and finally, 
the good ones win as the bland ones are ranked lower. I don't know if 
that would happen, but on the other hand, I haven't heard of bland 
candidate syndrome reports from any of the organizations that are 
currently using Condorcet methods.



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Re: [EM] Score Voting and Approval Voting not practically substantially different from Plurality?


On 06/25/2013 12:53 AM, Benjamin Grant wrote:

On Mon, Jun 24, 2013 at 6:06 PM, Kristofer Munsterhjelm
km_el...@lavabit.com mailto:km_el...@lavabit.com wrote:



Also, Range could possibly give different results than Approval
voting. Consider an election where 99% of the voters are strategic.
The vote comes out to a tie between Nader and Gore, according to
these 99%. Then the remaining 1%, voting sincerely, vote something
like [Nader: 90%, Gore: 70%, Bush: 10%] (strategic would be [Nader:
100%, Gore: 100%, Bush: 0%]). Then those votes break the tie and
Nader wins.
For reasons like this, a mix of strategic and honest voters give
better results than just having strategic ones.


Of course, there are (in the circumstance where Gore is the better
chance to beat Bush than Nader) likely more Gore:100 Nader:0 Bush) votes
than Nader: 90 Gore:70 Bush 10 ones.

In fact, given that we *are* talking about an election with two strong
front running candidates and one spoiler weaker one, isn't it *far*
more likely that Gore is far in front of Nader and the only real unknown
is if Gore will beat Bush or not? Which leads right back to the entire
scenario of issues I began with.

The thing is, whenever we have more than two parties running, I think we
will always have weaker spoiler parties that cannot really win, but
that can, if the system allows or encourages people to vote against
their best interest, cause people to get a much lower ranked choice,
possibly their least preferred choice - this is my whole concern.


But here's a thing also to note. Nader voters are never worse off by 
voting [Nader: 100, Gore: 100, Bush: 0] than by voting [Nader: 0, Gore: 
100, Bush: 0]. Because of this, a simple Approval strategy goes: Vote 
for the frontrunner if you prefer him to the second-place candidate. 
Then vote for everybody you like more than the candidate you approved in 
the first step.



Stage two and the transition to three is the tricky part. In rounds
of repeated polling, the voters start off cautious (approving both
Nader and Gore). Then they see that Nader has approval close to
Gore's level, so some start approving of Nader alone. This then
reinforces the perception that Nader is winning, so more voters
approve of Nader alone. And so it goes until Nader is slightly ahead
of Gore and wins.


Aha! But what if what is likely happens in stage two: People get ahead
of themselves and give their full support to Nader and less support to
Gore *before* Nader is strong enough to beat Bush? Then Bush wins, both
the Nader and Gore voters freak out, and now Nader people go back to
voting Gore with full support, because now they've been burned!

The only way to avoid this, I *think*, is with a system in which
expressing a preference of A over B doesn't let C win - and such a
system may well have worse flaws, possibly.


Yep. That's a very definite risk, and one of the reasons I don't think 
Approval is a good method in a vacuum. I'd support Approval as a 
compromise more because it gives a lot of benefit for a very small tweak 
to Plurality, than that it is good in itself: a value/cost consideration 
rather than a raw value consideration.


But you're right, the problem there is very real (unless somehow the 
voters only think of candidates as people I can accept and people I 
definitely don't want to see in office). And the burn, as you put it, 
could not just harm Nader, but it could harm Approval itself -- just 
like I've argued that the weird way IRV acts can backfire.


So, for rated methods, I suggest Majority Judgement. It's more resistant 
to strategy, the ballots are set up so as to encourage comparisons to a 
common standard (the grades) rather than comparisons between candidates, 
and the method passes IIA. There's also experimental data from its use 
in France. The proposers found out that IIA is too weak when the voters 
compare candidates to each other, because the addition or removal of 
candidates may lead the voters to change what they put on the ballots. 
Thus, they emphasize the importance of having the voter evaluate the 
candidates against a common standard rather than against each other: 
because otherwise, IIA doesn't amount to much.


For ranked methods, I support Condorcet methods, particularly the 
advanced ones like Ranked Pairs and Schulze.



So, the way I see it: Approval is very simple on the front end. It's
just count all the votes. Back end is a completely different
matter, as you see above. I think Approval pushes a lot of the
oddities of voting into the back-end - the space in which the
elections happen, as it were. The method itself appears to be very
good (pass FBC, etc), but that's because the calculations happen in
the minds of the voters before they submit their ballots and the
criterion failures are therefore hidden. If one were to make a
computerized system that took preferences as inputs

Re: [EM] Score Voting and Approval Voting not practically substantially different from Plurality?


On 06/25/2013 02:43 PM, Jameson Quinn wrote:

I've arrived at my destination, so I'll try to process through this
thread. It's substantial, so I'll probably have several comments to
make. I'll start with a quick response to Kristofer.

... So, for rated methods, I suggest Majority Judgement.


I absolutely agree that a median (aka Bucklin) method such as Majority
Judgment is a good solution to the problem you're talking about. But we
activists really should push for consensus on which of these methods we
should talk about, because the differences aren't important enough to
justify separating our efforts.

I would suggest that we unite behind Majority Approval Voting as the
exemplary median/Bucklin method. Kristofer: do you disagree? If so, why?


I haven't really been investigating MAV enough to say if it's got any 
weird behavior (asymmetries in tiebreaking, etc). Apart from that, I'm 
a bit conservative with names, but not so much that I can't switch over 
to MAV :-)


There could be another reason to using MJ, though: it's the name that 
was used in BL's paper. If you say MJ, then the people you're talking 
to can go and find the paper - and the experimental results - quite 
easily. But MAV? There's not much out there about it outside of Electorama.


Also, a somewhat more distant objection: I don't really see these 
methods from the iterated Approval or Bucklin POV. To me, they're 
rated methods that use certain statistical concepts (the median 
estimator, primarily) to be better at resisting strategy (and to handle 
monotone nonlinear transformations of the grade scale). So Majority 
Approval doesn't explain my way of looking at the method very well.


But: these are objections I can live with. If referring to the method as 
MAV is a good strategy and provides unity, then I will do so. I just 
thought I'd let you know what feelings I notice when I think of MAV - 
both the name and the method.



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Re: [EM] Is it professional?


On 06/24/2013 05:08 PM, David L Wetzell wrote:

To ignore the simple upgrade to IRV that I have proffered
and defended at length on this list-serve,
  when you argue against IRV?


Yes, for many reasons. Among them: because other simple upgrades give 
way greater bang for the buck.


Consider BTR-IRV: It's like IRV, except when eliminating, you don't 
remove the Plurality loser. Instead, you eliminate, of the two with 
worst Plurality results for that round, whoever is ranked below the 
other on the most ballots.


That's two sentences, and boom, Condorcet compliance (and thus 
resistance against Burlington scenarios).


I can hear the counter: But it's not IRV! It doesn't have momentum! 
But whatever force that counter has against BTR-IRV, it also has against 
your unproven hybrid.



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Re: [EM] Warren needs to double check his work.


On 06/24/2013 09:33 PM, David L Wetzell wrote:

There should be a few more fewer ranks in the red in his example.
http://rangevoting.org/IrvIgnoreExample.html

Also, I don't think voters care that much if their deeper preferences
aren't consulted when their top prefs get elected or come in 2nd place
and so it seems contrived to make a big deal out of it.  This does get
at why little is lost when only 3 rankings are allowed with IRV, which
then makes it easier to use those rankings as approval votes for a first
round that reduces the number of candidates much more quickly.


One man might say: This does get at why little is lost when only 3 
rankings are allowed with IRV.
The other man might say: This does get at why full IRV is not much 
better than 3-candidate IRV.




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Re: [EM] Question about the Plurality Criterion


On 06/24/2013 04:10 PM, Benjamin Grant wrote:

As I have had it explained to me, the Plurality Criterion is: If there
are two candidates X and Y so that X has more first place votes than Y
has any place votes, then Y shouldn't win.

Which I think means that if X has, for example, 100 votes, then B would
have to appear on less than 100 ballots and still **win** for this
criterion to be failed, yes?

I cannot imagine a (halfway desirable) voting system that would fail the
Plurality Criterion – can anyone tell me the simplest one that would?
Apart from a lame one like “least votes win”, I mean?


That depends on what you put into a candidate not being ranked on the 
ballot. If you think that voters mean that all the candidates they rank 
are better than those they don't rank, then Plurality obviously makes 
sense. On the other hand, if not ranking a candidate simply means the 
voter has no opinion, then the Plurality criterion is no longer as obvious.


A very simple system that fails the Plurality criterion for this reason 
is mean (average) Range. In this system, you take the mean rating of 
each candidate, and greatest mean wins; but in this particular variant, 
if you don't rate candidate X, you don't change his mean in any way.


So you could have a candidate A that's ranked with a mean of 8.5 by 1 
million voters, and a candidate B that's ranked with a mean of 9 by 500 
000 voters (and otherwise not ranked). Say more than 500k of the ballots 
list A first. Then B is barred from winning by the Plurality criterion. 
Yet by the logic of mean Range, B should win because, according to that 
logic, the voters who didn't list B were just saying they didn't *know* 
what rating B should have and instead left the task of determining B's 
mean to the others who did rate B.


Now, pure mean Range has a problem in that candidates who are only known 
by a few fanatics could get an illegitimate win, so some sort of soft 
quorum (like IMDB does for its movies) is probably better. I just use 
mean Range as an example of a system that isn't obviously insane yet 
fails the Plurality criterion (or one particular way the Plurality 
criterion might be extended to rated ballots).



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Re: [EM] Score Voting and Approval Voting not practically substantially different from Plurality?


On 06/24/2013 03:06 PM, Benjamin Grant wrote:

Hi guys, I’m still here, still pondering, but now I have another
question. I’ve been thinking about score voting, approval voting, and
plurality (FPTP) voting, and I have a concern.

Say we have a situation where we have three candidates, say Gore, Nader,
and Bush. Say we have a voter, Abe whose greatest concern is that Bush
NOT win. His second priority is that Nader win over Gore – but this
priority is a distant second. He *really* doesn’t want Bush to win. He
would prefer Nader over Gore, but he *hates* Bush.

Let’s also say that Abe is intelligent, and he is committed to using his
vote to maximize his happiness – in other words, rather than vote
sincerely and cause his preferences harm, he will always vote
strategically where it is to his benefit to do so.

If Score Voting was in place, and he were to vote sincerely, Abe
probably would vote something like ‘Gore:75, Nader: 100, Bush: 0’.
However, he’s no fool, and he knows that while it is theoretically
possibly that Nader *might* win, Gore is his best chance to stopping
Bush, and that withholding score from Gore might (if all Nader
supporters did it) result in Gore not getting enough of a score,
therefor Bush could win.

So strategically speaking, Abe reasons that although he supports a less
likely candidate more, he strategically should score the front-runner
Gore at full strength, so long as keeping Bush out is the greatest need
– and so long as Nader’s win is unlikely.

So, as far as *I* can see, this converts Score Voting into Approval
voting.


You're generally right. There are some very particular situations with 
incomplete information where it makes the most sense to use partial 
ballots, but those happen way too rarely to make a difference.


You can see this from the other end, too: say you're in an Approval 
election and want to vote 0-10-range style. You want to give X a rating 
of 4, but it's an Approval election. To do this, you generate a random 
number on 0...10. If it is lower or equal to the rating (in this case 
4), you approve of X, otherwise, you don't. If everybody did that, the 
Range and Approval results would give the same winner (with high 
probability). So in a real sense, Range is Approval with fractional 
votes permitted.


Also, Range could possibly give different results than Approval voting. 
Consider an election where 99% of the voters are strategic. The vote 
comes out to a tie between Nader and Gore, according to these 99%. Then 
the remaining 1%, voting sincerely, vote something like [Nader: 90%, 
Gore: 70%, Bush: 10%] (strategic would be [Nader: 100%, Gore: 100%, 
Bush: 0%]). Then those votes break the tie and Nader wins.
For reasons like this, a mix of strategic and honest voters give better 
results than just having strategic ones.



And say what you want about intelligence being a bar to entry, you can
bet that the smart people behind ALL candidates will make sure that
everyone gets the message, so we can largely ignore #3.  Most people I
imagine would be pragmatic enough to worry more about the end result and
less about sincere vs. strategic, so we ignore #2. And #1 people are
going to vote the same way anways, so they may as well use Approval voting.

OK, so let’s throw out Score Voting and use Approval voting. Gore v
Nader V Bush.  Abe (who hates Bush but prefers Nader) gives an approval
vote to Nader, his top-most preference, but knowing that withholding
approval from Gore could elect Bush (and not wanting to play the
spoiler) he also gives an approval vote to Gore. Since Gore in this
example is far and away receiving much more support than Nader, Gore now
beats Bush.

Let’s call the party that put Nader on the ballot the Green party, and
that they continue to field candidates in further elections that use the
Approval voting system.  Abe notices the following pattern: when the
Green party fields a candidate that doesn’t even have a glimmer of hope
winning the election (like the Gore/Nader/Bush one) that people that
support the Green party candidate also approve the Democrat candidate as
a bulwark against the Republican. And since in those elections the Green
party never really had a hope of winning, the Green approval vote is
ultimately irrelevant – those elections would have proceeded no
differently than if the Green supporters had simply voted Democrat.

But much worse yet, Abe notices that in *some* election, the Green party
actually gets a chunk of people thinking that Green could actually win.
And emboldened by their hopes, many Green supporters decide to go for
it, approve of the Green candidate, but *not* the Democrat one. Result:
in elections where more voters think more favorably towards Green’s
chances, their least preferred choice (the Republican) tends to win more!

This are my two thoughts:

a)Intelligent use of Score Voting becomes Approval Voting, and the harm
in unwise use of Score voting means that Approval Voting is superior to
(and simpler

Re: [EM] Warren needs to double check his work.


On 06/24/2013 11:22 PM, David L Wetzell wrote:

Another might add, This is why the number of competitive candidates and
the extent of low-info voters matters in the comparison.


Alright, then tell me what kind of evidence would change your mind as to 
whether the scarcity of competitive candidates is an artifact of 
Plurality or inherent to single-winner elections. (If no such evidence 
can exist, then there's no point in discussing.)


And furthermore, tell me why we shouldn't just use what you call 
multi-winner elections like runoffs and not have to take on faith that 
no single-winner method can produce diversity.



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Re: [EM] Is it professional?


On 06/24/2013 11:28 PM, David L Wetzell wrote:

The short-cut in my hybrid has been used in some elections  and it had
potential to coopt the momentum of IRV, but I think that FairVote's
upgrade to top-two might take its place...

Now, The same might be true of BTR-IRV, the main draw-back is that seems
to work best with voters ranking the candidates.


Consider these three scenarios.

Scenario 1: Voters don't rank now, but will rank when they see it's 
worth it. Here IRV will eventually crash but BTR-IRV is, well, better.


