from:"Kristofer Munsterhjelm"


Dave Ketchum wrote:

  Or do we want the voter to be able to cancel the ballot and let
  the poll workers know that he needs a paper ballot instead that
  he can mark himself?
 
  I'm fine with the latter.  Actually that seems like a reasonable
  thing to do.

I agree, but that is not happening on all of todays' voting systems.
Election officials seem to be hopelessly slow to grasp the problem or
the solution.


This is a possible place for some new, clear, thinking - the Election 
officials likely couldn't fix this by themselves.


We are in trouble - failures have been proved too often, and there is 
good reason to believe most failures do not even get proved.


Even if the voting machine would be perfect - have no flaws at all - 
having a backup paper balloting option would be a good idea, I think. To 
the extent that democracy is not only about who won, but also about the 
losers (and their voters) being confident that they lost in a fair 
manner, any voter who doesn't trust the machine can request a paper 
ballot instead; and candidates that distrust the machinery can tell 
their voters to use the paper ballot backup.


If the machine works correctly, and candidates and voters know that, the 
load on the backup system will be minimal. However, if the machines are 
untrusted or haven't earned the reputation for being fair, the backup 
will at least limit fraud somewhat.


A possible problem with the solution may occur if many more voters use 
backup ballots than was predicted, and the infrastructure (parties' 
counters, and so on) can't keep up with the load. This weakness is the 
consequence of that the load is going to be dynamic (depending on 
voters' trust in the machines), and in the worst case, the backup might 
be neglected completely.


Even working correctly, Plurality voting is not adequate.  While there 
are many competing methods, Condorcet is discussed here:

 Ballot is ranked, as is IRV's.
 Plurality voting is permitted, and can satisfy most voters most of 
the time - letting them satisfy their desires with no extra pain while 
getting their votes fully credited.

 Approval voting is likewise accepted, satisfying a few extra voters.
 Fully ranked voting is Condorcet's promise, giving full response to 
those desiring such when desired.


From a purely technical point of view, I agree. I think the good (at 
least cloneproof) Condorcet methods to focus on here would be either 
Ranked Pairs (easy to explain) or Schulze (seems to be gaining momentum 
for non-governmental purposes, e.g MTV and Debian), both wv as their 
definitions state. That shouldn't keep us from trying to find things 
like good burial-resistant Condorcet methods, though.



Open source is ESSENTIAL:
 While it encourages quality programming by those who do not want to 
get caught doing otherwise, it also encourages thorough testing by the 
community.

 But, there is a temptation for copying such without paying:
  Perhaps the law should provide a punishment for such.
  Perhaps customers should pay for such code before it
becomes open - and get refunds of such payments if the code, once open,
proves to be unreasonably defective.

The community should be demanding of Congress such support as may help.

While open source could be thought of as just the voting program, 
proper thinking includes the hardware, protecting the program against 
whatever destructive forces may exist, and verifying what happens.


Secret ballot is essential.  While voter should be able to verify the 
vote before submitting such, this is only to verify - goal above is 
election programs that REALLY DO what they promise.


Let's look at this again. What does a voting machine do? It registers 
votes. Surely, that can't be a difficult task, so why use a computer? 
Why not (for Approval or Plurality) just have a simple chip connected to 
a PROM, with the chip in turn connected to a bunch of switches, one for 
each candidate, with a matrix display next to each switch, and a final 
switch to commit the ballot? Such a machine would be provably correct: 
as long as you have a PROM that hasn't been preprogrammed (this can be 
checked at the beginning), and the machine hasn't been compromised 
(rewired switches, backdoor chips), then it'll work as promised.


Reading off the PROMs would require more complex machinery, but it's 
really just an adder. In a Condorcet election, it's a two-loop adder 
(for each candidate, for each ranked below, increment vote_for[a][b]). 
That, too, is not too difficult a task and it should be possible to 
prove that it'll work in all cases.


One might also have to take TEMPEST sniffing and similar things into 
account, but the point is that both actually registering ballots and 
counting the votes is a simple task, and therefore one can inspect the 
device or program to see that it works properly, and more than that, 
that it'll always work properly within

Re: [EM] Can someone point me at an example of the nonmonotonicity of IRV?

Chris Benham wrote:

*Kristofer Munsterhjelm* wrote (Sun. Aug.10):

There's also the it smells fishy that nonmonotonicity - of any kind or
frequency - evokes. I think that's stronger for nonmonotonicity than for
things like strategy vulnerability because it's an error that appears in
the method itself, rather than in the move-countermove game brought on
by strategy, and thus one thinks if it errs in that way, what more
fundamental errors may be in there that I don't know of?. But that
enters the realm of feelings and opinion.

Kristopher,
The intution or feeling you refer to is based on the idea that the
best method/s must be mathematically elegant and that methods tend to
be consistently good or consistently bad. But in the comparison among
reasonable and good methods, this idea is wrong.
Rather it is the case that many arguably desirable properties (criteria
compliances) are mutually incompatible. So on discovering that method X

has some mathematically inelegant or paradoxical flaw one shouldn't
immediately conclude that X must be one of the worst methods. That
flaw may enable X to have some other desirable features.

To look at it the other way, Participation is obviously interesting and
viewed in isolation a desirable property. But I know that it is quite

expensive, so on discovering that method Y meets Participation I know
that it must fail other criteria (that I value) so I don't expect
Y to be one of my favourite methods.

Looking at this further, I think part of the intuition is also one of
the frequency of the situations that would bring about the paradox. In
the case of Participation, you'd have to have two districts that later
join into one, which is not frequent; but for monotonicity, voters just
have to change their opinions (which voters often do). That's not the
entire picture, though; perhaps I consider monotonicity an inexpensive
criterion, and thus one that reasonable methods should follow, or
perhaps the degree of paradox (winner becomes loser) along with Yee-type
visualization, makes nonmonotonicity seem all the worse.

The frequency idea is also related to the explanation of criteria
failure conditions. If a person says that this method can cause winners
to become losers when voters change their minds in favor of the
now-loser, that appears completely ridiculous. On the other hand,
LNHarm/LNHelp failure could be explained as a consequence of the method
finding a common acceptable compromise, and so there's at least a
natural reason for why it'd exist. Participation would be more
difficult, but maybe one could draw parallels to the Simpson paradox of
statistics like one would with Consistency failure.

This is like the IRV method-focus versus Condorcet goal-focus, in
reverse. Criterion failure that is the necessary consequence of some
desirable trait can work (and even more so when one can easily see that
there's no way to have both), but criterion failure that's based on how
the method works rather than what it aims to achieve doesn't pass as easily.

I think that all methods that work by calculating the ranking according
to a positional function, then eliminating one or more candidates, then
repeating until a winner is found will suffer from nonmonotonicity. I
don't know if there's a proof for this somewhere, though.

A positional function is one that gives a points for first place, b
points for second, c for third and so on, and whoever has the highest
score wins, or in the case of elimination, whoever has the lowest score
is eliminated.