Scenario 2: Voters rank, contrary to your assumptions (but suggested by 
international evidence). Again, BTR-IRV does better.


Scenario 3: Voters don't rank and never will. BTR-IRV is here no worse 
than IRV.


Under what scenario does BTR-IRV *lose* against ordinary IRV?


I've been presuming that many voters won't want to do a lot of research
and rank all the candidates.


Yes, but to back up that presumption, you have to more or less assume 
that America is so special that the claim itself is impossible to disprove.



My suggestion doesn't require that to improve on FPP.


Plain IRV itself is enough to improve upon FPP. This is like saying 
that I don't have to run very quickly to outrun a turtle.



And, the same can be said for the new upgrade FairVote is pushing for.
  Maybe with only 4 candidates, voters will take the time to look at all
four...


That won't help when the correct candidate is center-squeezed out of the 
way. The only way to ensure there is no center squeeze is to limit the 
number of candidates to two - and then you have plain old runoff.




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Re: [EM] Monetized score voting

2013-06-17 Thread Kristofer Munsterhjelm


On 06/17/2013 03:10 AM, Warren D Smith wrote:

is my name for an idea advanced in atrocious work by several
economists (2012-2013) and improved/corrected/examined by me. The idea
is by paying to cast your score voting ballot according to certain
carefully designed price formulas, you will become inspired by the
profit motive to vote honestly. Unfortunately this disregards some
massive real world problems, but perhaps might be ok in some corporate
votes and also (if the whole max-profit-motive-theorem is abandoned
instead merely seeking to discourage exaggeration in range voting) as
modified by us even perhaps in governmental ones.

Analysis here:
http://rangevoting.org/MonetizedRV.html



The first thing that comes to mind, and you probably said so already, is 
that the mere fact that people are voting in large public elections in 
the first place implies that the voters are not voting simply to 
increase expected return by changing who is in power. The probability of 
a single vote making a difference is just too low.


Perhaps monetized voting systems could be used to make different types 
of prediction markets. I know little about the subject, though; it's 
just another idea that came to mind, since the players in such a market 
would act to try to maximize their profits.



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Re: [EM] Voting Criteria 101, Four Criteria

2013-06-17 Thread Kristofer Munsterhjelm


On 06/16/2013 06:55 PM, Benjamin Grant wrote:

With your kind indulgence, I would like some assistance in understanding
and hopefully mastering the various voting criteria, so that I can more
intelligently and accurately understanding the strengths and weaknesses
of different voting systems.

So, if it’s alright, I would like to explain what I understand about
some of these voting criteria, a few at a time, perhaps, and perhaps the
group would be willing to “check my math” as it were and see if I
actually understand these, one by one?


No problem :-)


*Name*: *_Plurality_*

*Description*: If A gets more “first preference” ballots than B, A must
not lose to B.


Be careful not to mistake Plurality, the criterion, from Plurality the 
method. Plurality, the criterion, says: If there are two candidates X 
and Y so that X has more first place votes than Y has any place votes, 
then Y shouldn't win.


The Plurality criterion is only relevant when the voters may truncate 
their ballots. In it, there's an assumption that listed candidates are 
ranked higher than non-listed ones - a sort of Approval assumption, if 
you will.


To show a concrete example: say a voter votes A first, B second, and 
leaves C off the ballot. Furthermore say nobody actually ranks C. Then C 
shouldn't win, because A has more first-place votes than C has any-place 
votes.



*Name: _Majority_*

*Description*: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.


That's right. More specifically, if a candidate has a majority of the 
first place votes, he should win. There's also a setwise version (mutual 
majority) where the criterion goes if a group of candidates is listed 
ahead of candidates not in that group, on a majority of the ballots, 
then a candidate in that group should win.




*Thoughts*: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him,
any other approach would seem to create minority rule? I guess a
challenge to this criteria might be the following: using Range Voting, A
gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from
80 out of 100 voters. A’s net is 5400, but B’s net is 6400, so B would
win (everyone else got less).  Does this fail the Majority Criterion,
because A got a higher vote from over half, or does it fulfill Majority
because B’s net was greater than A’s net??


There are usually two arguments against the Majority criterion from 
those that like cardinal methods.


First, there's the pizza example: say three people are deciding on 
what piza to get. Two of them prefer pepperoni to everything else, but 
the last person absolutely can't have pepperoni. Then, the argument 
goes, it would be unreasonable and unflexible to pick the pepperoni 
pizza just because a majority wanted it.


Second, there's the redistribution argument. Consider a public election 
where a candidate wants to confiscate everything a certain minority owns 
and then distribute the loot to the majority. If the electorate is 
simple enough, a majority might vote for that candidate, but the choice 
would not be a good one.


Briefly: the argument against Majority is tyranny of majority. But 
ranked methods can't know whether any given election is a 
tyranny-of-majority one, and between erring in favor of the majority and 
in favor of a minority (which might not be a good minority at all), the 
former's better. Condorcet's jury theorem is one way of formalizing that.


Rated methods could distinguish between tyranny-of-majority cases, were 
all the voters honest, but being subject to Gibbard and Satterthwaite 
just like ranked methods, they too can be gamed. There's usually a way 
for a majority to force a win if they absolutely want to, too[1].



*Name: _Participation_*

*Description*: If a ballot is added which prefers A to B, the addition
of the ballot must not change the winner from A to B

*Thoughts*:  This seems to make sense. If we do not require this, then
we permit voting systems where trying to vote sincerely harms your
interests. Also, any voting system that would fail Participation would
be I think fragile and react in not always predictable ways – like IRV.
SO this seems to me to be a solid requirement, that I can’t imagine a
system that failed this Criterion to have some other benefit so
wonderful to make failing Participation worth overlooking – I cannot
imagine it.


Welcome to the unintuitive world of voting methods :-) Arrow's theorem 
says you can't have unanimity (if everybody agrees that AB, B does not 
win), IIA (as you mention below) and non-dictatorship. Since one can't 
give up the latter two and have anything like a good ranked voting 
method, that means every method must fail IIA.


The trade-off with Participation is similar. It is impossible, for 
instance, to have a method that passes both Participation and Condorcet, 
so one has to choose which is more important. Similarly,

Re: [EM] Absolutely new here

2013-06-16 Thread Kristofer Munsterhjelm


On 06/16/2013 05:26 AM, Benjamin Grant wrote:

I just started trying to wrap my brain around all the ins and outs about
voting methods, and I wanted to check two things with my elders (on this
subject):

1)As far as I can see, the reason IRV has some strange/unusual results
is because it is absolutely critical what order you eliminate
candidates. So an election where Voting Bloc 1 has a 13% share of the
ballots and Voting Bloc 2 has a 16% share of the ballots can utterly
flip around using IRV if VB1 goes up two points and VB2 goes down 2.
Because with IRV, the order of elimination is really the first-most
deciding factor in who wins.


[snip]


A few percent either way on the last line changes **everything**.

This seems to be a flaw with IRV, yes? It is “too sensitive” on small
changes because they can change the order of elimination.


Yes. Like a chaotic process such as a fractal, it exhibits sensitivity 
to initial conditions. Reiterating an IRV round can draw similar points 
very far away from one another, and on some level, it feels similar to 
the kind of effects you get by say, reiterating the Henon function on 
two close points until they're no longer close at all.


You can see some visualization of this phenomenon here: 
http://zesty.ca/voting/sim/



2)I haven’t seen a voting system like this – what are the issues with
it? Upsides and downsides?

A)Each voter ranks their choices on their ballots, first through last place.

B)If one candidate got a majority of 1^st place votes, they win. If not,
the second place votes are added. If still no majority he third place
votes are added, and so on, until one candidate has a majority.

Would the above system work?


That's Bucklin. http://en.wikipedia.org/wiki/Bucklin_voting . It's one 
of the few ranked methods that have been used in political elections in 
the United States, and it has a connection to median rating (which 
elects the candidate with highest median rating or grade).


It would work, but the rating variant is better. In the context of 
ranking, Bucklin fails Condorcet, for instance.


It also has some bullet-voting incentive. Say that you support candidate 
A. You're reasonably sure it will get quite a number of second-place 
votes. Then even though you might prefer B to A, it's strategically an 
advantage to rank A first, because then the method will detect a 
majority for A sooner.


One of the points of the graded/rated variants is to encourage the 
voters to think in absolute terms (is this candidate good enough to 
deserve an A) rather than relative terms (is this candidate better 
than that candidate). If they do, then the method becomes more robust.



Thanks, very new to all these considerations, still trying to learn the
names of the different methods as well as the names and meaning of the
different criteria like Condorcet, Later No Harm, etc.


Alright. If you have more questions, just ask!


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Re: [EM] A better 2-round method that uses approval ballots

2013-06-16 Thread Kristofer Munsterhjelm


On 06/14/2013 09:06 PM, Abd ul-Rahman Lomax wrote:

At 12:44 AM 6/14/2013, Chris Benham wrote:



My suggested 2-round method using Approval ballots is to elect the
most approved first-round candidate A if A is approved on more than
half the ballots, otherwise elect the winner of a runoff between A and
the candidate that is most approved on ballots that don't show
approval for A.


Yeah. My general position is that runoff voting can be *vastly improved*
by some fairly simple tweaks, or by using an advanced voting system, in
the primary and maybe in the runoff. Approval is an advanced voting
system *and* a tweak on Plurality.



Parties fielding 2 candidates is a disempowering move, in general,
weakening campaigning. I'm generally opposed to open primaries in
partisan elections. A unified primary makes sense in a non-partisan
election.


Couldn't open primaries weaken party leadership and so encourage the 
transition from Duverger-style two party rule into multipartyism? As 
long as the primary/runoff method can handle multiple candidates, that 
is. Or do you think the leadership would instead say that we need to 
stick together or the other party, that keeps party discipline, will 
divide and conquer us with much stronger focused campaigning?



And we need to understand something about nonpartisan elections. They
are *very different* as to voter behavior from partisan elections. What
seems to be, from the behavior of nonpartisan IRV, is that voters vote
on name recognition and affect. It is the kind of thing that is heavily
influenced by public exposure of the candidates, and it has little to do
with political position on a spectrum. Voters do not appear to be
voting as if there is this spectrum, with second preferences then being
predictable from spectrum position of the candidates and the voter.


It'd be interesting to run some kind of SVD on cardinal polls in such 
elections to confirm whether that's the case, but I trust you :-) You 
certainly know more about non-partisan elections than I do, since pretty 
much every election here is partisan. It's a consequence of the party 
list method we use.


(However, I do note that in one of the few cities that have direct 
mayoral elections, a candidate from a very left-wing party was elected. 
This party has about 2-3% national support, and I get the impression he 
was elected on nonpartisan grounds - by character and quality rather 
than by political affiliation.)



I would conceptualize Chris's system this way. It's a 2-winner approval
method, designed to maximize *representation* on the runoff ballot.
Voters who approve A are already represented, so, it makes sense to only
consider ballots not approving of A in determining the other runoff
candidate.


Yes, and it probably does so to a greater degree than a PR method would. 
Consider a case where we have a candidate that's preferred nearly 
unanimously, and then another candidate preferred by the slight minority 
that remains. Assuming Chris's method doesn't have a threshold similar 
to the greater than majority support and he wins threshold of TTR, the 
method would pick both candidates mentioned above for the runoff. On the 
other hand, if the majority is sufficiently large, a PR method could 
pick two candidates preferred by the near-unanimous majority.


I don't think that would make much of a difference in a runoff, though. 
If candidate A is preferred (approved) by a near-unanimous group, 
meaning that candidate is considered to be vastly superior to everybody 
else, then that group will have the power to make him win in the runoff. 
The issue is more whether a runoff should aim towards maximizing 
representation (as Chris's method, as well as minmax Approval, tries to 
do), common center focus (as top-n Approval would do absent deliberate 
clones) or some combination of both (as PR methods would do).



However, limiting the runoff or general election ballot to two
candidates is an unnecessary restriction. It is only a false majority
that is created when candidates are eliminated, and, as we know, the
pathologies of elimination systems are rooted in that elimination.

As a compromise, up to three candidates can be permitted on the runoff
ballot, using an advanced voting system that can handle three candidates
well, and the selection can include much better criteria that mere top
two. If a ranked ballot with sufficient ranks is used, condorect winners
can be identified and placed in the runoff, thus making the overall
method condorcet compliant, i.e., a persistent Condorcet winner would be
identified as such -- publically known -- and would win *unless voter
preferences change or turnout shows that the condorcet preference
strength is low.*


One possible way of doing that would be to use a combinatorial PR method 
where you force-include the winner from the other type of system. For 
instance, you might render cardinal ballots into ordinal ballots and 
then run Schulze STV on them - but force

Re: [EM] Does Top Two Approval fail the Favorite Betrayal Criterion [?]

2013-06-13 Thread Kristofer Munsterhjelm


On 06/08/2013 10:16 PM, Chris Benham wrote:

Yes.
Say there are three candidates: Right, Centre-Right and Left, and the
approval votes cast are



49: Right
21: Centre-Right (all prefer Right to Left)
23: Left
07: Left, Centre-Right (sincere favourite is Left)



Approval votes: Right 49, Left 30, Centre-Right 28.

The top-2 runoff is between Right and Left and Right wins
70-30.



All the voters who approved Left prefer Centre-Right to Right. The 7
voters who approved both Left and Centre-Right can change the winner to
Centre-Right by dumping Left (their sincere favourite) in the first
round.



49: Right
28: Centre-Right
23: Left
Now the top-2 runoff is between Right and Centre-Right and Centre-Right
wins 51-49.

Seven voters have succeeded with a Compromise strategy.


It seems that this could be generalized to any top-two runoff method. 
Consider a base method X, that picks two candidates for the runoff. 
Then, even if X passes the FBC, if the situation is so that:


- Candidates A and B go to the runoff if voting is honest,
- some voters that have sincere preferences ACB can replace A with C 
by favorite-betrayal,

- in an {A,B} runoff, B will win; in a {B, C} runoff, C will win,

then there's an incentive for favorite betrayal. To completely protect 
against that, a method would have to pass a criterion where voters who 
prefer C to the honest runoff winner B can't replace either of the 
candidates by betraying their favorite (who might not be C). Call this 
passing double FBC. But I don't see how a method could possibly do that.


Does that mean that we can't have both FBC and LIIA? The argument would 
go in this vein:
- assume X passes both FBC and LIIA, and that the same set of votes are 
used for both rounds.

- then the winner in round 2 is the winner in round 1, by LIIA.
- This means that we don't need to consider the runoff as such, only the 
base method X.
- And by FBC, for any strategy that involves favorite betrayal, there's 
another, non-favorite-betraying strategy that also works.
- So the runoff, being equivalent to just running base method X under 
the assumptions given, should pass the FBC.

- But it can't, by the argument above.
- Hence having both FBC and LIIA is impossible.

But something is strange here. Approval is said to pass both FBC and IIA 
(which is a superset of LIIA). So where's the flaw?


Thinking a bit further, it seems the flaw is in that the votes don't 
change. In the example above, if the runoff is Centre-Right vs. Right, 
the 21 CR  R  L voters aren't going to approve both Centre-Right and 
Right in the second round. Since Approval ballots are binary, it's 
impossible to express a rank preference over more than two levels, and 
so the assumption only holds if the voters' preferences are inherently 
dichotomous (in which case the voters who approved of both runoff 
candidates would just stay home on the second round).


The argument would still seem to hold for ranked voting, however - at 
least if you include the assumptions that voters who vote A = B  C 
would vote A = B in the runoff. To make the impossibility proof 
formal, one would just have to show that no ranked method can pass 
double FBC.


-

Finally, I'd like to say that I do understand that reality is a lot less 
neat. What Abd says about differences in turnout in the first and second 
rounds of a runoff means that criteria are not as useful as for 
single-round methods because the votes in the different rounds would 
change.


One could even argue that if they don't, there's no reason to add a 
runoff to an advanced method, and the only reason for Plurality to have 
a runoff is to patch problems in Plurality itself. I have seen reasoning 
of this sort from some IRV advocates who both say top-two runoff is 
also nonmonotonic, so don't go around saying TTR is better than IRV and 
IRV is better than TTR in every way because it's clearly better than 
the contingent vote.



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[EM] Focus of runoffs?

2013-06-13 Thread Kristofer Munsterhjelm

Say we have an organization or government that wants to use a better 
type of two-round runoff than top-two Plurality. What kind of 
distribution should the candidates for the second round have?


To be a little more specific, and to make the concept a bit easier to 
think about, consider a top-n runoff with Approval ballots in both 
rounds. Furthermore, to not have to deal with differences in cloning 
problems, say that each group has at least n candidates, so you have at 
least n centrists, n left-wing candidates, n right-wing candidates and 
so on.


Then what candidates should the runoff method pick for the second round? 
It could pick according to ordinary Approval. If we consider the 
electorate to be centrist, that would lead to n centrists being elected 
to the second round. The lack of variety might keep the voters from 
bothering to turn up in the second round. On the other hand, because 
they're all similar, it might lead to a more detailed discussion of 
different shades of centrist policy, thus informing the voters more and 
letting them make better choices in the second round.


On the other extreme, the method could pick the candidates for second 
round using minmax Approval. This would produce a great variety of 
candidates, so the second round decision would probably seem more 
meaningful to the voters. On the other hand, because the ideological 
positions are so clearly defined and the n candidates would be spread 
across the spectrum, it would be easier for say, a right-wing candidate 
to say that guy over there is a leftist; vote for me if you like 
capitalism (or whatnot) instead of discussing the more subtle aspects 
of politics.


Between these extremes, we have selection by proportional 
representation. For Approval, that would be PAV or one of the 
combinatorial methods (biweight, etc). This approach is not as focused 
on the candidates everybody agrees are good (as in ordinary Approval) 
not on the candidates at least someone thinks is very good (as in minmax 
Approval), and thus, basically, is a combination of both.


Which do you think would be best? What kind of discussion would give the 
best candidates in the long run -- one of subtleties in centrist policy, 
of breadth among a very wide variety of positions, or proportional 
representation?


I suppose TTR lies somewhere around the PR choice, selecting candidates 
by SNTV. But SNTV is not a good proportional representation method, n=2 
doesn't give a great variety of candidates anyway, and TTR may be set up 
the way it is to fix problems in Plurality, not just to let the voters 
get a second look at the most suited candidates.



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Re: [EM] Electorama wiki requires login to view????

2013-06-12 Thread Kristofer Munsterhjelm


On 06/12/2013 07:04 AM, Rob Lanphier wrote:


Responding to Abd's points: We're operating under very different
parameters than, say, a Wikimedia-operated wiki like Wikiversity.  In
particular, we don't have the infrastructure to deal with user creation
spam.  There are big advantages to sharing spam fighting resources with
Wikipedia.


I imagine that using some spam-deterring plugins would go a lot of the 
way. See http://www.mediawiki.org/wiki/Manual:Combating_spam . I don't 
know this, though, as I haven't administered any Mediawiki sites myself.




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Re: [EM] In political elections C (in terms of serious candidates w. an a priori strong chance of election) will never get large!

2013-06-03 Thread Kristofer Munsterhjelm


On 05/29/2013 08:06 PM, David L Wetzell wrote:


My apologies.   I'm not always good w. names.


I had a really long reply queued up here, but now that I've got a few 
days to think since RL business has not been quite as hectic, I think 
there's one thing we need to establish before we continue discussion.


The one thing that I felt was most of a discussion-stopper the last time 
we talked was how you'd reply to almost all evidence I gave you by oh, 
but it's different in the United States. So, therefore, before I start 
spending lots of time on making counter-arguments and backing them up, I 
think I'll have to know: what kind of evidence will you accept? That 
way, my work won't be in vain.


Can you accept US polls done with advanced methods? Can you accept 
results from organizations using advanced methods? Can you accept 
multipartyism in the past in areas of the US as strengthening the 
argument that multipartyism can happen in the present? Can you accept 
results from areas with runoff, again suggesting greater diversity? Can 
you accept results from other presidential FPTP nations suggesting the 
extreme expense of US elections is an anomaly?


And finally, can you accept results from the other IRV-using nations? 
There are not many of them, so it's very easy to this place is 
different them away. To me, the repeated use of that response just 
feels rude: like you've constructed a self-consistent system that 
explains little but is impervious to counters, wherever they may come from.


In short, what will it take to change your mind?

(What would it take to change mine? Some evidence that the US really is 
that special, perhaps. But it's hard to see how one could show that. So, 
of course, if you think I'm pulling the same rude trick, you can also 
say that and stop the thread there.)


There is one thing I *can* reply to, however.


I could also then point at other nations, either other
presidential  countries making use of runoff (to strengthen the
first claim), or other presidential countries in general, even
thoseunder Plurality (to
strengthen the second), and say that the expense of presidential
elections in the US is pretty much unequaled elsewhere in the world.
That is, I think it is, but I'm not going to investigate in detail
unless I know you won't pull the it's different in the US than in every
one of those other countries response.


dlw: I'm not sure I'm tracking which are your two different claims.


Claim 1: Plurality leads to really expensive campaigns.
Claim 2: Plurality + US political dynamics lead to really expensive 
campaigns.



As you know, I believe runoff elections are not pure single-winner
elections, since the first stage is a multi-winner election. And so some
of our diffs come from a different taxonomy for election rules.


Why does that matter? If runoffs can be used to elect single 
candidates[1], and the method produces diversity, what does it matter 
whether it's a multi-winner or a single-winner method? It does what 
we want -- or it's better at it than IRV, anyway.


If I'm looking for a flier, I shouldn't care whether it flaps its wings 
like a bird or has fixed wings like a plane. If it's a good flier for 
the conditions I need, that's enough.


And if it is indeed better than IRV, which I think I can show if the 
evidence isn't it's different-ed away, then FairVote is doing a great 
disservice when it's pushing to replace runoff with IRV. If the 
organization was primarily pushing to replace Plurality with IRV, then 
you *could* reason that well, at least 2.5-party rule is better than 
2-party rule[2]. But if IRV is being touted as Instant Runoff to 
replace delayed runoff, and this leads to a reduction in the diversity, 
then it's a loss that pushes the country *towards* Duvergerian outcomes, 
not away from it. Abd has more data about this, if you're interested.


If your contention is that runoff's performance can't be generalized to 
advanced methods, fine enough. Let's consider whether there's any way to 
find out if that claim is true... and in the meantime, let's not replace 
runoffs with IRV.


//

[1] I.e. it can be used to elect presidents, governors, etc., as opposed 
to being a PR method that elects a bunch of members of parliament (etc.) 
all at once.


[2] Or, more precisely well, at least 'slight departure from 
Duvergerian oligopoly' is better than being stuck at Duvergerian 
oligopoly'. 2.5-party rule and 2-party rule are just short ways of 
saying the same, since while it does not need to correspond to only 
having two parties, that's how it usually goes. I imagine you could have 
diversity with physical 2-party rule, but you'd need a whole lot more 
oversight to keep the two parties from conspiring or becoming corrupt. 
Kind of like how you might be able to have a planned economy that 
produces good results, but you'd need heavier checks and balances to 
keep the SoEs from colluding or becoming corrupt than if you just had a 
bunch of

Re: [EM] In political elections C (in terms of serious candidates w. an a priori strong chance of election) will never get large!

2013-05-29 Thread Kristofer Munsterhjelm


On 05/29/2013 12:15 AM, David L Wetzell wrote:



On Tue, May 28, 2013 at 4:36 PM, Kristofer Munsterhjelm
km_el...@lavabit.com mailto:km_el...@lavabit.com wrote:

On 05/27/2013 09:19 PM, David L Wetzell wrote:

Smith's http://rangevoting.org/__PuzzIgnoredInfo.html
http://rangevoting.org/PuzzIgnoredInfo.html

needs to be taken w. a grain of salt.

The short-comings of IRV depend on the likely number of serious
candidates whose a priori odds of winning, before one assigns
voter-utilities, are strong.  If real life important single-winner
political elections have economies of scale in running a serious
election then it's reasonable to expect only 1, 2 or 3 (maybe 4
once in
a blue moon) candidates to have a priori, no matter what
election rule
gets used, serious chance to win, while the others are at best
trying to
move the center on their key issues and at worse potential
spoilers in a
fptp election.


That argument is too strong in the sense that it can easily be
modified to lead to any conclusion you might wish. And it can be
modified thus because it is too vague.


Hi Karl, good to hear from you again.  I doubt economies of scale args
are completely flexible and the evidence need not be as rigorously
presented when one is initially communicating ideas.


Who is Karl?


Let me be more precise. You may claim that if there're some
economies of scale, then it's reasonable to only expect 1, 2 or 3
viable candidates. But here's a problem. Without any data, you can
posit that the economies of scale kick in at just the right point to
make 2.5-party rule inevitable even under Condorcet, say. But
without any data, I could just as well posit that the economies of
scale, if any, kick in at n = 1000; or, I could claim that the
economies of scale kick in at n = 2 and thus we don't need anything
more than Plurality in the first place[1].


No, because non-competitive candidates still serve a useful purpose even
if their odds of winning are low.  And a non-plurality election is
harder to game, as illustrated by the GOP's 40-yr use of a nixonian-
Southern Strategy of pitting poor whites against minorities when
outsiders are given voice to reframe wedge issues that tilt the de facto
center away from the true political center.


So you say the non-competitive candidates still serve a purpose. But 
your economics-of-scale argument only considered competitive candidates. 
Call the set of competitive candidates X, and the set of noncompetitive 
candidates that still matter, Y. Then I could just as easily apply 
your objection so that it argues in favor of advanced methods, too. I 
just say that even if you're right about economics of scale for X, that 
says nothing about the relative size of Y under IRV with respect to Y 
under an advanced method.


The problem with the argument is that it's very hard indeed to construct 
a simple model that considers Plurality inadequate, IRV good enough, and 
the advanced methods wasteful, yet can't also be tuned to either 
consider Plurality adequate or IRV inadequate. The model has to be 
complex or the parameters finely adjusted, and complex models without 
evidence have little value.



So one may claim that important single-winner political elections
necessarily have economies to scale that make anything beyond
2.5-party rule exceedingly unlikely. But without data, that's claim
isn't worth anything. And without data that can't be explained as
confusing P(multipartyism) with P(multipartyism | political dynamics
given by Plurality), the simpler hypothesis, namely that there is no
such barrier that we know of, holds by default.


How about economics?  There exists X a cost of running a competitive
campaign.  There exists Y a reward, not per se all economic, for winning
a campaign.  There exists P a probability of winning.  P is roughly
inversely proportional to the number of competitive candidates, albeit
less for the last candidate to decide to compete.  If there exists N
likely competitive candidates then if the calculation is k*Y/(N+1)X
holds, w. k1, for the N+1 candidate, who then chooses not to run, it
implies that N(kY-X)/X.   A better election rule might increase k some,
but arguably X will also tend to be higher for the less well-known
candidate, regardless of the election rule used.

So I agree that the average number of competittive candidates can be
increased by the use of a different single-winner election rule, but
with limits due to the other aspects of running an election and how a
single-winner election tends to discourage too many from putting a lot
into running for the office.


Then I set (assume, claim) k high enough that the stability Condorcet 
(etc) provides is worth it. You set k low enough that it isn't, and then 
we sit on each our numbers and claim that our

Re: [EM] In political elections C (in terms of serious candidates w. an a priori strong chance of election) will never get large!

2013-05-28 Thread Kristofer Munsterhjelm


On 05/27/2013 09:19 PM, David L Wetzell wrote:

Smith's http://rangevoting.org/PuzzIgnoredInfo.html

needs to be taken w. a grain of salt.

The short-comings of IRV depend on the likely number of serious
candidates whose a priori odds of winning, before one assigns
voter-utilities, are strong.  If real life important single-winner
political elections have economies of scale in running a serious
election then it's reasonable to expect only 1, 2 or 3 (maybe 4 once in
a blue moon) candidates to have a priori, no matter what election rule
gets used, serious chance to win, while the others are at best trying to
move the center on their key issues and at worse potential spoilers in a
fptp election.


That argument is too strong in the sense that it can easily be modified 
to lead to any conclusion you might wish. And it can be modified thus 
because it is too vague.


Let me be more precise. You may claim that if there're some economies of 
scale, then it's reasonable to only expect 1, 2 or 3 viable candidates. 
But here's a problem. Without any data, you can posit that the economies 
of scale kick in at just the right point to make 2.5-party rule 
inevitable even under Condorcet, say. But without any data, I could just 
as well posit that the economies of scale, if any, kick in at n = 1000; 
or, I could claim that the economies of scale kick in at n = 2 and thus 
we don't need anything more than Plurality in the first place[1].


So one may claim that important single-winner political elections 
necessarily have economies to scale that make anything beyond 2.5-party 
rule exceedingly unlikely. But without data, that's claim isn't worth 
anything. And without data that can't be explained as confusing 
P(multipartyism) with P(multipartyism | political dynamics given by 
Plurality), the simpler hypothesis, namely that there is no such barrier 
that we know of, holds by default.


And, if you're not claiming that there is such economics of scale, but 
simply that there *might* be, then it's still less risky to assume 
multipartyism is right and use an advanced method. If we're wrong, 
nothing lost but momentum. If we're right, we avoid getting stuck at 
something that would still seriously misrepresent the wishes of the people.


(I'd claim, based on (among other things) international data under 
Runoff, that there's little evidence that multipartyism is inherently 
incompatible with single-winner rules in general. But such data can 
easily be specially pled away by making the rules about what counts 
circuitous enough. So if I'm going to go in that direction, I'd like to 
have some idea of, before the fact, what kind of evidence will convince 
and what will not.)