Less abstractly, these methods are nonmonotonic if I'm right: Coombs
(whoever gets most last-place votes is eliminated until someone has a
majority), IRV and Carey's Q method (eliminate loser or those with below
average plurality scores, respectively), and Baldwin and Nanson (the
same, but with Borda).

That's right, but I think that Carey's method (that I thought was
called Improved FPP)
is monotonic (meets mono-raise) when there are 3 candidates (and that is
the point of it.)

Yes, Carey's method is called IFPP, as defined on 3 candidates. I think
he used the name Q method for IFPP generalized to more than three
candidates. The Q method is nonmonotonic - see
http://listas.apesol.org/pipermail/election-methods-electorama.com/2001-September/006656.html

Carey later tried to patch Q for 4 candidates. The first patch failed,
and he later came up with P4
(http://listas.apesol.org/pipermail/election-methods-electorama.com/2001-September/006721.html
) which I haven't tested. While Carey said that he didn't get around to
rewriting it in stages (elimination) form, if that is possible, it's
monotonic, and it's possible (in theory) to patch to five candidates,
then patch that to six and so on up to infinity, the statement would
have to be rephrased to positional loser/below-average elimination
methods are nonmonotonic. That's a lot of ifs, but to be charitable,
I'll use that phrasing next

Re: [EM] [Election-Methods] [english 94%] PR favoring racial minorities


[EMAIL PROTECTED] wrote:

  Jobst Heitzig said:

  It is of no help for a minority to be represented proportionally when 
  still a mere 51% majority can make all decisions!


I disagree.  The advantage is that it allows 'on the fly' coalition 
re-organisation.


If all the legislators are elected via a single seat system, then in 
effect, the 2 coalitions must be decided prior to the election.  In

fact, in the US, the Republican and Democrat 'coalitions' last on a

 multi-decade scale.


A block of 15% of the legislature would be a minority.  However, if 
something oppressive was attempted against them, they could switch
sides. 


However, if all the legislators were elected via a single seat method, then
the supporters of those 15% would have to wait until the subsequent election
and it might be to late by then.


This appears to be, more generally, an issue of feedback. Democracy 
itself does better than dictatorship (even from a purely technical point 
of view, as opposed to a moral one) because the people can steer the 
representatives in the right direction. If the rulers get too detached 
from this correction, they get corrupted by the power and bad things happen.


If that's correct, then we should try to find ways of connecting the 
system even more tightly. Proportional representation would fit within 
this idea set for the reasons you point out, or broadly, that as 
minorities change, the representative-voter links update more quickly 
than they do within a majoritarian system.


Predictions based on that idea would consider the ideal to be direct 
democracy. Next to that would be continuous update of representative 
power (continuous elections). While both of these might work if we 
were machines, the former scales badly and the latter would put an undue 
load on the voters unless they could decide whether to be part of any 
given readjustment.


If we consider the case where decisions have effects that don't appear 
instantly, it gets more complex. For instance, democratic opinion could 
shift more quickly than the decisions made by one side has time to 
settle or actually do any difference. But even there, if we consider it 
an issue of feedback, we have parallels; in this case to oscillations or 
hunting, and to control theory regarding how to keep such oscillations 
from happening.


The feedback point of view is not an end-all-be-all. If there's a static 
or consistent majority that decide to, as an example, exclude 
minorities, that is democratic, but still not a good state of things, 
and no amount of making the democracy more accurately translate the 
wishes of the majority into action can fix that, since the majority 
wants to keep on excluding the minority.



PS
Anyone know a better free mail system that doesn't cause lots of ??? when
I post to this group?
The usual suspects should work: Gmail, hotmail, Yahoo; or see the 
Wikipedia comparison page at 
http://en.wikipedia.org/wiki/Comparison_of_webmail_providers . Most ISPs 
also provide mail accounts of their own for their subscribers, and 
(without knowing more) I'd assume yours do as well; if that is so, you 
could use that account and a dedicated mail reader like Thunderbird.


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Re: [EM] [Election-Methods] [english 94%] PR favoring racialminorities

Also, such a scheme would be, I think, highly susceptible to agenda 
manipulation: who decides which issue is to be effectively on the 
ballot, and who decides that the candidates associated with X and 
not-X are sincere?


Citizens are free to form such lists. Each list may support and oppose 
any topics, and the lists are supposed to collect similar minded 
candidates together. Ballots may be just votes for individual candidates 
(not for issues). I don't see any specific problems in this case.


Does that mean that a single candidate can be a member of more than one 
list? If so, how are ties handled? Depending on how that's done, it 
could cause complex interactions depending on which party a voter 
decides to support.


If a single candidate can't be on more than one list, then agenda 
manipulation still has some power. If a candidate has to commit to a 
list that is based primarily on issue X, but where he also supports Y, 
he has to make a choice (distinct from the choices voters make) of X 
over Y. That could be technically solved by making 2^n lists for n 
issues, but then you'd have to let candidates be on multiple lists, and 
pure party-neutral PR becomes much simpler.


Tree lists would help, but say that a voter likes Y, but not X any more 
than the candidate in question does. Then he wouldn't want to have his 
vote contribute to any of the other X-favoring candidates.


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Re: [EM] [Election-Methods] [english 94%] PR favoring racialminorities

2008-08-16 Thread Kristofer Munsterhjelm

I could see a kind of proxy front end to STV elections. I'm not sure I'm 
convinced it would be a good idea, or even practical to implement, but 
suppose that any person or group (including parties) could register an 
STV ranking, and a voter could select that ranking instead of ranking 
individual candidates. The logistical difficulty would be in determining 
how a voter specified their proxy, along with the possibility of 
ambiguity deliberate or accidental (Siera Club, John Smith).


There's another difficulty with that idea, and one that Juho has shown 
earlier, as related to the inheritance order of candidates in the 
electoral system of Fiji. Candidates may put preferences in different 
orders than you do, or come to an agreement with other candidates to 
support each other.


To some extent, that could be fixed by publishing the ranking 
beforehand, but one should still be aware of the difficulty.




I think that the simplest way of adding proxying to STV, user interface 
wise, would be to have a delegation mark, where your stated preference 
ordering overrides that of the candidate. For instance


A  B*  C (rest left blank)
with * as the delegation mark, and B having the preference ordering B  
E  F  C, would give


A  B  E  F  C

by substitution, whereas

A  C  B*

would give

A  C  B  E  F

since the A  C preference that the voter manually stated overrode the F 
 C preference of candidate B.


Paradoxical preferences could be resolved by highest ranked first. If

A  B*  C*

and B prefers D to E, but C prefers E to D, then the final ordering 
prefers D to E since B is ranked above C. An even more sophisticated 
version could run a single-winner social order election for equal-ranked 
candidates, so that


A  B* = C*

gives A  (result of social ordering, according to single-winner method, 
for those candidates for which B and C gave any preference)


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Re: [EM] Why We Shouldn't Count Votes with Machines


Jonathan Lundell wrote:

On Aug 16, 2008, at 12:54 AM, Kristofer Munsterhjelm wrote:

I am for a record on disk of each ballot, but done in a maner to 
not destroy secrecy.