[1] Possibly with stricter rules to entry so that insignificant third 
parties don't spoil the elections. Adding such rules, e.g. requiring 
more signatures for candidates to run, would be a lot simpler and less 
expensive to implement than switching to IRV.



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Re: [EM] In political elections C (in terms of serious candidates w. an a priori strong chance of election) will never get large!

2013-05-28 Thread Kristofer Munsterhjelm


On 05/28/2013 01:54 AM, Richard Fobes wrote:

On 5/27/2013 12:19 PM, David L Wetzell wrote:

...
The short-comings of IRV depend on the likely number of serious
candidates whose a priori odds of winning, before one assigns
voter-utilities, are strong.  If real life important single-winner
political elections have economies of scale in running a serious
election then it's reasonable to expect only 1, 2 or 3 (maybe 4 once in
a blue moon) candidates to have a priori, no matter what election rule
gets used, serious chance to win, while the others are at best trying to
move the center on their key issues and at worse potential spoilers in a
fptp election.


Plurality voting and limited voting (and the Borda count if the voters
are undisciplined) are about the only methods that _cannot_ handle 3 or
(maybe) 4 popular choices along with any number of unpopular choices.


Don't forget IRV. If the three candidates are competitive, then IRV can 
unpredictably fail due to center squeeze. That is what happened in 
Burlington.


IRV works as long as the third party or candidate is small enough that 
it couldn't possibly be a true center choice.



So it seems disengaged from reality to let C, the number of candidates,
go to infinity... and if a lot of candidates are not going to get
elected then to disregard voter info/preference over them is of much
less consequence.


Although the number of popular candidates is now small, that's because
we use plurality voting.  When we use better voting methods, the number
of popular candidates will increase; of course not to infinity, but
frequently beyond the 3 or 4 popular choices that IRV can handle with
fairness.


Yes. That is also my point when I talk about confusing p(multipartyism) 
with p(multipartyism | dynamics given by plurality).


Incidentally, if we generalize the effective number of political parties 
formula of Laasko and Taagpera to effective number of candidates, then 
the mean effective number of political candidates in the Louisiana 
gubernatorial elections, from 1991 to 20011 inclusive, is 3.5. Louisiana 
uses delayed runoff. The maximum was 5.52 (in 1995); and this is in a 
two-party environment. And already, even with the centralizing burden 
imposed by two-party rule, the elections stray into the multiple viable 
candidates territory where IRV may no longer be safe.



Although it's a non-governmental example, take a look at the current
VoteFair American Idol poll.  The number of popular music genres is
about 5, and there are about 7 singers who get more than a few
first-choice votes.

 http://www.votefair.org/cgi-bin/votefairrank.cgi/votingid=idols

IRV would correctly identify the most popular music genre (based on
current results), but probably would not correctly identify the most
popular singer.


That's not going to convince IRV promoters, since it's not a political 
election. http://rangevoting.org/RangePolls.html may be better in this 
respect. It gives results of Range and Approval-style polling for real 
presidential candidates, and shows races where the polls say that other 
candidates than the Plurality winner was preferred. For instance, McCain 
was preferred to Bush in 2000, yet McCain lost in the primary.


And then you have other Range/Approval polls as well, like 
http://rangevoting.org/PsEl04.html.


Now, one may claim that dynamics are not taken into account here. I 
think that's a valid counter against Range as such (but others may 
disagree). Yet if one starts involving dynamics, organizations that use 
Condorcet don't seem to slide into two-faction rule; and the various 
delayed runoff countries don't, either.



Why would voters trust a voting method that stops getting fair results
with so few popular candidates?

Yes, IRV is easy to explain, but that advantage becomes unimportant as
the number of popular candidates increases, which it will when better
voting methods are adopted.


I think that if we absolutely had to settle on a compromise, it'd 
probably be Approval, which is a lot simpler than IRV. I don't like it 
that much, since it encourages the voters to engage in what I called 
manual DSV. However, it's not as fragile as IRV, and the Range and 
Approval advocates who don't like Condorcet can accept Approval.


I seem to recall someone saying that an informal EM poll picked Approval 
as the CW. That's probably the reason, as I could easily imagine votes 
going:


x: Range  Approval  Condorcet (Range advocates)
y: Condorcet  Approval  Range (Ranked ballot dudes)
z: Approval  Range  Condorcet (Approval advocates),
for comparable numbers x, y, and z.

But we don't have to settle on one compromise method. We don't have to 
use Plurality logic to go beyond the problem of Plurality. That's what 
the Declaration is all about; and the NZ referenda show that it's not 
even necessary to use Plurality logic when asking the people what kind 
of election rule to switch to.



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Re: [EM] Approval Voting

2013-05-06 Thread Kristofer Munsterhjelm


On 05/06/2013 11:21 PM, Jonathan Denn wrote:

In these likely scenarios, and assuming there is no electoral
college, doesn't a runoff of the top two seem the best method until
someone gets a majority?


It would solve that problem, but the problem can be reintroduced if each
party gets greedy.

Say each party thinks like this: We can get our partisan voters to vote 
for only our own candidates. If we'd win an ordinary Approval with a 
single candidate, then by fielding n candidates, we can win a top-n 
runoff. So they each field two clones, and you get a result like:


H1: 34%
H2: 34%
D1: 33%
D2: 33%
R1: 33%
R2: 33%

now H1 and H2 go to the runoff.

For Approval, it'd be better to pick the challenger as the candidate 
who's approved by most people who didn't approve of the winner. Then H1 
and a non-H candidate go to the runoff, and the non-H candidate wins.


There may be more sophisticated methods that solve that problem as well. 
My pick the candidate who's approved by most who didn't approve of the 
winner was just something I thought of as I wrote this, and it may (for 
all I know) have strange strategy incentives.



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Re: [EM] Associated Student Government at Northwestern University uses Schulze Method

2013-04-21 Thread Kristofer Munsterhjelm


On 04/20/2013 10:32 PM, r...@audioimagination.com wrote:


From: Kevin Venzke step...@yahoo.fr

  It's true that *with the ballots as cast* any Condorcet-compliant
method would have
  worked identically.

including no specific Condorcet method, since there was a CW.

  What you don't know until you try it, is whether voters would
  actually cast those ballots, given the incentives created by the method.

well, when at first i (mistakenly) thought that there were only 3
candidates (or candidate tickets, in this case), i could not see how
there would be any different outcome at all because, even if there was a
cycle, it would be a cycle with 3 in the Smith set.


I think his point was that the criterion compliances of the method might 
induce certain behavior that would not be in place with another method.


As a very drastic example, consider a Condorcet election where the CW is 
also the Plurality winner *given those ballots*. Strictly, one could 
argue that Plurality would have sufficed and would have produced the 
same winner - but the significant vote-splitting problems of Plurality 
might have led to a lesser-of-two-evils thinking and so the winner would 
have changed under the ballots that the voters would have submitted in 
Plurality.


On the other hand, one could also argue that there's too little 
difference between various Condorcet methods for this to happen. That 
is, the overwhelming majority of Condorcet elections in practice end 
with a CW, so the difference between Schulze and Copeland (or 
Borda-elimination) is so small one should just pick whichever the 
electorate will accept.


I don't know whether that is true or not - one would have to gather 
evidence to say either way - but in the absence of such, I prefer 
advanced Condorcet methods just to be on the safe side (or if the 
electorate learns to make use of the safety provided by them, they can 
comparably speaking be more expressive before being limited by the 
method). But if the voters absolutely won't accept the advanced methods, 
simple ones are better than Plurality.



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Re: [EM] Instead of Top 2

2013-04-21 Thread Kristofer Munsterhjelm


On 04/20/2013 12:09 AM, Forest Simmons wrote:

Suppose the two methods were IRV and Approval, and that each voter could
choose which of the two methods to vote on their strategic ballots, and
then rank the candidates non-strategically as well for the choice
between the two method winners.

We would learn something about the popularity of the two methods, which
one chose the final winner the most often, which one elicited the most
order reversals, etc.

The same experiment could be done with any two methods.


For that matter, the experiment could be done with ordinary runoff to 
check if the voters change their minds between the rounds of the runoff.


The experiment would go like this: first round, the voters vote using 
the two methods in question, and also give a honest preference ordering 
for a virtual runoff. Second round, they vote in the actual runoff 
between the winner candidates (or some complex tiebreak if the winner is 
the same for both methods). Then one compares the preference orderings 
with the runoff results. If the runoff is A vs B, A won, but the 
preference ordering says B should have won, there's your reversal.


And I've mentioned it before, but I suppose I can do so again, since 
we're talking about two-method runoffs :-) From time to time I've 
thought about the idea of having a runoff using a strategy-resistant 
method and a method that provides good results under honesty. This could 
be useful in a society where people have become used to strategizing. If 
they strategize wildly, then the honest method fails but the resistant 
method keeps the result from being too bad; and if they don't, then the 
honest method's candidate wins the runoff and all is good.



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Re: [EM] secret ballots and proxy voting

2013-04-10 Thread Kristofer Munsterhjelm


On 04/09/2013 04:01 AM, Abd ul-Rahman Lomax wrote:


You can make up complicated scenarios that bear no resemblance to what
would actually happen, and scare yourself with them.

The Mafia is just another interest group. Attempting to apply
large-scale coercion tends to piss people off. They don't want that. No,
classic corruption goes after a power node, a focus of substantial
power. So ... does the Mafia in New York threaten City Council members?


Isn't that just what a protection racket is - large-scale coercion? It 
seems to work for the Mafia, inasmuch as they're still being involved in 
protection rackets... and the presence of organizations like Addiopizzo 
seems to show that they are.



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Re: [EM] Sequential STV method

2013-04-07 Thread Kristofer Munsterhjelm


On 04/07/2013 03:59 AM, Ross Hyman wrote:

More general variant: Candidate sets of N candidates are notated by
Greek letters.


[snip]

You said that this method was based on a cloneproof single-winner method.

Woodall generalized the clone criteria in 
http://www.votingmatters.org.uk/issue3/p5.htm to Clone-in, 
Clone-no-harm, and Clone-no-help, so clone independence could more 
easily be applied to multiwinner methods. He noted that Clone-no-harm 
conflicts with the DPC, and generally, isn't desirable in proportional 
multiwinner methods.


My question is then: do you know whether the multiwinner method you've 
given passes the clone independence criteria useful for multiwinner 
methods (i.e. clone-in and clone-no-help)?



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Re: [EM] Sequential STV method

2013-04-07 Thread Kristofer Munsterhjelm


On 04/07/2013 03:59 AM, Ross Hyman wrote:

More general variant: Candidate sets of N candidates are notated by
Greek letters.


[snip]

You said that this method was based on a cloneproof single-winner method.

Woodall generalized the clone criteria in 
http://www.votingmatters.org.uk/issue3/p5.htm to Clone-in, 
Clone-no-harm, and Clone-no-help, so clone independence could more 
easily be applied to multiwinner methods. He noted that Clone-no-harm 
conflicts with the DPC, and generally, isn't desirable in proportional 
multiwinner methods.


My question is then: do you know whether the multiwinner method you've 
given passes the clone independence criteria useful for multiwinner 
methods (i.e. clone-in and clone-no-help)?



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Re: [EM] Sequential STV method (Oops)

2013-04-07 Thread Kristofer Munsterhjelm


On 04/07/2013 10:19 AM, Kristofer Munsterhjelm wrote:

On 04/07/2013 03:59 AM, Ross Hyman wrote:

More general variant: Candidate sets of N candidates are notated by
Greek letters.


[snip]

You said that this method was based on a cloneproof single-winner method.


Sorry about the 3x duplication. My mail server glitched.

If any moderators see this, just remove the other duplicates :-)


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Re: [EM] Cloneproofing Random Pair and Random Candidate?

2013-04-05 Thread Kristofer Munsterhjelm


On 04/04/2013 09:31 PM, Abd ul-Rahman Lomax wrote:

At 12:12 PM 4/4/2013, Kristofer Munsterhjelm wrote:

On 04/04/2013 08:02 PM, Abd ul-Rahman Lomax wrote:

At 02:24 AM 4/3/2013, Kristofer Munsterhjelm wrote:

However, there is a rated method that is also strategy-proof. It is
called Hay voting. Some time ago, I stumbled across
http://www.panix.com/~tehom/essays/hay-extended.html , which seems to
be a proposal to make Hay voting cloneproof. I haven't really
understood the details yet, but I'm wondering if this could be used to
also make the two Random methods cloneproof.


Hay voting, as described, is a multiple-round system, it appears. Now,
why would this complex system be superior to standard Robert Rules
elections, i.e., vote for one, repeated ballot if no majority, no
eliminations with only voluntary withdrawals -- or shifts in voter
preferences -- , in an Assembly able to change rules, effectively, by
agreement?


Not as I understood the description. Ordinary (not Extended) Hay
voting consists of voters submitting the rated ballots, and the Hay
method probabilistically picks a candidate. The method is designed so
that the optimal thing to do is for each voter to report ratings
proportional to their real utilities.

The multiple rounds of Extended Hay (again, if I understood it
right) don't actually happen. They're like the multiple rounds of IRV:
the algorithm goes through multiple stages, between which the
effective ratings change according to the logic of the algorithm
itself, but each voter only has to submit a single ballot.

Thus, I don't think your comments about organizational unity and
deliberation apply to this method. And yes, repeated ballot may be
more effective than single ballot, but that's not what extended Hay is
about.


Okay -- the pages were not explicit about this. Is there a simple
description of Hay Voting?


See here: http://www.spaceandgames.com/?p=8

It's more of a post of everything that led to the logic of Hay voting in 
the first place. Warren also has described it, and his comments in his 
IEVS voting program say:


Probability of election proportional to sum of squared roots of 
normalized utilities.


As for why this works, see the URL. (Though it appears the mathematical 
symbols on that page aren't rendering properly on my end. I hope this is 
just a client problem.)


I also think of Extended Hay as something more like the Chicago pile 
than a practical reactor. It's completely impractical, but if it works, 
it may give some ideas on how to make something that also works and 
isn't so impractical. In that sense, it's like my (weakly) monotone 
Bucklin multiwinner method, which also is very complex, but manages 
something no other Droop-proportional multiwinner method I'm aware of does.



However, the obvious complexity could be a fatal flaw in itself. The
impact of strategic voting on Range has been vastly overstated, if the
Range resolution is adequate. Such voting has a limited impact, because
Range never encourages preference reversal. Some have claimed that
optimal range voting will suppress preferences; my own opinion is that
this will happen to a much lesser degree than some expect.


Then how does that explain Youtube ratings going to min-max to such an 
extent that they replaced Range (star ratings) with Approval (thumbs 
up/down)?


(I'm curious. One possible explanation is of course that the change 
didn't arise from min-maxing, but the impression I got was that there 
was quite a bit of min-maxing going on before the change to Approval-style.)