You have to be very careful when doing so, because there are many 
channels to secure. A vote-buyer might tell you to vote exactly at 
noon so that the disk record timestamp identifies you, or he might, in 
the case of Approval and ranked ballots, tell you to vote for not just 
his preferred candidate, but both the low-support communist and the 
low-support right extremist as well, so that he can tell which ballot 
was yours and that you voted correctly.


In the US, at least, voting by mail has become so prevalent that I 
wonder whether it's worthwhile making voting machinery absolutely 
impregnable to vote-buying. All else being equal, sure, why not, but if 
we trade off other desirable properties to preserve secrecy, and leave 
the vote-by-mail door unlocked


I think it'd be better to lock the vote-by-mail door. One simple way of 
doing that has already been given, with the two envelopes under a 
verified setting. If you like technology, you can achieve the same 
effect, without the need for the physical verified setting, by using 
blind signatures. However, that runs into the same problem where the 
voters may not know what's going on.


The fingerprinting vulnerability of ranked ballots is annoying, because 
I like ranked methods (rated ones would have even greater a 
vulnerability). I can think of a crypto solution where the recording is 
done under k of n secret sharing, and the secret-holders don't disclose 
their key parts unless it becomes necessary to do a recount. But yet 
again, how could the voters know that'll actually work? Even if they 
don't, it may still be better than nothing, though.


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Re: [EM] Why We Shouldn't Count Votes with Machines


Dave Ketchum wrote:
So you're saying that computers are better than specialized machines? 
I'm not sure that's what you say (rather than that machines are better 
than paper ballots), but I'll assume that.


Your specialized machines can each do a fragment of the task. However, 
dependably composing a capable whole from them requires big efforts from 
humans.

 Composing the same capability whole from a computer and adequate
programming can be easier.


Each does a fragment of the task, yes; that's the point of modular 
design, so that you can treat the local units differently from the 
central units and don't have to prove everything everywhere.


Consider a general computer. Even for general computers, it makes little 
sense to have the district joining software - that counts the results 
from various districts and sum them up in the case of a summable method 
- on the individual units. As such, the general-purpose computers are 
already specialized, only in software instead of hardware.


Because the specialized machines are simpler than computers, once mass 
production gets into action, they should be cheaper. The best here 
would probably be to have some sort of independent organization or 
open-source analog draw up the plans, and then have various companies 
produce the components to spec.


They can be cheaper by not doing the complete task - make the task an 
election system and the cost goes up and dependability becomes expensive.


By extension, they can be cheaper by, in concert, doing just enough and 
no more. One doesn't need Turing-completeness to count an election. 
(Perhaps unless it's Kemeny.)


The simplicity of voting could also count against general-purpose 
computers as far as manual labor is concerned. If the machine has been 
proved to work, you don't need to know what Access (yes, Diebold used 
Access) is to count the votes, and you don't need a sysadmin present 
in case the system goes to a blue screen.


You need equivalent of a sysadmin to sort out getting a whole composed 
of your specialized machines.


The way I would set up the system, there would be different counting 
units. The group of units would need a person to unlock them each time 
a new voter wants to vote; that could be included in the design so that 
you don't need a system administrator for it. Then, once the election 
day is over, gather the read-only media (CD or programmable ROM), and 
either send them or the summable result (given by a second machine) to 
the central. Count and announce as you get higher up in the hierarchy.


If the components are constructed correctly, and proved to be so (which 
can be done because of the units' relative simplicity), then there won't 
be any bluescreens and little need for maintenance - except for cases 
where the machines simply break.


In this manner, the setup is more like paper balloting than it is to 
ordinary computer systems. The read-only media take the place of the 
ballot box, and the aggregating machines the place of the election count 
workers.


Computers get cheaper and cheaper - think of what is hidden inside a 
cell phone.


That's true. Maybe a compromise could be using cheap computer hardware 
with read-only software, standardized components, and have the software 
not be a full OS, but instead just enough to get the job done and be 
provable. You'd have to rely on that there are no hardware backdoors, 
but the existence of such would be very unlikely, and the entire thing 
would have to be put inside some sort of tamper-resistant enclosure so 
hackers can't attach keyloggers or do similar things.


That's true, but it's still fairly simple. Assume the ranked ballot is 
in the form of rank[candidate] = position, so that if candidate X was 
ranked first, rank[X] = 0. (Or 1 for that matter, I just count from 
zero because I know programming)


Then the simple nested loop goes like this:

for (outer = 0; outer  num_candidates; ++outer) {
 for (inner = 0; inner  num_candidates; ++inner) {
  if (rank[outer]  rank[inner]) {  // if outer has higher rank
   condorcet_matrix[outer][inner] += 1; // increment
  }
 }
}


What ran this loop outside a computer?


A chip with just enough transistors to do this task. I'm not a hardware 
expert, but I think it could be done by the use of a HDL like Verilog.


It's less than instead of greater than because lower rank number means 
the rank is closer to the top.


Write-ins could be a problem with the scheme I mentioned, and with 
transmitting Condorcet matrices. One possible option would be to 
prepend the transmission with a lookup list, something similar to:


Candidate 0 is Bush
Candidate 1 is Gore
Candidate 2 is Nader
Candidate 3 is Joe Write-In
Candidate 4 is Robert Write-In, etc

and if the central gets two condorcet matrices that have the same 
candidates in different order (or share some candidates), it flips the 
rows and columns to make the numbers the same before adding up.


Do you concede central

Re: [EM] Why We Shouldn't Count Votes with Machines


But murderers get away with murder, police are being bought
off by criminals, government employees steal office supplies.  No one knows
exactly how much any of things happen.  We try to limit them (balancing the
degree of the problem and the cost of addressing it), and we go on with our
lives.


OH. So you see it as no big problem to pretend to live in a democracy
(where you can pretend to yourself that most election outcomes are
accurate) and continuing to let elections be the only major industry
where insiders have complete freedom to tamper because 49 US states
never subjected their election results to any independent checks,
except the wholly unscientific ones in NM.

Even when Utah used to use paper punch card ballots, one person did
all the programming to count all the punch cards for the entire state
of Utah, and no one ever checked after the election to make sure that
any of the machine counts were accurate.

You sure must believe in the 100% infallibility and honesty of this
one person, and all the other persons who have trivially easy access
to rig elections.

Apparently  none of the plethora of evidence that election rigging has
been occurring ubiquitously in the US is of any interest or concern to
you.


I'm not Rob, so excuse the interruption, but some questions and ideas here:

Won't the people, as a last stop, keep fraud from being too blatant? You 
don't need scientific methods to know that something's up if a state was 
80-20 Democratic one cycle and then suddenly becomes 80-20 Republican 
(or vice versa) the next. Fraudsters could swing 45-55 results, but it 
doesn't completely demolish democracy, since the 60% (or whatever 
margin) results would presumably be left alone.


Fraud corrupts results, but it seems to me that fortunately we have some 
room to implement improvements that get us closer to verifiability 
without having the fraud that exists plunge the society directly into 
dictatorship.


New voting methods and improved fraud detection could also strengthen 
the prospects of each other. If you have an election method that 
supports multiple parties (since the dominant parties can't rig all the 
elections everywhere), then instead of only one other party, you have 
n-1 parties actively interested in keeping an eye on what rigging 
attempts do occur, and a lesser chance of entrenched forces colluding to 
ignore each other's attempts, since collusion among multiple entities 
become much harder as the number of entities grow.


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Re: [EM] PR favoring racial minorities

Predictions based on that idea would consider the ideal to be direct 
democracy. Next to that would be continuous update of representative 
power (continuous elections). While both of these might work if we 
were machines, the former scales badly and the latter would put an 
undue load on the voters unless they could decide whether to be part 
of any given readjustment.


I don't see the burden to voters as a big problem since the system 
allows some voters to follow and influence politics daily and some to 
react only on a yearly basis.


Hence the unless they could decide whether to be part of any given 
readjustment part. Irrespective of that, there's also the 
paradox-of-choice type load that one gets upon permitting voters to 
alter their decisions at any time, but perhaps the voters would get used 
to it and down-adjust the effort they exert at any given time, reasoning 
that if they elect wrongly, they can fix it at any later time.


(Continuous elections could also increase the level of participation in 
decision making in the sense that old votes could be valid for a long 
time even if the voter wouldn't bother to change the vote often. Well, 
on the other hand the votes must have some time/event limits after which 
they become invalid. Otherwise the system would e.g. make any changes in 
the party structure very unprofitable.)


Another option that presents itself is that of candidates handing over 
their power to their successors, but one should be very wary of 
unintended consequences if one makes power transferrable in 
non-transparent ways. Party list elections could just have the party 
instead of the candidates gain the power, but I think that would defeat 
some of the dynamic purpose of continuous elections, and possibly lead 
to pseudoparties whose only purpose is to shield the candidates from 
changes of opinion.


If we consider the case where decisions have effects that don't appear 
instantly, it gets more complex. For instance, democratic opinion 
could shift more quickly than the decisions made by one side has time 
to settle or actually do any difference. But even there, if we 
consider it an issue of feedback, we have parallels; in this case to 
oscillations or hunting, and to control theory regarding how to keep 
such oscillations from happening.


When thinking about the problems of continuous elections and direct 
democracy maybe the first problem in my mind is the possibility of too 
fast reactions. Populism might be a problem here. Let's say that the 
economy of a country is in bad shape and some party proposes to raise 
taxes to fix the problem. That could cause this party to quickly lose 
lots of support. These rather direct forms of democracy could be said to 
require the voters to be more mature than in some more indirect 
methods in the sense that the voters should understand the full picture 
and not only individual decisions that may sometimes even hurt them. In 
an indirect democracy painful decisions are typically not made just 
before the elections. This is not an ideal situation either. But all in 
all, the more direct forms of democracy seem attractive if the voters 
are mature enough.


From the feedback point of view, populism would be another form of 
overreaction or opinion shifting too quickly. Consider the tax case. For 
the sake of the argument, let's say that the tax raise is going to make 
things better in the long run. Then the problem is that the adjustment 
mechanism (the people using the election system) react too quickly. A 
common way of fixing this for ordinary feedback systems is to introduce 
smoothing. In a continuous election, this may take the shape of that, if 
you change your vote, the power given to the previous candidate slowly 
decreases while the power given to the new candidate slowly increases 
instead of happening immediately. This would take the edge off 
populism and other overreaction-related problems while avoiding the 
representative problem of don't do anything before the elections, 
since the elections can still be any day of the year, and a different 
day for different supporters of any given candidate.


Still, there are limits. When dealing with machine feedback loops, one 
usually has the luxury of being able to tune loop characteristics (such 
as the degree of smoothing, reaction to increasingly large changes, and 
so on) beforehad, which wouldn't be applicable for a political process 
since the situation of the world may change with time. Second, there's 
no sure way of knowing, ahead of time, whether the tax (in the example) 
really would benefit the society or not, at least not without being 
given more data; so smoothing could both harm and help, and knowing what 
level to set it to, even if we had a completely unbiased and trustworthy 
engineer to adjust the dynamics, seems to be a problem for which we 
can't even know whether any given answer is correct. It would be like 
setting the federal interest rate, yet more

Re: [EM] [Election-Methods] [english 94%] PRfavoringracialminorities

2008-08-18 Thread Kristofer Munsterhjelm


Juho wrote:


This is a very interesting real life example on how such horizontal 
preference orders may impact the elections and strategies in them.


Do you have a list of the strategies/tricks that are used?


One trick that appears, as has been mentioned in other posts here, is 
vote management. In vote management, parties aim to make voters vote for 
each party candidate so that the accumulated strength is nearly the 
same, minimizing the chance that any get lost or go to other candidates.


Schulze wrote about vote management strategies at [ 
http://m-schulze.webhop.net/schulze2.pdf ] as part of his STV method, 
which is intended to have vote management work only when to do otherwise 
would make the method fail Droop proportionality. I'm not completely 
sure if I've got it right, but I think it does it somewhat like DSV, by 
running vote managements for every voter so that manually doing a vote 
management confers no advantage.



I tend to favour counting exact proportionalities at national (=whole
election) level ((if one wants PR in the first place)).


One slight issue here is how to define proportionality.  It is implicitly
assumed that if a voter votes for a candidate, they also support the
candidate's party.  However, as can be seen with personal votes,
this is not always the case.


If candidates are seen as individuals then the rounding errors of such 
small units are typically higher than the rounding errors of big units 
like parties.


(What I was thinking was basically that if there is one quota of voters 
that have opinion X then the representative body could have one 
representative that has opinion X. This could apply to parties but also 
to smaller groupings and individuals as well as other criteria like 
regions (= regional proportionality) (and even representation of other 
orthogonal groups like women, age groups, religions, races if we want to 
make the system more complex).)


This is the idea that I've based my honest voter multiwinner 
comparison program on. With a party-neutral voting system, 
proportionality of individuals make no sense since there's only one 
individual - the only way to make that work would be to have weighted 
power in the assembly. Therefore, what is important is proportionality 
of opinion, if we assume that voters prefer those with opinions similar 
to their own to those with opinions less similar to their own.


If you want to make it even more abstract, you could say: if there's a 
method to how voters rank (or rate) candidates, and this method ranks 
candidates according to proximity of some standard of information, then 
the assembly should be proportional with regard to that standard of 
information.


Party-neutral methods like STV use no inputs other than the ballots 
themselves, so those have to infer the proximity or proportionality 
directly. In a way, party list cheats (or goes beyond the assumptions) 
because it lets voters give their opinions (on one axis - the party 
membership axis) directly. One could also make a system that similarly 
cheats by knowing the location of every representative and voter, 
minimizing the average distance, for each voter, to the closest 
representative. I think that would be unwieldy, though, and there'd be 
the issue of weighting (how much better/worse is a close representative 
that disagrees with you than a faraway representative that agrees with 
you?).