The gain from  bumping up a candidate a single rating to make it equal,
in Range of sufficient resolution, when one actually has a preference,

 is small,

and the satisfaction of actually expressing true preference is high.
We overthink how much people want to win elections.


I doubt you'd get intermediate strategy in Range. You'd either have 
Approval strategy or not, at least among the serious contenders.


But hopefully, Jameson's experimental data will shed some light on how 
much strategy you'd get in the various methods, and of what kind. Then 
we don't have to think as much about what seems intuitive that the 
voters would do.



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Re: [EM] Election-Methods Digest, Vol 106, Issue 2

2013-04-05 Thread Kristofer Munsterhjelm


On 04/05/2013 01:50 AM, Forest Simmons wrote:

Kris,

Optimal MJ strategy is still approval strategy.  You can instruct the
voters to make absolute choices, but you cannot enforce it.  Their
willingness to abide by the instructions is purely psychological.  The
same psychology will work, only better for Consensus Threshold Approval.


True, but BL have some evidence that

- the grade ballot in conjunction with MJ produces that kind of 
psychological willingness,
- an Approval ballot as usually phrased induces relative comparisons 
instead,
- and the text (instructions) on a ballot can reduce or increase the 
degree to which the voters make relative choices.


They also suggest that the grade format itself is important in creating 
a setting where the voters have a psychological willingness to make 
absolute choices. They use two arguments:


First, that grades have common meaning as categories in themselves 
whereas a finely graduated scale induces a numerical (comparative) kind 
of thinking;


and second, that MJ, not caring about the distances between the grades, 
supports a view where grades are seen as categories in themselves, and 
thus where it's natural to do absolute comparisons rather than relative 
ones.


What I mean by not caring about the distances between the grades may 
need a little more explanation. Say the voters have a common concept of 
the grades as being points from -10 to 10 on some utility scale. Then 
say there's an MJ election and X wins. After the election, perturb the 
grades-utility mapping according to some monotone transformation and run 
the MJ election with the same underlying utilities again. X will still win.


Unless I'm mistaken, I think that'll be true of any system that only 
considers the order of the ratings (as median does, picking the 
middlemost) rather than making use of the ratings' numerical value. And 
since it only makes use of the order of the ratings (the grades, in this 
case), it doesn't need to assign an explicit value to any of them. 
They're just letters and it only needs to know that an A is better than 
a B and so on down.


Is that true of CTA as well?


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Re: [EM] Condorcet IRV Hybrid

2013-04-05 Thread Kristofer Munsterhjelm


On 04/05/2013 09:37 PM, Forest Simmons wrote:


The following observation about Condorcet IRV Hybrids has probably
already been made (but I have been gone for a while):

These hybrids have no good defense against burying.  For example

Sincere  ballots:

40  AC
35  BC
25  CA

If the A faction decides to bury C, there is nothing the C faction can
do about it unilaterally. They have to depend on the willingness of the
B faction to elevate their compromise over favorite.


That's strange, because one of the points of James Green-Armytage in his 
voting strategy paper was that the Condorcet-IRV hybrids were 
significantly less prone to burying than ordinary Condorcet methods. 
Quoting,


All Condorcet-efficient methods are vulnerable to burying, but this 
vulnerability seems to be substantially less frequent in the 
Condorcet-Hare hybrids than in most other Condorcet methods. The reason 
for this is that voters who prefer q to w will already have ranked q 
ahead of w, so that further burying w will not affect w's plurality 
score unless q has already been eliminated.


(Four Condorcet-Hare Hybrid Methods for Single-Winner Elections, 
http://www.econ.ucsb.edu/~armytage/hybrids.pdf, p. 8)


Or are we talking about different things? Perhaps C/IRV methods are less 
vulnerable to burying in the first place, but when they are, it's harder 
to employ defensive strategy to correct the burial?


-

Also, I seem to recall that Uncovered,X is generally more susceptible to 
burial than is X for various types of X, unless X is already rather 
susceptible to burial. It might be interesting to run a JGA type 
analysis on your eliminate until covering method, and compare to the 
Smith-IRV methods.



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Re: [EM] Election-Methods Digest, Vol 106, Issue 2

2013-04-04 Thread Kristofer Munsterhjelm


On 04/04/2013 02:40 AM, Forest Simmons wrote:



On Wed, Apr 3, 2013 at 12:07 AM, Kristofer Munsterhjelm
km_el...@lavabit.com mailto:km_el...@lavabit.com wrote:




Perhaps there's some value in making methods that appeal to the
right sentiment, even if one has to trade off objective qualities
(like BR, strategy resistance or criterion compliance) to get there.
The trouble is that we can't quantify this, nor how much of
sentiment-appeal makes up for deficiencies elsewhere, at least not
without performing costly experiments.


If I am not mistaken, both methods (Chiastic and this one) are
strategically equivalent to Approval from a game theoretic point of
view.  But psychologically they are quite different.  I think that this
new version is much less likely to elicit approval style responses (at
the extremes) than ordinary Range voting for example, or even the median
method with J in the title (I can't think of it at the moment).



I found a quite broad reduction for ratings-type methods. I posted it 
when I did, but I'll repeat it.


Say you have a rated ballot set, and candidate C's set of scores is 
represented by the vector s_C (first element in the vector is the first 
voter's rating of the candidate, and so on), then:


- if each candidate gets a meta-score, call it m_C, from some function 
f(s_C),

- the candidate with the highest meta-score wins,
- and f(s_C) is monotone in the sense that increasing a rating in s_C 
never makes f(s_C) evaluate to a lower value than before, and decreasing 
a rating in s_C never makes f(s_C) evaluate to a higher value than before,


- then Approval strategy is optimal.

The reason is that if a voter likes a candidate X, he can never be worse 
off by not giving X a higher score; and if he dislikes X, he can never 
be worse off by not giving X a lower score. Thus the scores migrate to 
the Approval extremes.


And unless I'm missing something, both the chiastic method and your 
method fulfill the properties above.


There's a caveat: the optimality might be of a form where it never 
hurts you to go to an extreme, but it doesn't hurt not to either. To 
eliminate that kind of equilibrium, one would have to replace the 
monotonicity property with something stronger.


-

As for the median method, you're probably thinking of Majority 
Judgement. As long as the voters act in the way BL say they should do, 
and judge candidates to absolute grades rather than comparing the 
candidates to each other, it avoids Approval reduction. BL use evidence 
from France to argue that enough voters judge to absolute grades that it 
effectively works this way. Maybe your method would also do so, but then 
it would have to be phrased in terms of grades rather than numbers.


I think that Range encourages rating at the extremes, though it doesn't 
seem to always do so. Web sites lend evidence to both sides: IMDB used 
(and uses) Range for the movie ratings, while Youtube switched from 
ratings to Approval-style up-and-down voting. IMDB does some filtering 
on the votes, though, so perhaps that's what is keeping it from reducing 
to approval. In any case, it shouldn't be hard to make a method that's 
more resistant than bare Range in that respect.



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Re: [EM] Election-Methods Digest, Vol 106, Issue 2

2013-04-03 Thread Kristofer Munsterhjelm


On 04/03/2013 12:01 AM, Forest Simmons wrote:

Jobst has suggested that ballots be used to elicit voter's consensus
thresholds for the various candidates.

If your consensus threshold for candidate X is 80 percent, that means
that you would be willing to support candidate X if more than 80 percent
of the other voters were also willing to support candidate X, but would
forbid your vote from counting towards the election of X if the total
support for X would end up short of 80 percent.

The higher the threshold that you give to X the more reluctant you are
to join in a consensus, but as long as your threshold t for X is less
than than 100 percent, a sufficiently large consensus (i.e. larger than
t percent) would garner your support, as long as it it is the largest
consensus that qualifies for your support.

A threshold of zero signifies that you are willing to support X no
matter how small the consensus, as long as no larger consensus qualifies
for your support.

I suggest that we use score ballots on a scale of 0 to 100 with the
convention that the score and the threshold for a candidate are related
by  s+t=100.

So given the score ballots, here's how the method is counted:

For each candidate X let p(X) be the largest number p between 0 and 100
such that p(X) ballots award a score strictly greater than 100-p to
candidate X.

The candidate X with the largest value of p(X) wins the election.


I think a similar method has been suggested before. I don't remember 
what it was called, but it had a very distinct name.


It went: for each candidate x, let f(x) be the highest number so that at 
least f(x)% rate the candidate above f(x).


I *think* it went like that, at least. Sorry that I don't remember the 
details!



If there are two or more candidates that share this maximum value of p,
then choose from the tied set the candidate ranked the highest in the
following order:

Candidate X precedes candidate Y if X is scored above zero on more
ballots than Y.  If this doesn't break the tie, then X precedes Y if X
is scored above one on more ballots than Y.  If that still doesn't break
the tie, then X precedes Y if X is scored above two on more ballots than
Y, etc.

In the unlikely event that the tie isn't broken before you get to 100,
choose the winner from the remaining tied candidates by random ballot.


I imagine Random Pair would also work.


The psychological value of this method is that it appeals to our natural
community spirit which includes a willingness to go along with the group
consensus when the consensus is strong enough, as long as there is no
hope for a better consensus, and as long as it isn't a candidate that we
would rate at zero.


That's an interesting point. I don't think that factor has been 
considered much in mechanism design in general. Condorcet, say, is 
usually advocated on the basis that it provides good results and resists 
enough strategy, and then one adds the reasoning it looks like a 
tournament, so should be familiar afterwards.


Perhaps there's some value in making methods that appeal to the right 
sentiment, even if one has to trade off objective qualities (like BR, 
strategy resistance or criterion compliance) to get there. The trouble 
is that we can't quantify this, nor how much of sentiment-appeal makes 
up for deficiencies elsewhere, at least not without performing costly 
experiments.



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[EM] Cloneproofing Random Pair and Random Candidate?

2013-04-03 Thread Kristofer Munsterhjelm

Unless I'm mistaken, the method called Random Favorite is cloneproof, 
for an extended variant of independence from clones that says that the 
probability of a clone set member being chosen can not depend on the 
size of the clone set.


Say the first ballot is chosen. Then before cloning, the first choice is 
obviously picked. If the first choice was part of a clone set and the 
clone set is either made larger or smaller, a member of that clone set 
is still picked. So Random Favorite appears cloneproof.


The other two random strategy-proof ranked methods we know of - Random 
Pair and Random Candidate - are not. Random Candidate is obviously 
vulnerable to teaming. So is Random Pair, because adding clones means 
there's a greater probability one or both of the pair come from the 
clone set.


However, there is a rated method that is also strategy-proof. It is 
called Hay voting. Some time ago, I stumbled across 
http://www.panix.com/~tehom/essays/hay-extended.html , which seems to be 
a proposal to make Hay voting cloneproof. I haven't really understood 
the details yet, but I'm wondering if this could be used to also make 
the two Random methods cloneproof.



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Re: [EM] Parliamentary compromising strategy

2013-03-21 Thread Kristofer Munsterhjelm


On 03/19/2013 03:08 AM, Richard Fobes wrote:

I continue to fail to understand why citizens think of politics as a
left-versus-right tug-of-war. That's what it used to be before special
interests hired election experts to advise them on how to take advantage
of vote splitting.

Now, the much bigger gap is up-versus-down. The vast majority of
voters are up and the biggest campaign contributors are down.
(The downers are also known as special interests.)


Here, it seems that up vs down compresses a lot more, i.e. resolves 
itself. We're not perfect (by any means), but if income inequality is 
any metric, Norway's Gini coefficient is at around 26 while the United 
States exceeds 40 (and is around the same level as China last I checked).


Although I should be careful not to be blinded by my own position, it 
would seem to me that working political systems provide a tighter link 
to the people. Thus, when the people want redistribution, they're more 
likely to get it. If the connection between those doing the governing 
and those governed is weaker, it's no surprise that the actions of the 
managers tilt to their own advantage rather than that of the people.



Getting back to your prefer-left-of-center-coalition or otherwise
prefer-right-of-center-coalition scenario, it involves coalitions. I
advocate letting the political parties themselves be coalitions, and let
there be fewer of them, and allow the voters to shift those coalitions.
That reduces the effect of parties having lots of negotiation room in
the backroom deals that choose coalitions.

To further reduce the relevance of coalition-building backroom deals,
VoteFair negotiation ranking would be used by the parliament to make
laws on an issue-by-issue basis, rather than on a backroom-deal (by the
coalition leaders) -by-backroom-deal basis.


Okay. So just to see if I got it right, you're saying that instead of 
PR, you'd have larger groups, and then these groups would negotiate 
among themselves, in the open, using the VoteFair method?



Richard Fobes


I was thinking that a better option would be to have some kind of DSV
that can make that choice on the voters' behalf. However, this DSV can't
act until parliamentary negotiations start, because it doesn't out of
nothing know the relative strengths of the different groups. And thus,
it would seem that the election method would have to formalize some
concept of coalitions and parties beforehand, which is undesirable.
Either that or use liquid democracy, Asset or some other
negotiation-based protocol.


DSV stand for what?


I didn't see this at first because your name was before it, but DSV 
stands for Declared Strategy Voting. Basically, it's a voting method 
that acts strategically for you so that you (usually) don't have to. In 
the setting of the parliamentary compromising strategy, the left-wing 
voter would rank the left-wing party ahead of the center-right party, 
and then the method would give the vote to the correct party so the 
voter didn't have to hedge his bets.


Strictly speaking, it's possible to out-strategize DSV (or it would have 
been a strategy-proof method, and Gibbard-Satterthwaite and 
Duggan-Schwartz prevents that). But the idea is that the algorithm would 
generally be much better at it.



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Re: [EM] Parliamentary compromising strategy

2013-03-18 Thread Kristofer Munsterhjelm


On 03/15/2013 06:55 PM, Richard Fobes wrote:

On 3/15/2013 2:22 AM, Kristofer Munsterhjelm wrote:

On 03/14/2013 11:26 PM, Richard Fobes wrote:

...

One way is to eliminate the need for coalitions. This is the purpose of
VoteFair negotiation ranking, which allows the elected representatives
to rank various proposals on various (hopefully-at-least-somewhat)
related issues. Based on these rankings the software calculates which
proposals would produce a proposed law that is best supported by the
elected representatives -- including support by small (but not tiny)
opposition parties. (Details about VoteFair negotiation ranking are at
www.NegotiationTool.com.)



On 3/11/2013 1:33 AM, Kristofer Munsterhjelm wrote:

I suppose that making every government a minority government would also
work here. The cost would be greater instability, though. How would the
negotiation ranking handle the instability (or general delay and
gridlock) that might appear?


I do not understand what you mean by making a government a minority
government. What is a minority government?


In parliamentary systems, a minority government is a government that is 
not supported by a majority of the parliament. Except in systems that 
require constructive votes of no confidence, the minority government can 
always be brought down by a vote of no confidence. Therefore, the 
minority government has to go from issue to issue, finding majorities on 
each issue separately so that the government is not replaced.