The extreme would be a voting system where people just say how much they 
agree with an opinion, for all relevant opinions, and then the system 
picks the maximally representative assembly. Such a method is not 
desirable, I think, because it would be very vulnerable to strategy, and 
someone would have to say which opinions were relevant and then redo 
the list when voters' priorities change and other opinions become 
relevant. In a simulation, one can do this easily because the voters 
vote mechanically (and so the what the opinion really is doesn't 
matter), but in the real world, not so much.



Another option is to allow a voter vote for local candidates and then
as their last choice, vote for a national list.


This is maybe yet one step more complex since now candidates can belong 
to different orthogonal groupings (several local parties; one party 
covers all local regions). Or maybe you meant to allow voting only 
individuals locally, not to support all local candidates of all parties 
as a group.



The local count would be standard PR-STV, but with the same quota
nationwide (and a rule that you must reach the quota to get elected).


Ok. National level proportionality could influence the election of the 
last candidates in the districts.



Unallocated seats would then be assigned using d'Hondt or similar
method based on the amount of votes transferred to the national list.

Also, it could be in effect an open list.  The person elected would be
from the district that transferred the most votes to the party's national
list.


Maybe all

Re: [EM] [Election-Methods] Re: final attempt for a strategy-free range voting variant, and another proportionally democratic method


Raph Frank wrote:

I had a similar though previously.

It was based on a legislature rather than individual voters.

I called it 'consumable votes'.
Here is one example, though there was a fair few versions.

http://listas.apesol.org/pipermail/election-methods-electorama.com/2006-March/017903.html


One problem of a straightforward every candidate gets p voting money 
units at the beginning of each block of time is that, on one hand, the 
situation may be serious enough that one needs to pass more than p 
units' worth. In that case, we'll have a problem. On the other hand, it 
may be a calm time, in which case less than p units are used, which 
would also be a problem except if there's a ceiling to how many voting 
units one can hold. But if there's a ceiling, it may inspire frantic 
voting near the end of the block of time so as not to waste the voting 
units. A better solution to that would be to, if there are q days, 
supply p/q (subject to ceiling) every day, or p/(q*24*60) every minute.


That still leaves the former problem, though. Reweighting would escape 
it, but the relation to voting money (which is easy to understand) would 
be somewhat obscure. In order to prevent dictatorship of the rich, the 
weights would then be reset, for all candidates, to one at the beginning 
of each period, or for a continuous variant, the differences would be 
smoothed out at a certain rate so that it goes towards equality.


Voting-money or legislative consumable votes/reweighting values might 
also give a back-and-forth effect, but I'm not sure how serious that is. 
One can observe the oscillation in two-party states, where the first 
party spends a lot of its time undoing what the second party passed in 
the previous period. Then the second party is elected later on and uses 
its time tearing down the efforts of the first party. That's really 
wasteful. At least your supermajority clause would help keep this from 
happening.


I suppose one possible way of making an intuitive reweighting system is 
to allow legislators to go into the red as far as they want, but that 
the decision is checked by others. Thus the opposition could cancel a 
proposal if they've used less voting money in the past, no matter how 
much each side has used. There might be unintuitive consequences, 
though; for one, it won't have the incentive (on all parties) not to 
vote any more than they have to.



 My thoughts were to have accounts decay and each voter
would be given a fixed income. This also handles the effect of new
citizens becoming adults and also elections if it is for a legislature.
However, that creates deflation (or at least encourages 'spending now').


Adding up to a ceiling would mitigate this somewhat; as long as the 
current amount isn't close to the ceiling, there's no incentive to spend 
it now. However, when it gets close, the incentive returns.



b) Can voting money really be considered a form of money, and can we
expect it to be linear in individual utilities? My hope is that this is
so because the virtual money is only used to buy immediate voting
power and pay with potential later voting power. I think it would not be
necessary that utilities be comparable between different persons. Just
the utilities some fixed person assigns to options in the decision at
hand need be comparable to utilities the same person assigns to options
in a later decision.


It has the advantage that everyone has equal access to it.
This would eliminate the complaint that people with higher
wealth would end up controlling the process.

It might even be constitutional despite the ban on poll taxes.

Depending on your view of utility, it could be considered
just as valid as any other distribution.

However, there could be complaints since people can lose
their voting power.  In fact, since in nearly all cases, there would
be no change to vote totals and then suddenly, a large
chunk of people would lose some of their votes and thus
power, there could be major complaints (or riots).  Also,
they would have little expectation of increasing their totals again
as it would be a while before another change to the totals.

I think in practice, it would just be treated like a range voting
election and thus changing account totals is like reweighting
people's votes.


It seems to be not only like reweighting, but simply another form of 
reweighting. Well, that depends on how it's used. If it's used to pay 
for a decision, then it's indirect reweighting, but if it's used to 
reduce the strength of votes, then it's direct reweighting.



Finally, with a national election, it is unlikely that the results
would be accurate to a single vote, so even if it was balanced,
a recount would probably change things.


c) How would the exchange rate of this virtual money be established?


I don't think it should be transferable, or otherwise, you
might as well just use normal money.

If you do want it to be exchangable, then just let the
market decide.


I agree,

Re: [EM] PR favoring racial minorities


Juho wrote:

On Aug 18, 2008, at 12:10 , Kristofer Munsterhjelm wrote:

The extreme would be a voting system where people just say how much 
they agree with an opinion, for all relevant opinions, and then the 
system picks the maximally representative assembly. Such a method is 
not desirable, I think, because it would be very vulnerable to 
strategy, and someone would have to say which opinions were relevant 
and then redo the list when voters' priorities change and other 
opinions become relevant. In a simulation, one can do this easily 
because the voters vote mechanically (and so the what the opinion 
really is doesn't matter), but in the real world, not so much.


In principle STV allows (especially if ties are allowed) voters to 
determine any sets of candidates (without requiring someone to fix them 
beforehand). Voters may e.g. list all female candidates. It is also 
possible that any number of such group definitions would be available. 
Candidates could indicate themselves which opinions they support, and 
voters could include references to those lists in their ballot. Also 
opinions created by others than candidates themselves could be 
available. The lists could freely overlap. Someone could vote e.g. Women 
(1st priority), candidates that indicate that they support election 
reform (2nd priority) and candidates that were listed by the election 
reform society (3rd priority). An STV like ballot would be derived from 
this information.


To a limit, yes. But say that you prefer women and leftists. Also assume 
that there are some women who are leftists, some leftists that are not 
women, and some that are both. Then you'd rank those who were both above 
either of the two.


In my simulation, a voter who preferred women and leftists would rank 
male leftists and right-wing women randomly with respect to each other. 
In reality there could be different preferences among those. The point 
is that no concatenation of two lists would produce the correct result. 
If the list is by political ideology, then it could rank men on the left 
ahead of women, and if it was by gender, then it could rank right-wing 
women ahead of left-wing ones.


A tree could solve this, but it'd get increasingly more complex for 
numerous opinions. The complexity is probably a true issue - that is, 
not an artifact of the system - and one may wonder if voters would 
compare candidates on all issues in order to figure out a true 
consistent ballot (even for a party-neutral system). I have no data for 
that, so my simulation assumes the voters do so, since that taxes the 
proportional representation of the method more than if the voters didn't.