A minority government is thus ultimately a device of the legislature. It 
does the legislature's work, and if it doesn't, it is replaced. It 
doesn't have internal party loyalty because it can't demand standards of 
its own. This is opposed to, say, a coalition deciding to negotiate 
among themselves in the executive, where all the coalition parties are 
instructed to support the executive.



VoteFair negotiation ranking gives the majority the most control. Yet it
also gives influence to minorities -- if:

* They are joined together with a common interest -- which amounts to an
opposition coalition that is internally identified by the algorithm
based on votes, without being based on any additional information (such
as party membership).

* Or, they have some overlap with some representatives in the majority.

* Or, when they support something that does not conflict with what the
majority wants.

Expressed another way, the method is a calculation algorithm that
implements log rolling (combining separate proposals into a single
package to be voted on) and vote trading (where representatives agree
to vote for something they don't care for in exchange for another vote
that supports what they do care about).

The algorithm produces a suggested list of compatible proposals that
would be likely to get majority support if they are packaged into a
single yes-or-no vote among all the representatives (which in this case
are the MPs).

If the package does not pass with majority support, then the (elected)
representatives can change their rankings and their identification of
which proposals are incompatible with one another. This is a diplomatic
way of saying that they either were not paying full attention when they
were voting on the proposals, or they were not honest in their voting.


Or the negotiation was not successful in the first place, perhaps.


The other approach is to replace traditional PR with an election method
that gives no advantage to strategic voting. This is what the full
VoteFair ranking system is designed to do. Specifically, each district
would use VoteFair representation ranking to elect one majority MP
(member of Parliament) and one opposition MP, and the remaining
parliamentary seats are filled using VoteFair party ranking (to identify
party popularity) and VoteFair partial-proportional ranking (to choose
which district-losing candidate wins each party-based seat). The result
does not allow even a group of well-coordinated voters to meaningfully
and predictably alter the results.


How would that method solve the left/right scenario I mentioned? Would
it give the right-of-center parties (or people) position if they had a
majority, and otherwise let the left-of-center voter's vote go to a
left-of-center candidate?


Your scenario (as I recall) involved using a voting method in which
there are strategies that enable the voters to produce a different
outcome -- without any risk that a dramatically worse outcome can occur.


The whole problem is that there's a strrategy but the strategy isn't 
risk free. The problem itself is a strategy that could make the gun fire 
back at the user, and so the voters face a quite unpleasant dilemma if 
they're instrumental.


The problem is this. You have a bunch of voters who are left of center, 
and there's going to be a parliamentary election. Given past history, 
after the election, if the center-left coalition has a majority, it will 
form the government. Otherwise the center-right

Re: [EM] Historical perspective about FairVote organization

2013-03-18 Thread Kristofer Munsterhjelm


On 03/17/2013 06:32 PM, Richard Fobes wrote:

On 3/15/2013 2:12 AM, Kristofer Munsterhjelm wrote:

On 03/14/2013 06:45 PM, robert bristow-johnson wrote:

IRV will prevent a true spoiler (that is a candidate
with no viable chance of winning, but whose presence in the race changes
who the winner is) from spoiling the election, but if the spoiler and
the two leaders are all roughly equal going into the election, IRV can
fail and *has* failed (and Burlington 2009 is that example).


If you think about it, even Plurality is immune to spoilers... if the
spoilers are small enough. More specifically, if the spoilers have
less support in total than the difference in support between party
number one and two, Plurality is immune to them.

So instead of saying method X resists spoilers and Y doesn't, it seems
better to say that X resists larger spoilers than Y. And that raises the
question of how much spoiler-resistance you need. Plurality's result is
independent of very small spoilers. IRV's is of somewhat larger
spoilers, and Condorcet larger still (through mutual majority or
independence of Smith-dominated alternatives, depending on the method).


This is a good example of the need to _quantify_ the failure rate for
each election method for each fairness criteria.

Just a yes-or-no checkmark -- which is the approach in the comparison
table in the Wikipedia Voting systems article -- is not sufficient for
a full comparison.


Spoiler resistance is to some degree already quantified. If a method 
passes the majority criterion, then it's resistant to spoilers when a 
party or candidate has a majority. A method that passes mutual majority 
is resistant to spoilers outside a group that's ranked first by a 
majority. Independence from Smith-dominated alternatives gives 
resistance to spoilers not in the Smith set; and so on.


But you have a point. In the practical view, these are only interesting 
inasfar as they cover enough to make the method resistant against 
spoilers in general. That is, if an oracle told us that to get 
multiparty democracy where people don't think spoilers get in the way, 
all you need is ISDA and everything else is icing on the cake; then we 
wouldn't need to bother about anything more than ISDA. At least not 
unless the voters would find it unfair *on principle* to have something 
that didn't pass, say, independence from covered alternatives.


That's the division into three I've mentioned before. Performance under 
honesty, things that deter or make strategy unnecessary so we get to 
honesty in the first place, and consistency with itself (or, more 
broadly speaking, compliance with what the voters think should be held 
for the method to be fair).


In all three cases, we have approximations.

Bayesian regret is an approximation to performance under honesty. It 
holds if you assume certain things about what performance actually 
means: how to do interpersonal comparisons, and utilitarianism[2].


Criteria are approximations to the other two. The good thing about 
criteria is that they provide a bound. If I prove that a method passes 
independence from Smith-dominated alternatives (ISDA), then it passes 
ISDA outright. You don't have to worry about that the method only passes 
ISDA in the cases that are irrelevant to a real election. If it passes 
ISDA, it passes ISDA *everywhere*[1]. And I think that's why I try to 
make methods that pass many criteria, because if they pass some 
criterion X, then I can say done and move on without having to 
quantify *where* they're passed. This saves a lot of detective work 
determining if the areas where they pass are the areas we care about.


But beyond that, you're right. The approximations are not the real 
things. They're proxies we use because they're easier to investigate. 
And a method might seem to have contradictions when you look upon every 
possible ballot set yet be without such in the real world. For instance, 
if people voted exclusively on a left-right scale, then Condorcet always 
finds a CW and so passes later-no-harm, later-no-help, IIA and so on, in 
these cases. In that case, we could even use Borda IRV if that's what 
the people would prefer. The various monotonicity failures wouldn't be a 
problem because we'd never get to that domain. And if we had some way of 
knowing what level of spoiler resistance is enough (or conversely, what 
isn't), then we could exclude a lot of methods for either being too 
complex or for not passing the mark.



It's like reinforcing a bridge that would collapse when a cat walks
across it, so that it no longer does so, but it still collapses when a
person walks across it. Cat resistance is not enough :-)


Great analogy. We need to start assessing _how_ _resistant_ each method
is to each fairness criteria.


Yes, and these fairness criteria might not even be the same sort as the 
traditional criteria. They might be more vague, like spoiler 
resistance, which then fails when the voters complain like

Re: [EM] Helping the Pirate Party to vanish

2013-03-17 Thread Kristofer Munsterhjelm


On 03/15/2013 09:27 PM, Abd ul-Rahman Lomax wrote:

At 04:16 AM 3/14/2013, Kristofer Munsterhjelm wrote:

On 03/13/2013 05:09 AM, Michael Allan wrote:


If the experts in the Election Methods list can't find a serious fault
with this method, then it might be possible to bring down the party
system in as little as a few years. Mind you, it would be no bad
thing if it took a while longer, given the disruption it might cause.


Regarding liquid democracy methods in general, I think the vote-buying
problem is pretty serious. Or rather, that's not the worst part of it,
but it's a symptom of a more general aspect.


Kristofer is asseting as a serious problem something on which there is
zero experience. It's not clear that vote-buying is *ever* a serious
problem. A system that seeks broad consensus, where possible, is only
vulnerable to *truly massive vote-buying, where it is more like
negotiation than vote buying. I.e., Walmart will donate $100,000 to
the town if voters allow a store to be sited there. Much more likely to
be successful than trying to pay voter $100 or whatever and run legal
risks.


Given that there has been zero experience with the use of liquid 
democracy for the exercise of power, yes, I am asserting something on 
which there is zero experience. There's zero experience either way.


Since I make the assertion, I should provide something on which to base 
it, though. And my assertions are based on analogous systems.


In the matter of vote-buying and coercion, that analogous system is 
simply the election of candidates for office. Vote-buying and coercion 
were here serious enough problems that one moved from the initially open 
ballot onto a secret ballot. Clearly enough, openness at the lower end 
was not a good thing.


The same arguments you provide against vote-buying and coercion could be 
applied to a regular election. You say that vote-buying is illegal. Yes, 
so it is in regular elections, but we still have secret ballots. You say 
that if the small town is too oppressive, then just move. You could say 
that about public balloting for candidate elections, too. And since we 
still have secret ballots, it would seem that those arguments for a 
public ballot are not considered sufficiently strong.


Would you prefer public (open) ballots for regular elections? If not, 
what's the difference between your arguments as applied to liquid 
democracy, and as applied to regular elections?


For that matter, liquid democracy (for the exercise of power) could need 
more protection than ordinary elections. The argument would go something 
like: if a minority is being oppressed in a small town, then it doesn't 
matter because the majority will win anyway. However, being a consensus 
system, liquid democracy needs to protect minorities as well, so that it 
is safe to be a proxy and thus to pull the center of political gravity 
in the right direction.



First of all, Kristoger is assuming exercise of power through delegable
proxy. I don't recommend it for that, not without substantial experience
first. I recommend it for *advisory structures.*


With this (except for the spelling of my name :-), I do agree. If 
experience is the most solid evidence, then let's get some of that 
evidence. And since it's an optional matter whether one follows advice, 
the stakes should be lesser.


I mentioned liquid democracy in the sense of exercising power because 
that was what I was discussing in the parliamentary compromising problem 
thread.



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Re: [EM] Historical perspective about FairVote organization

2013-03-15 Thread Kristofer Munsterhjelm


On 03/14/2013 06:45 PM, robert bristow-johnson wrote:

IRV will prevent a true spoiler (that is a candidate
with no viable chance of winning, but whose presence in the race changes
who the winner is) from spoiling the election, but if the spoiler and
the two leaders are all roughly equal going into the election, IRV can
fail and *has* failed (and Burlington 2009 is that example).


If you think about it, even Plurality is immune to spoilers... if the 
spoilers are small enough. More specifically, if the spoilers have 
less support in total than the difference in support between party 
number one and two, Plurality is immune to them.


So instead of saying method X resists spoilers and Y doesn't, it seems 
better to say that X resists larger spoilers than Y. And that raises the 
question of how much spoiler-resistance you need. Plurality's result is 
independent of very small spoilers. IRV's is of somewhat larger 
spoilers, and Condorcet larger still (through mutual majority or 
independence of Smith-dominated alternatives, depending on the method).


Some rated methods are claimed to pass IIA outright and so not be 
affected by spoilers no matter how large they are. That is true - as 
long as the voters submitting the ratings are comparing the candidates 
to a common standard rather than to each other.


So IRV advocates can say that IRV will prevent a spoiler from spoiling 
the election, according to some definition of spoiler. So does Plurality 
for a less useful definition of spoiler. In any case, it seems that 
IRV's resistance against candidates that don't win isn't good enough.


It's like reinforcing a bridge that would collapse when a cat walks 
across it, so that it no longer does so, but it still collapses when a 
person walks across it. Cat resistance is not enough :-)


It would be really useful to know what level of resistance is enough, 
but that data is going to be hard to gather. It also depends on your 
bar. If you're perfectly content with Australian two-and-a-half party 
rule, then IRV is good enough. If you want resistance even in a game 
theoretical situation where everybody can communicate with everybody 
else and votes are purely instrumental, then no ranked voting system is 
going to work... and so on.


And beyond that we have even harder questions of how much resistance is 
needed to get a democratic system that works well. It seems reasonable 
to me that advanced Condorcet will do, but praxeology can only go so 
far. If only we had actual experimental data!


(We do have, to some extent. We have Wikimedia elections and Pirate 
Party primaries. We also know that unless the voters would have reacted 
to the presence of Condorcet by counter-Condorcet strategy, Condorcet 
methods would have avoided the IRV crash in Burlington. And if we 
stretch enough, we have multiwinner ranked voting results, such as with 
New York, that give some bound on whether they provide multiparty rule.)



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Re: [EM] Corrections to inaccurate FairVote historical perspective

2013-03-15 Thread Kristofer Munsterhjelm


On 03/14/2013 11:40 PM, Richard Fobes wrote:


Does anyone know of any other political party that uses the
election-method reform that they promote?


The Pirate Party of Sweden uses Schulze for their primaries. They don't 
promote Schulze, though. Since Sweden is parliamentary, there are no 
single-winner elections and so Schulze doesn't apply.


Ideally, the Pirate Party would use Schulze STV internally and also 
promote it for election reform. But that's cherry on the top. I'm not 
going to be annoyed at their use of Schulze simply because they could 
have picked SSTV instead. I just hope their use of ordinary Schulze for 
composing the party list won't lead to too many centrists on the list 
and thus opposition and replacement with some worse but more 
proportional method.




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Re: [EM] Parliamentary compromising strategy

2013-03-15 Thread Kristofer Munsterhjelm


On 03/14/2013 11:26 PM, Richard Fobes wrote:

On 3/11/2013 1:33 AM, Kristofer Munsterhjelm wrote:
  Here's a scenario I've been thinking about lately.
 
  Say that you have a parliament using proportional representation, and
  the voting method is party list. Then say that the situation is
  so that after the election, either the left-of-center parties or the
  right-of-center parties form a coalition.
 
  Given this, you might get a compromising strategy. [...]
 
  But if enough people vote this way, then the right-wing wins, even if
  the polls were inaccurate and it would not have won if people had
  voted honestly.
 
  Is there any way of ameliorating this? [...]

The need for a coalition -- which often occurs when PR is used --
introduces an extra layer in the political system. The layer is between
the elected representatives and the majority coalition (or ruling
coalition).

This extra layer can easily result in the opposite of what some voters
want. As an exaggerated, simplified, and non-realistic example, suppose
that half the voters in the Green party are women, and their votes for
this party are based on the party's support for gender equality. And
suppose that the Green party forms a coalition with another major party,
and in the backroom negotiations a majority of the Green party leaders
are men and agree to compromise on gender issues, in exchange for
increased focus on environmental issues.

Of course, in reality the backroom compromises are both unknown and
intertwined. Yet this example illustrates the underlying problem.

I see two ways of resolving this dilemma.

One way is to eliminate the need for coalitions. This is the purpose of
VoteFair negotiation ranking, which allows the elected representatives
to rank various proposals on various (hopefully-at-least-somewhat)
related issues. Based on these rankings the software calculates which
proposals would produce a proposed law that is best supported by the
elected representatives -- including support by small (but not tiny)
opposition parties. (Details about VoteFair negotiation ranking are at
www.NegotiationTool.com.)


I suppose that making every government a minority government would also 
work here. The cost would be greater instability, though. How would the 
negotiation ranking handle the instability (or general delay and 
gridlock) that might appear?



The other approach is to replace traditional PR with an election method
that gives no advantage to strategic voting. This is what the full
VoteFair ranking system is designed to do. Specifically, each district
would use VoteFair representation ranking to elect one majority MP
(member of Parliament) and one opposition MP, and the remaining
parliamentary seats are filled using VoteFair party ranking (to identify
party popularity) and VoteFair partial-proportional ranking (to choose
which district-losing candidate wins each party-based seat). The result
does not allow even a group of well-coordinated voters to meaningfully
and predictably alter the results.


How would that method solve the left/right scenario I mentioned? Would 
it give the right-of-center parties (or people) position if they had a 
majority, and otherwise let the left-of-center voter's vote go to a 
left-of-center candidate?



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Re: [EM] Historical perspective about FairVote organization

2013-03-14 Thread Kristofer Munsterhjelm


On 03/13/2013 10:48 PM, Abd ul-Rahman Lomax wrote:

At 03:16 PM 3/13/2013, Richard Fobes wrote:

For the benefit of those who don't understand why FairVote promotes
IRV (instant-runoff voting) in opposition to many forum participants
here, I'm posting this extract from an excellent, well-written, long
message by Abd.

On 3/13/2013 11:46 AM, Abd ul-Rahman Lomax wrote:
[not copied]



I'll add that in Canada the FairVote group directly advocates STV and
European-based PR methods, not the stepping-stone IRV path.

(BTW, please don't confuse the similarly named FairVote and VoteFair
names.)


I certainly won't.

Yes, STV is a far more sensible method, under certain multiwinner
conditions. However, the essential problem does remain, premature
elimination as a result of vote-splitting in first preference, further,
there is the problem that Dodgson (Lewis Carroll) identified in the
1880s, that voters don't necessarily have adequate information to
properly rank more than one candidate. Hence he proposed what we now
call Asset Voting, as a tweak on STV.


The good thing about multiwinner methods is that as the number of seats 
go up, the proportionality constraints matter more and more and the 
wiggle room between those proportionality constraints become less. So 
the more seats you have, the more bizarre the base method can be as long 
as it meets the proportionality criteria.


STV meets Droop proportionality, which is its proportionality criterion. 
If you have a great number of seats, you're pretty much bound to have 
some minorities be large enough that they'll proportionally get what 
they want.


Of course, this logic also goes the other way, so mutual majority for 
single-winner is a more loose constraint than DPC in the 10 seat case, 
thus making IRV comparatively worse compared to Condorcet than say STV 
with 10 seats compared to CPO-STV with 10. There's also the problem that 
ranking very long lists of candidates becomes a chore, and if there are 
many seats, there also are many candidates. The Australian way of 
turning STV into a party list method is one way of solving this, but 
in my opinion, that cure is worse than the disease.



With Asset Voting, candidates aren't actually eliminated; rather, they
aren't elected yet, but they can exercise the votes they hold, to create
winners, thus converting the voting system into a *deliberative
process.* In theory, if two candidates are holding votes for the last
seat, and can't come to an agreement, they can choose *someone else*,
who might not have been a candidate at all!


How does the process work? Is STV run through one round, and then the 
candidates to be eliminated are asked where to transfer their votes, and 
then STV is run through the next round, and then the candidates... and 
so on?


Also, I haven't heard of Asset being used in public elections, but I 
know of something similar where candidates provide a ranking of their 
own. This was used in Fiji, for example, before the coup. One common 
complaint about this is that it takes power out of the hands of the 
voters. That is, the parties make backroom deals about whom to support, 
and then the voters' votes are hijacked in the direction of the allies 
against the voters' wishes.


How does proper Asset handle that? I've heard counters to the effect 
that if you don't trust your favorite to manage your vote, then you 
shouldn't trust your favorite with policies either, and so you shouldn't 
vote for him. But in a similar way to how a majority of a majority is 
not a majority, the closest political candidate to your closest 
political candidate may not be your next-to-closest political candidate. 
Each link weakens the connection to the voter. Similarly, party pressure 
can be applied to the candidate's ranking of other candidates, but not 
as easily to the day-to-day workings of that candidate.


I guess Asset itself is not as susceptible to this problem if the 
candidates are free to declare where their votes should go, instead of 
having to commit ahead of time. But does it weaken it enough in a highly 
competitive environment with party discipline?



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Re: [EM] Parliamentary compromising strategy

2013-03-14 Thread Kristofer Munsterhjelm


On 03/12/2013 06:27 PM, Michael Allan wrote:

Hi Kristofer,

I think the liquid democracy solution can be salvaged by moving it
into an open primary.


I suppose the problem is that the coalition makeup is set up after
the election rather than during it. So the voting method has no idea
about how power is distributed and arranged after the election. ...


I agree, it's an information problem.


That leaves the second option, which sounds more like a form of
proxy voting or liquid democracy. Besides the problems with
vote-buying [1], there's also the instability. ...


Instead of a continuous election, what about a continuous primary?
Being continuous, the results are still informed by daily events in
the assembly.  But being a primary, there's no direct feedback to
cause instability.  Instead, elections are held at long intervals as
usual, and this is where the primary kicks in.  It's an open primary,
so it produces a single candidate list that cuts across all parties.
Any party may adopt this all-party list as its own.  This is political
suicide, of course, but it also wins votes.  The party surrenders its
power over the elected members, who now owe their seats entirely to
the open primary, and not to any party.  Electors and candidates will
be happy to support this arrangement.  It dissolves the power blocs
and frees the assembly to focus on its legislative functions. [2]


That would get rid of the instability, or at least slow it down to only 
oscillate between election periods. To use a metaphor, the elections 
serve as a low-pass filter.


But would it get rid of the parliamentary compromising strategy that I 
mentioned? It depends on how the lists are frozen before the election. 
If there's a negotiation step between the candidates on the list, then 
it could. Say a voter votes for a liberal. This liberal notices that 
according to predictions of support for the non-technical list, more 
conservatives than liberals will be elected. Thus he gives his support 
to the more liberal conservatives, pushing them above the less liberal 
ones on the final list.
If there is no negotiation, then the voters have to do the negotiation 
step, and that could lead to the kind of instability I mentioned. It 
might be less serious than the case with a continuous election, though. 
The voters know they have to make up their minds before the time the 
lists will be frozen (for the elections). The pressure is akin to that 
in Simmons's consensus method: reach an agreement or we'll pick at 
random. One might still want to have tools that could be used to escape 
local attractors, however. In the case where the right splits off the 
center to not be diluted, it would be nice to have some mechanism that 
could predicate the vote transfers on keeping the center, so the right 
can see that splitting off the center will never work. But I don't know 
what those tools would look like. I think a liquid system would be more 
free to develop these than a traditional party system would, since the 
tools and mechanisms would only inform the voters, not alter how they 
delegate.


As for parties adopting the list, I don't think they would. Consider it 
in systems terms. Then the party is a system that responds to influence 
from the outside in such a way as to retain its integrity. The party 
thus desires to push the political environment in a direction that 
supports its existence. Traditionally, that can be done by gaining 
influence. Increased influence means greater capacity to change the 
environment - and thus a greater ability to head off changes that would 
be a problem to the party's own integrity. Here, a problem to integrity 
would be something that either weakens the party or requires it to 
change enough that it's no longer that party.


Adopting a consensus list might give the party greater influence. But 
this influence is given at the cost of destroying integrity. In your own 
simpler words, it's political suicide. What good does it do the party to 
gain greater control, if the thing which gains control is not the party 
any longer? Control and influence are tools to keep integrity, but if 
there's no integrity to keep, it loses its point.


The party would have to redefine its identity so that it is not based on 
any political position before it could adopt the list. I don't think any 
usual parties would do that. They have not defined themselves as 
organizations that encourage democracy whatever its shape, but as 
organizations that politically represent a certain general position.


New parties could define themselves differently. If the party's 
considering itself an organization to introduce liquid democracy, for 
instance (as the Internet Party is, to my knowledge), it would have no 
difficulty moving to a consensus list.



The power structure is nominated in a separate, executive primary [3].
The assembly gives its confidence to the nominated government, or not,
and this information feeds back to both

Re: [EM] Helping the Pirate Party to vanish

2013-03-14 Thread Kristofer Munsterhjelm


On 03/13/2013 05:09 AM, Michael Allan wrote:


If the experts in the Election Methods list can't find a serious fault
with this method, then it might be possible to bring down the party
system in as little as a few years.  Mind you, it would be no bad
thing if it took a while longer, given the disruption it might cause.


Regarding liquid democracy methods in general, I think the vote-buying 
problem is pretty serious. Or rather, that's not the worst part of it, 
but it's a symptom of a more general aspect.


This general aspect is that the network of delegation can't decide when 
the power vested in a person is sufficiently great that he should be 
public, and conversely, when the voters have sufficiently little power 
that they should be anonymous.


Intuitively, for proxies with great power, the need for transparency 
outweighs the repercussions of doing so, while for individual voters the 
opposite is the case. But the voting method has no way of knowing where 
one changes into the other.


Thus there seems to be two standard solutions. The first is to keep 
everything private, and the second is to keep everything public. The 
first is rather more difficult than the second, since one has to know 
something about the proxies in order to subscribe to them; and neither 
is really desirable.


I should clarify that vote-buying is only one side of the 
transparency/anonymity problem. If you have a version where everything 
is public, then vote-buying is not the only weakness. There could also 
be vote coercion (subscribe to this proxy or else) or small-town 
effects (try being a liberal proxy in a particularly conservative town 
in the Deep South).


Now, some people say that this isn't a problem, and more broadly that 
complete disclosure is no problem. I've had that discussion on EM 
before, and I know of people who think that, more broadly, Brin's 
Transparent Society would be a good thing. Both from small-town 
effects[1] and from vote-buying, I disagree.


If only one could solve this problem, liquid democracy could be really 
good. I imagine it would be possible with judicious use of crypto, but 
that would obscure the system quite a bit. You'd also have to code into 
the system the sorites decision of where power becomes great enough 
that transparency outweighs privacy.


-

[1] The Law of Jante is a Scandinavian term, after all. Similar things 
exist elsewhere, e.g. the Japanese nail that sticks up.



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Re: [EM] proportional constraints - help needed

2013-02-16 Thread Kristofer Munsterhjelm


On 02/14/2013 07:07 PM, Richard Fobes wrote:


... as in
the top-down method of Otten?


I did not find any information about the top-down method of Otten. If
you send me a link to a place that describes it, then I can answer this
part of your question.


I've been really busy lately, so I haven't got anything else to add here 
of yet, but perhaps Peter meant this one?


http://www.votingmatters.org.uk/ISSUE13/P3.HTM

Possibly combined in some way with

http://www.votingmatters.org.uk/issue9/p5.htm .


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Re: [EM] proportional constraints - help needed

2013-02-12 Thread Kristofer Munsterhjelm


On 02/12/2013 12:24 AM, Jameson Quinn wrote:


What does monotone even mean for PR? You can make something that's
sequentially monotone, but it's (I think) impossible to avoid situations
where AB were winning but changing CAB to ABC causes B to lose (or
variants of this kind of problem). That's still technically monotone,
but from a voters perspective, it's not usefully so.


I was thinking of a one-candidate generalization to monotonicity, yes. 
That is, say that X is on the council. Then if some voters raise X on 
their ballots, that should not kick X off the council.


But wouldn't this imply the more strict monotonicity you're talking 
about? Say A and B are in the council. Then you raise B, changing CAB 
into CBA and then into BCA. By monotonicity, B shouldn't stop 
winning. Now you raise A by changing BCA into BAC and finally into 
ABC. Again, by monotonicity, A shouldn't stop winning.


I think I've described the method in an earlier post. (Incidentally, 
it's Bucklin-based.) I could also provide source code if you want to 
test it on a situation or impossibility proof that Droop proportionality 
is incompatible with monotonicity. It could use the review :-)



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Re: [EM] proportional constraints - help needed

2013-02-12 Thread Kristofer Munsterhjelm


On 02/12/2013 01:42 AM, Richard Fobes wrote:

On 2/11/2013 2:33 PM, Kristofer Munsterhjelm wrote:


Although what I'm going to say may be a bit offtopic, I think I should
say it. I think it could be useful to quantify exactly what is meant by
quoted-in proportionality in the sense that the Czech Green Party
desires it. Then one may make a quota proportionality criterion and
design methods from the ground up that pass it.


In my opinion, your comment is not off-topic.

Yes, I agree that it would be nice to more clearly define the goal.

Yet I've learned that reconsidering goals is a never-ending process
because, when a clearly defined goal is achieved, often it turns out
that a better goal becomes evident. (Especially if the intent behind the
original goal was not achieved, in spite of having achieved the clearly
stated goal.)

In this case I presume the gender-based quota requirement is a temporary
goal.

Hopefully, as more women get elected (because of using better ballots
and better counting methods), the need for it will disappear.

If it's easy to define the quota-based goal, such a definition would be
useful.

But, in my opinion, spending time developing an election method that
optimizes the clearly stated goal is not likely to provide a useful
return on investment (ROI) -- because it must be discarded when the
quota is no longer needed.


Indeed, that is a point. A more general criterion might be of more use. 
It could be something like: the method is preset with a number of sets 
and restrictions on which set can come in which place. Then the method 
must ensure this invariant is not broken while otherwise being 
proportional (in some manner).


When gender-based quotas are desired, the sets are just the set of all 
men and the set of all women, and the restrictions are on which gender 
can come in which place.


Another criterion could simply say: the proportion of set X in the 
council must be equal to some proportion set as input, +/- some error 
also given as input, unless there are no sets that satisfy this. Again, 
with gender quotas, one can set must have 50% women +/- 10%, for instance.


In both cases, the method reduces to plain old PR if one doesn't make 
use of the quota. One can easily not provide any constraints in the 
first criterion's case, and say must have 50% women, +/- 50% in the 
latter.


If nothing else, the method should be usable as a method without quotas, 
just like, say, Schulze STV is usable as a single-winner method. Then 
one may or may not use the additional quota functionality. In an 
organization, whether or not to have quotas (and how strict, and 
similar) could be decided by consensus, thus protecting the minority 
from being overruled by the majority.



I think it makes more sense to use an election method that provides fair
results in many/most situations, and do some adjustments to accommodate
a temporary situation (such as gender bias), and then abandon those
adjustments when the results match the ultimate goal.

Presumably the ultimate goal is gender equality -- which itself is
probably worth defining clearly (although not here!).


Yes. I think the quoting-in should be an additional feature that could 
be turned on or off. If one doesn't trust the organization (or 
government, or whoever is using the method) not to turn it off, one 
could just mandate in the bylaws that the setting be on, and that some 
supermajority is required to turn it off.