That sounds like MMP. I think MMP can work if done right (with STV 
instead of FPTP as base, and reweighting to avoid lista civetta). 
Using party list here is probably better than the party-neutral 
version where you'd rank representatives for local, regional, and 
national levels, and then it keeps the reweighting at each stage; 
simply because there would be an immense number of candidates at the 
national level, and ranking them all would be Herculean.


MMP style is also one option, although I was still thinking of methods 
where all representatives are of the same type. The method would in that 
case have to force the districts to elect so that also election wide 
balance is maintained.


What would the method look like, so that a voter could specify (for 
instance) women ahead of men on both a local and national scale? The 
only thing that seems to work is candidate ranking on both the local and 
national level, which would take a lot of time and produce extremely 
long ballot papers.


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Re: [EM] Why We Shouldn't Count Votes with Machines


Dave Ketchum wrote:
You claim that many fragments can be done by specialized machines. 
AGREED, though I do not agree that they can do it any better than a 
normal computer - which has equivalent capability.


In a technical capacity, of course not. Since a computer is 
Turing-complete, it can do anything the specialized machines can. 
However, and this is the point I've been trying to make, the specialized 
machines are simple enough that it's possible to formally prove that 
they do only what they're intended to do, and perhaps also to convince 
the voters that this is the case.


It's kind of like the difference between physics and mathematics. Doing 
tests is analogous to the hypothesis testing of physics: you can say 
that this particular machine does not exhibit any flaws that would 
compromise security, within some margin of error. However, if the 
machines are sufficiently simple, then one can use formal proving to 
show, mathematically, that there are no bugs; that the Condorcet counter 
will turn ballot records into Condorcet matrices and no more - that the 
machine with buttons on it will register votes, register them to the 
candidate shown on the display, and no more, and so on.


Now, the analogy is not total. Even a correct hardware system could be 
compromised by vendors adding backdoors to their fabrication (going 
outside of the spec) and so on, but those errors are much harder to 
conceal than simple software tinkering. Even if the software is open 
source (as you've stated that you want), knowing the full limits of the 
hardware keeps hackers out. The more complex the OS, the greater the 
chance that there's a bug: even Linux has had privilege escalation bugs, 
although they appear much less frequently than in closed-source 
software. What I'm saying here is that if you have to have machines, 
have a way of saying to, first, the experts that there is no way there 
can be an error, and second (if possible), the same to the ordinary 
voters as well.



However, the whole task involves connecting the fragments:
 One way is via computer capability.
 You seem to be doing without such, so What do you have other than 
humans HOPEFULLY correctly following a HOPEFULLY correct and complete 
script?


That's right - the links are the weak spots. The script can be devised 
just as any programming can be, and it would be quite simple, and 
ideally reminiscent of what one does when having a manual count regime. 
The PROMs or CDs are the ballot boxes, and they're transported from one 
location to another as one would ballot boxes.


That leaves the humans. The humans may do weird things, and the ensured 
limits that the specialized hardware would have would obviously not 
apply to them. But since the script is simple, various parties can 
monitor each other. In the worst case, the transportation and 
aggregation parts of the process are as insecure as they would be for 
manual ballots.
If that is still too risky, the ballot boxes could be numbered and 
digitally signed prior to being distributed to the machines for writing, 
so that if any are lost or replaced, it would immediately show up as an 
error. Such a process would add steps to the script, but I think it'd be 
managable.


Consider a general computer. Even for general computers, it makes 
little sense to have the district joining software - that counts the 
results from various districts and sum them up in the case of a 
summable method - on the individual units. As such, the 
general-purpose computers are already specialized, only in software 
instead of hardware.


???


That was simply intended to show that you don't need the full powers of 
a computer. It's convenient, but that convenience can tilt in the favor 
of manipulators or hackers as well.


That's true. Maybe a compromise could be using cheap computer hardware 
with read-only software, standardized components, and have the 
software not be a full OS, but instead just enough to get the job done 
and be provable. You'd have to rely on that there are no hardware 
backdoors, but the existence of such would be very unlikely, and the 
entire thing would have to be put inside some sort of tamper-resistant 
enclosure so hackers can't attach keyloggers or do similar things.


Hardware backdoors can be hard to find.  Still, if and when one is 
found, can there not be an appropriate punishment to discourage such 
crimes in the future?


Agreed defense against such as keyloggers is essential.

I still say OPEN SOURCE!


I was thinking more of hardware keyloggers, such as those that look like 
keyboard extension cords. Thus the computer should be tamper resistant 
so you can't just do these things. Ideally, for the cheap computer 
compromise, you'd use a cryptoprocessor (like banks use to keep their 
keys, but more general purpose) to run the actual software - perhaps an 
IBM 4758, though since I'm not a hardware expert I don't know if that 
one is sufficiently powerful to do what

Re: [EM] [Election-Methods] [english 94%] PRfavoringracialminorities


Juho wrote:

I could accept also methods where the voting power of each 
representative is different. The good part is that such a parliament 
would reflect the wishes of the voters more accurately than a parliament 
where all the representatives have the same voting power. Maybe one 
could force the voting power of different candidates within some agreed 
range. That could be done by cutting only the power of the strongest 
representatives and forwarding their excess votes to the nearest group 
(or as indicated by the STV ballots).


Having different amounts of voting power would simplify multiwinner 
election systems considerably. One could, for instance, just do a FPTP 
count and then elect the n highest scoring, giving them voting power 
equal to the share of the total vote they got.


Still, that doesn't happen, and no assembly is set up that way. Why? 
Does it seem too unfair?


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Re: [EM] Why We Shouldn't Count Votes with Machines


Kathy Dopp wrote:

On Thu, Aug 21, 2008 at 10:00 PM, Dave Ketchum [EMAIL PROTECTED] wrote:


First, this is not intended to be used in a zillion precincts - just to
validate the programs.


OK. Well if you don't care about validating the election outcome
accuracy, and just want to verify the small amount of programs on
voting machines that pertain to voting, then you could do parallel
(Election Day) sampling of memory cards (memory cards unbelievably
have  today interpreted code on them on most voting systems) like
the University of CT engineering dept. has designed for checking the
voting code on CT's voting systems.


That's bad design. The election machine shouldn't have code that can be 
simply replaced by switching memory cards. The code should be loaded at 
some time prior to the election and then locked in, and the machine 
should verify that it's the right code, perhaps by checking a digital 
signature. Anything less is, well, just bad.


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Re: [EM] PR favoring racial minorities


Raph Frank wrote:

On 8/22/08, Juho [EMAIL PROTECTED] wrote:

 In Finland where the number of candidates is relatively high some less
obvious candidates may have some trouble getting in to the lists but on the
other hand some well known figures (that have become popular (and respected)
in other areas than politics) tend to get offers from multiple parties to
join their lists (even as an independent candidate on their list, without
becoming formally a party member).


Would they be expected to vote with the party if they do end up getting elected?
Is the theory that they will pull in more than 1 seat's worth of
votes, so it is worth
having them on the list no matter what they do?

Under PR-STV, the whole vote management thing means that parties cannot
just let their candidates run completely independent campaigns and also that
the number of candidates run must be controlled based on tactical
considerations.


Fortunately, that isn't a limitation to party-neutral multiwinner 
methods in general - not any more than single-winner strategic 
nomination due to a method failing independence of clones is a 
limitation of single-winner methods in general.


If I understand Schulze's STV method correctly, it calculates vote 
management strengths and so does vote management on behalf of the voter 
and on all candidates. I may be wrong, though, and Schulze STV uses a 
very large amount of memory for elections with many candidates and 
winners. Still, it shows the possibility of having a method that resists 
vote management.


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Re: [EM] PR favoring racial minorities

2008-08-24 Thread Kristofer Munsterhjelm


Raph Frank wrote:

On 8/22/08, Kristofer Munsterhjelm [EMAIL PROTECTED] wrote:

 What I had in mind was something like this: Say there's a single-winner
election where the plurality winner has 35% support. Then those voters
effectively got 0.5 (+1) worth of the vote with only 0.35 mass. The total
voting power of the entire electorate should not be altered.


Well, they actually got 1 constituency's worth of voting power at
parliament for 35% of the vote in the constituency.  This is just
fundamentally unfair and the problem cannot really be eliminated
while also allowing independents to run.

If there are no independents, then the problem pretty much goes
away.


 Thus

 pA (unscaled) = 0.35/0.5 = 0.7
 pB (unscaled) = 1.3

 For the sake of the example, consider the case of 1000 votes. Then the
scaling factor is x, so that 0.7 * x * 350 + 1.3 * x * 650 = 1000. x is then
about 0.918, so the voters for the winner now have voting power 0.6426 and
all the other voters have voting power 1.1934.


This would mean that if a candidate had 55% support, his voters would
have their voting power boosted (though, I guess in that case, there would
be no change).  It still has the problem that the constituency gets a non-party
candidate and also its voters get to vote for a party.


In MMP, party voters also get to elect a candidate and also contribute 
to the national level (to the extent that the total constituency result 
is disproportionate). The reasoning would then go that even a voter that 
elects a nominal independent may have a preference for a certain party 
(the party that is closest to the views of the independent). Thus the 
system should treat the vote as if it was a vote for the party in 
question, if it has to treat the vote as a party vote in the first 
place, and it should do so in order that all voters have equal power 
(influencing both local and national levels).


As for fairness, consider the case where more than just enough voters 
voted for candidate X. With your you either get full strength or no 
strength scheme, some voters are going to look at the result and say 
hey, my vote wasn't required yet I have no power. This means my vote 
was wasted, so I'm going to be more careful later. To some extent, this 
unfairness observation would exist in all the cases where some voters' 
votes were unneeded, but at least with continuous reweighting you get 
the counter that your vote did in fact have an effect, in that all the 
others who shared your preference for the independent got more of a say 
in the national round. That's about the best you can do for the 
single-seat local election, since you can't transfer votes when there's 
only one seat.



I think fairer might be to just exclude the voters who voted for the
independent from consideration at the party level (if the independent
is elected for the constituency.)
They have already obtained 1 full seats worth of representation for
1/3 of a seat's worth of votes, there is no point in also giving them
more representation by including them in the party allocation. Voters
who voted for other independents or party members would still be included.


I can see two points of view here. The first is that they got more than 
their share by the extent that they were less than a majority, and the 
second is that they got more than their share by the extent that they 
didn't represent every voter. In either case, I think that there should 
be a continuous function, but the point of view matters when considering 
how much power should be retained in contrast to those who didn't get 
anything at all (that is, whose candidate lost).


Looking at it again, the point of view that it should be with respect to 
100% is probably better than the one that it should be with respect to a 
majority. Consider the case where's there unanimity towards which 
candidate should win. Then I think the right way to treat that is as if 
no votes had been cast at all, rather than to give those who unanimously 
decided to elect the constituency candidate double power in contrast to 
those who did not vote (or a hypothetical voter that'd only vote in the 
national election, if that was possible).



Another option is to have a reasonable number of top up seats.  If 1/3 of
the seats were top-up seats, then 2/3 of a constituency would be enough
to be entitled to a seat.  This would mean that independents would be
able to archive a quota in 1 constituency.  They would have to obtain 2/3
of the votes to be eligible for election.


If you run the national and local election as a single STV election, I 
think you could get the result where many national candidates get a 
quota and outcrowd the various regional candidates, even if those got 
close to a quota. The problem here is that a local plus national 
election has a subset constraint (on number of local and national 
candidates) which a plain STV election doesn't have.


Or to put it differently, in a general case. Say that you have

Re: [EM] PR favoring racial minorities


Raph Frank wrote:

On 8/22/08, Kristofer Munsterhjelm [EMAIL PROTECTED] wrote:

 If I understand Schulze's STV method correctly, it calculates vote
management strengths and so does vote management on behalf of the voter and
on all candidates. I may be wrong, though, and Schulze STV uses a very large
amount of memory for elections with many candidates and winners. Still, it
shows the possibility of having a method that resists vote management.


That is interesting.  I have had a look at his paper, but
the method itself seems pretty complex.

Is there a simple/basic explanation of the method?


You would have to ask Schulze that. I don't know of any, at least.


- capturing a greater proportion of personal votes for the party

Any surplus of a candidate who easily reaches
quota will be a mix of personal and party votes.
Thus some of the votes that went to a party member
will end up being transferred away.

If less party supporters vote for the candidate, then
they can be used at full strength for other party members.
This means that that the party gets better use of the personal
vote of the member.

This is the vote management version of Hylland free
riding.  Party voters are en mass downgrading their
top choice as he is likely to get elected anyway.

Meek's method solves the first problem by adjusting the quota
and CPO-STV solves the 2nd problem by not eliminating anyone.
The 3rd one like Hylland free-riding on an individual level is
very hard to fix.  (Schulze aims for equality of effect rather than
trying to eliminate it).


If it turns out that we can't get rid of Hylland free-riding, then 
equality of effect might be the best thing to have: while it degrades 
the performance of the method, hopefully it won't degrade it too much, 
and it'll keep the dynamics from going in the wrong direction of 
encouraging party centralization.



Meek's method also solves Woodall free-riding, though I'm not
sure if there is a vote management method that takes advantage
of it.  A party would need to flood the constituency with 'no-hope'
candidates so there is enough of them for all of their supporters
to vote for.  That might be a little to obvious, but it could work.


Schulze considered the case with write-in candidates. Obscure write-ins 
are pretty much ensured not to win, and could be used as Woodall 
free-riding dummies. He then checked an STV election where write-ins 
were permitted (the city council of Cambridge, MA), but found no obvious 
evidence of Woodall free-riding.


See the free-riding section of http://m-schulze.webhop.net/schulze2.pdf .


None of your party's supporter's votes would be wasted electing
candidates for other parties who get elected on the first count.