In a way, that would be the case even if the method had the 
quota-setting forced to on. Say we have a gender-equalized version of 
Schulze STV (call it SSTVG). Then consider a meta-method that uses SSTVG 
if one has agreed a quota is to be used, otherwise uses ordinary Schulze 
STV. That metamethod is now an adjustable gender-equalized method. 
Similarly, there's nothing to prevent a majority or supermajority 
(depending on the regulations) from replacing a gender-equalized version 
of some method with the same method lacking that feature, given power to 
alter the rules.



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Re: [EM] proportional constraints - help needed

2013-02-12 Thread Kristofer Munsterhjelm


On 02/12/2013 04:59 PM, Kristofer Munsterhjelm wrote:

On 02/12/2013 12:24 AM, Jameson Quinn wrote:


What does monotone even mean for PR? You can make something that's
sequentially monotone, but it's (I think) impossible to avoid situations
where AB were winning but changing CAB to ABC causes B to lose (or
variants of this kind of problem). That's still technically monotone,
but from a voters perspective, it's not usefully so.


I was thinking of a one-candidate generalization to monotonicity, yes.
That is, say that X is on the council. Then if some voters raise X on
their ballots, that should not kick X off the council.

But wouldn't this imply the more strict monotonicity you're talking
about? Say A and B are in the council. Then you raise B, changing CAB
into CBA and then into BCA. By monotonicity, B shouldn't stop
winning. Now you raise A by changing BCA into BAC and finally into
ABC. Again, by monotonicity, A shouldn't stop winning.


I think I see now. The problem is that raising B may kick A off the 
council. So we could define a strong and weak mono-raise. The strong 
mono-raise says that if you raise any subset of candidates in the 
council (not necessarily all by the same amount), none of those should 
be kicked off the council by your actions. The weak monotonicity is just 
that for a single candidate.


However, strong monotonicity may be too strong because you could imagine 
saying the set is the set of all the initial winners, and then you raise 
only one of them first. For the criterion to change, the outcome must 
not change at all. So the strong criterion might easily mean if you 
raise a winner, the outcome shouldn't change, and managing that would 
be impressive indeed.


I can't off-hand say it's incompatible with Droop, though. Perhaps 
impossibility can be shown by making use of Schulze's vote management 
proofs. Schulze did qualify Schulze STV by saying it would be 
susceptible to vote management where resisting it would mean breaking 
Droop proportionality, thus implying that full resistance to vote 
management is incompatible with Droop proportionality. Yet I'm not sure 
it's entirely the same situation.



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Re: [EM] proportional constraints - help needed

2013-02-11 Thread Kristofer Munsterhjelm


On 02/09/2013 09:41 PM, Richard Fobes wrote:

  2013/2/6 Richard Fobeselectionmeth...@votefair.org:
  How many candidates would/could compete for the five (open)
  party-list positions?
On 2/6/2013 3:12 PM, Peter Zbornik wrote:
  Say twenty, for instance.

To: Peter Zbornik

After considerable thinking about your request, I've come up with a
recommended election method for your situation.

The method has these advantages:

* Uses open-source software that is already available.

* Does not require any modification of the software.

* Provides proportional results for the five seats.

* Provides quota-based representation for women -- which, as I
understand it, you specified as requiring a woman in one of the top two
positions, and another woman in the next three positions.

* Is very resistant to strategic voting.

* Produces better representation compared to using STV (single
transferable vote).

The method consists of running VoteFair _representation_ ranking
calculations. Five levels of representation would be requested. As a
part of that calculation, VoteFair _popularity_ ranking results are also
calculated for all twenty or thirty candidates.


Although what I'm going to say may be a bit offtopic, I think I should 
say it. I think it could be useful to quantify exactly what is meant by 
quoted-in proportionality in the sense that the Czech Green Party 
desires it. Then one may make a quota proportionality criterion and 
design methods from the ground up that pass it.


It's very easy to otherwise come up with something that sounds nice 
(hey, I did it myself) but that doesn't pass the idea of quota 
proportionality as envisioned.


(Also, speaking of criteria: if I had enough time, I would try to find a 
monotone variant of Schulze STV. I think one can make monotone 
Droop-proportional multiwinner methods, since I made a Bucklin hack that 
seemed to be both monotone and Droop-proportional. However, I have no 
mathematical proof that the method obeys both criteria.)



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Re: [EM] proportional constraints - help needed

2013-02-06 Thread Kristofer Munsterhjelm


On 02/06/2013 08:56 PM, Jameson Quinn wrote:



2013/2/6 Peter Zbornik pzbor...@gmail.com mailto:pzbor...@gmail.com

Jameson,

I am not sure if we understand each other here.
I am looking for an election system, where the quoted-in seat gives
(or moves toward) a proportional distribution of the quoted-in gender.
If we fix the seats which will be quoted-in at no. 2 and 5, the
quoted-in gender will in some cases not be proportionally distributed,
for instance when the same group of voters get both quoted-in
candidates at places 2 and 5.


OK. I was responding to your initial statement of the problem, without
this additional proportionally-quoting-in constraint.

The issue with this constraint is that it is only meaningful if the
electorate is meaningfully separable into parties. If, on the other
hand, the electorate is in a 2D issue space, it's hard to see exactly
what this constraint even means. Thus I suspect no non-partisan system
can be made to fit this constraint. I could easily see how to meet this
constraint with a party list system (preferably open, because closed
list systems are bad), and possibly I could work it out with a
pseudo-list system like PAL, but with STV it looks to me like an
impossible task.


With a council size of 5, it might be possible to do an election between 
all consistent sets. The general idea would be something to the effect 
of that you first use a proportional ordering, setting constraints at 
different places (force woman at position one, position two, etc). Then 
you find all the sets the proportional ordering produces, and you hold a 
supermajority election to decide which to use.


The supermajority election could be a parliamentary procedures one if 
the number of members is small, otherwise it would have to be by means 
of an election method (or Asset/liquid democracy). I say it'd have to be 
supermajority so that the majority can't force disproportionality on the 
minority. However, a consensus election might on the other hand give 
undue power to the minority. So that leads to another problem, which is 
similar to the question of how to get a proportionally represented 
council if the only thing you can do is ask the voters to rank the 
different councils.


Simmons had some ideas relating to lotteries in that respect, if I'm not 
mistaken. I don't remember the details, though. Could they be applied here?



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Re: [EM] The Green scenario, and IRV in the Green scenario, is a new topic here. Hence these additional comments. Clarification of position and why.


On 02/05/2013 12:52 AM, Peter Zbornik wrote:

Kristoffer,

no the example below applies for my two-round proposal as well, thus
rapidly sinking what I previously proposed :o)
Nice to having had done away with the two-round variant of IRV.
Now I don't have to bother about it any more.

For Condorcet I am not sure.
I guess, there might even be a new criterion invented: multiple-round
strategy-proof , but I don't know of any method satisfying this
criterion.


I don't think any ranked nonprobabilistic method can pass that. To 
repurpose the proof of the previous posting.


Say you have a multiple-round strategy-proof method (by which I imagine 
you mean that taken as a whole, the method is strategy-proof, even if 
some of the rounds by themselves aren't; I'll get to the other option 
later).


Then this multiple-round method works by that the voters do something in 
the first round, then the method proceeds, then the voters do something 
in the next, and so on.


So invent an algorithm so that you can replace the voters with this 
algorithm for everything but the first round. This algorithm then 
emulates how the voters act if their internal preferences don't change 
between rounds and their internal preferences are ranked.


By replacing the voters with an algorithm, you make a DSV ranked method. 
This ranked method must by necessity be subject to Gibbard-Satterthwaite 
and to Arrow's impossibility theorem. In particular, there are times 
when dishonesty pays for the voters using this method.


Consequently, by doing the transformation in reverse, if there's an 
election where all the voters act according to the algorithm, it must 
sometimes pay for a voter to act as if his internal preferences were 
different. Thus, the multi-round method also is subject to G-S and Arrow 
in the worst case. It might not be subject to Arrow if the internal 
preferences are never only ranked, but it would still be subject to G-S.


Thus, the only way in which a method would be strategy-proof would be if 
the voters never acted like any of the (numerous) sets of algorithms 
that would make the transformation above work.


(A similar DSV construction can be used to show that Approval, Range, 
and MJ are subject to Balinski  Laraki's Arrowian objection when voters 
act in a comparative manner -- at least if we define comparatively 
properly.)


On the other hand, some runoff systems have equilibria that elect the 
honest Condorcet winner whenever there is one. That is, there's no 
incentive for any of the voters to strategize because it can only lead 
to counterstrategy that makes things worse for them. However, these 
equilibria usually require communication and so may not be very 
relevant. See for instance Messner et al. (2002-11-01), Robust 
Political Equilibria under Plurality and Runoff Rule, 
http://politics.as.nyu.edu/docs/IO/4753/polborn.pdf



The two-round method would however be suitable when trying out which
of two methods is the best by letting the winners meet in the second
round (like plurality vs. IRV winner), in order to gather political
support, but that's an other topic.


I think that some kind of demonstration of or experiment to determine 
the voting method's accuracy could also be useful. For instance, one may 
have a game where a large group of voters decide what to do next - 
either from suggestions given by the players, or directly - and then the 
game proceeds. The better play ensues, the better the method. Such 
demonstrations could also be used to determine if one can make direct 
democracy that outperforms representative democracy, or if asset voting 
or liquid democracy can work better than both. It might not capture the 
principal-agent problem of real politics, though, unless there's some 
kind of side benefit (e.g. the player and/or voters whose suggestions 
was picked the most get a bonus).



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Re: [EM] proportional constraints - help needed


On 02/05/2013 06:50 PM, Peter Zbornik wrote:

Dear all,

We recently managed, after some effort to elect some people in our
party using STV (five of seven board members of the Czech Green Party
and more recently some people to lead the Prague organisation etc.).
We used standard fractional STV, with strict quotas, valid empty
ballots, Hagenbach-Bischoff quota, no Meek.
It was the first bigger usage of STV in the Czech republic.
As a footnote, I would like to add, that one big advantage of
proportional election methods, is that it elects the best people,
i.e. meaning the people, who have the biggest support in the
organisation.

Now we would like to go on using STV for primary elections to party
lists in our party.
I have a good idea on how to do it using proportional ranking, but am
not entirely confident in how to implement the gender quotas.
So here I would like to ask you, the experts, for help.
I have only found some old papers in election-methods, but they are
not of any great help to resolve the following problem, unfortunately.

The problem (after a slight simplification) is as follows:
We want to elect five seats with any proportional ranking method (like
Schulze proportional ranking, or Otten's top-down or similar), using
the Hagenbach-Bischoff quota
(http://en.wikipedia.org/wiki/Hagenbach-Bischoff_quota) under the
following constraints:
Constraint 1: One of the first two seats has to go to a man and the
other seat has to go to a woman.
Constraint 2: One of seat three, four and five has to go to a man and
one of those seats has to go to a woman.
Say the default proportional ranking method elects women to all five
seats, and thus that we need to modify it in a good way in order to
satisfy the constraints.

Now the question is: How should the quoted seats be distributed in
order to insure
i] that the seats are quoted-in fairly proportionally between the
voters (i.e. the same voters do not get both quoted-in seats) and at
the same time
ii] that the proportional ranking method remains fairly proportional?


How about this:

First run an STV election. When the number of candidates of any gender 
is at two, no more candidates of that gender may be eliminated; instead, 
eliminate the candidate of the other gender with the least first place 
count. When more than one candidate is to be elected, always pick the 
candidate of the minority gender in the council so far; and if a given 
gender has three candidates on the council already, no more candidates 
of that gender may be elected.


(E.g. at the point where there are only two women left, the elimination 
part of STV removes the man with least first place votes instead. And if 
you have two women and a man elected so far, and the next round sees the 
election of both a woman and a man, pick the man first.)


Now you have a council with a 3:2 distribution. Do a sequential 
election. First do a ranked single-winner election for first place. Say 
the first-place candidate is a man. Then you do a ranked single-winner 
election for second. Pick the highest ranked woman in the social 
ordering for second place on the list. Continue in this manner: if the 
rules force you to pick a certain gender, pick the highest ranked 
candidate of that gender.


If you want to save on the sequential elections, just do a single round 
with a single-winner method, then remove elected candidates from the 
ranking as you go. For instance, say that the outcome is


W1  W2  M1  M2  M3

First place on the list goes to W1. Cross off that candidate and now the 
social ordering is


W2  M1  M2  M3.

Now you can't elect a woman, so the second place on the list goes to M1. 
Cross off and now the ordering is


W2  M2  M3.

This ordering can then be transplanted right to the list, so third place 
goes to W2, fourth to M2, and fifth to M3.


This approach isn't ideal: first, the sequential method that STV is 
might not do optimally with restrictions (i.e. might produce more 
disproportional results than you could get with a combinatorial method). 
Second, the single-winner run is majoritarian, so you'd get, at least 
with a good method, centrists at the top of the list and then the wings 
further down. Both of these problems could be solved by using a 
proportional ordering method, but I assume you can't get such a radical 
change, since proportional ordering methods are relatively unknown.



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Re: [EM] proportional constraints - help needed


On 02/05/2013 06:50 PM, Peter Zbornik wrote:

The problem (after a slight simplification) is as follows:
We want to elect five seats with any proportional ranking method (like
Schulze proportional ranking, or Otten's top-down or similar), using
the Hagenbach-Bischoff quota
(http://en.wikipedia.org/wiki/Hagenbach-Bischoff_quota) under the
following constraints:
Constraint 1: One of the first two seats has to go to a man and the
other seat has to go to a woman.
Constraint 2: One of seat three, four and five has to go to a man and
one of those seats has to go to a woman.
Say the default proportional ranking method elects women to all five
seats, and thus that we need to modify it in a good way in order to
satisfy the constraints.


Oh, sorry. I didn't see the part about that you could use a proportional 
ranking method. In that case, the answer's simple. Pick the highest 
ranked council extension that doesn't violate the constraints.


E.g. for Schulze's proportional ranking method, say the candidates are 
W1, W2, W3, M1, M2, M3 (for Woman and Man respectively).


First round, you have a matrix with W1, W2, W3, M1, M2, and M3. Say the 
Schulze winner is M1. That's okay, M1 gets first place.


Second round, you have a matrix with {M1, W1}, {M1, W2}, {M1, W3}, {M1, 
M2}, and {M1, M3}. Determine the Schulze social ordering according to 
the Schulze proportional ordering weights (as defined in his paper). 
Remove {M1, M2} and {M1, M3} from the output social ordering since these 
aren't permitted. Say {M1, W1} wins.


Then you just continue like that. In essence, you're picking the best 
continuation of the ordering given what the constraints force you to do.


You could also just null out the defeat strengths in the proportional 
ordering matrix, but that would produce strategy incentives since 
Schulze doesn't satisfy IIA.



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Re: [EM] proportional constraints - help needed