At least not until the other parties do the same. The absurd result 
would be an STV election with thousands of candidates, none of which can 
win, getting eliminated at the start of the election before the real 
candidates appear.


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Re: [EM] PR favoring racial minorities


Raph Frank wrote:

On Sun, Aug 24, 2008 at 8:03 PM, Kristofer Munsterhjelm
[EMAIL PROTECTED] wrote:

As for fairness, consider the case where more than just enough voters
voted for candidate X. With your you either get full strength or no
strength scheme, some voters are going to look at the result and say hey,
my vote wasn't required yet I have no power. This means my vote was wasted,
so I'm going to be more careful later.


With a result like

A: 40%
B: 30%
C: 20%
D: 10%

Each voter for A could still be weighted as

(VA - VB)/VA = (40-30)/40 = 0.25

as only 75% of each of their votes was required to win the constituency.

Under plurality, you don't even need a majority, you just need to beat
the 2nd best candidate.


That could work, since additional votes for A increase the weighting, 
meaning that a vote for A isn't wasted even if A wins.



I can see two points of view here. The first is that they got more than
their share by the extent that they were less than a majority, and the
second is that they got more than their share by the extent that they didn't
represent every voter. In either case, I think that there should be a
continuous function, but the point of view matters when considering how much
power should be retained in contrast to those who didn't get anything at all
(that is, whose candidate lost).


I don't think there is a really a way to square this.  If a party had
51% of every constituency, they could guarantee that they win 100% of
the seats.


Let's look at that case, with two parties. Call them A and B. A wins 51% 
of every constituency, and that this amounts to 51 votes (thousand 
votes, whatever) out of 100. Then if there are as many top-up seats as 
there are ordinary seats, nearly all of the latter should go to B. Since 
there are two parties, by the reweighting above, the A voters would have 
strength (51-49)/51 = about 0.04. If there are 90 constituencies and 
thus 90 list seats, and all the A voters vote for A, nationally, as 
well, they'll have 51 * 90 * 0.04 = 183.60 votes worth. Meanwhile, the B 
voters have 49 * 90 = 4410 votes worth. The total is 183.60+4410 = 
4593.60, so A gets round(p * 183.60/4593.60) and B gets round(p * 
4410/4593.60) with p chosen so that the sum is 90. This turns out to be 
p = 90, A gets 4 seats and B gets 86 seats.


In total, A has 94 seats and B has 90. 94 out of 180 is 51.1% which 
isn't too bad, considering A had 51% support everywhere.


So reweighting seems to work, at least in this case. If there are fewer 
top-up seats than constituency seats, the equation would have to be 
adjusted.



I think maybe my issue is that constituencies which elect party
candidates are 'playing fair'.  The candidate that they elected gets
added to the party total and thus has an effect on the national level
seats.  A constituency which elects an independent elects an
independent, but that has no effect on the number of seats affecting
each party and yet they still get to decide how the party
proportionality is decided.  This ensures national proportionality and
then they get to add their independent representative on top of that.
This shifts the legislature in the direction of the constituency in
question.


Instead of a party point of view, how about an opinion point of view? 
The voters for independents also have opinions, and so their opinion 
should affect the national level (as it would explicitly if this was a 
national election). As mentioned earlier, the voters that vote for an 
independent would probably vote for the party closest to the point of 
view of that independent if they have to vote for a party. As such, the 
shift in national influence is not an artifact, since the voters do have 
the corresponding opinion. With a good normalization system (reweighting 
or quota-based), the shift won't be very large if the independent 
actually got elected, but it'll exist -- ideally to the extent that 
there was a surplus.



Looking at it again, the point of view that it should be with respect to
100% is probably better than the one that it should be with respect to a
majority. Consider the case where's there unanimity towards which candidate
should win. Then I think the right way to treat that is as if no votes had
been cast at all, rather than to give those who unanimously decided to elect
the constituency candidate double power in contrast to those who did not
vote (or a hypothetical voter that'd only vote in the national election, if
that was possible).


Right, to allow them participate in the national vote would give them
double power.

However, it depends on how many additional seats are being used.  If
1/3 of the seats were national seats, then their votes should still be
counted but at a reduced weighting.

The voters in each constituency elect 1 and 1/3 of the seats, that
means that if a district elects an independent locally, then their
votes should count but with a weight of 1/4 of the votes in other
constituencies.


Seems that we're

Re: [EM] PR favoring racial minorities


Juho wrote:

On Aug 24, 2008, at 1:34 , James Gilmour wrote:


Juho   Sent: Saturday, August 23, 2008 9:56 PM

Trying to guarantee proportionality for women at national level may
be tricky if there is no woman party that the candidates and voters
could name (well, the sex of a candidate is typically known, but that
is a special case).


I think you need to define what you mean by proportionality for women 
at national level.  Do you mean numbers of representatives
proportional to the numbers of women among the registered electors 
(typically 52%), or among the voters (women frequently
predominate), or do you mean proportional to the extent that the 
voters wish to be represented by women?  These criteria are all
quite different, and none of them is the usual 50:50 that is commonly 
called for.


I treated women just as a random example of voter indicated preference 
to favour some set of candidates.


(This was Kristofer Munsterhjelm's example. I hope he thought the same 
way. This example group has also the other problem that we know which of 
the candidates are women, but I think this is not intended to limit the 
example either. = Just random sets of candidates.)


It can be treated as either. Some properties, like whether a candidate 
is a woman, can be objectively ascertained. Others, like opinion, can't 
be determined as readily - all we have for opinion is what the 
candidates actually say, as well as their past history, and there's no 
mechanism that can say yes, he truly believes this in contrast to no, 
he's only saying it because that's what the voters want to hear.


Reading my past posts, I intended woman to be just another binary 
property, but in some other branches of this thread, I've also 
considered methods that use the objective verification property of 
being a woman (to balance assemblies if that is desired).



And why should there be guaranteed proportionality for women?


In this example, just because that can be derived from the ballots cast, 
no other reasons (although of course there could be in some other 
elections).



  The logical corollary is guaranteed proportionality for men.


This was not intentional. Since I assumed this to be a random group this 
just indicated a requirement to guarantee that at least indicated number 
of women should be elected (and said nothing about the non-women). In 
practice this may lead to proportional representation of non-women too 
but I didn't consider that to be that to be a requirement.


Depending on some method treats this kind of freely defined sets, it is 
also possible that only 10% of the voters would indicate support to 
women. This should not be taken to mean that the proportion of women 
should be limited to 10% since many voters may be neutral with respect 
to this particular opinion.


I was going to say that it'd seem, from a binary point of view, that 
valuing proportionality x of those in a given set implies valuing 
proportionality (1-x) of those not in the set. But the binary point of 
view is wrong. As you say, many people would have no particular interest 
in which way the distribution goes. A variant of the argument may still 
apply, though. If 10% really want women candidates and 90% don't care, 
then having 11% or 9% would be equally bad (presumably) from the point 
of view of the 90% of the voters that don't care. Therefore, it's not 
critical that there are 10% women candidates. The slack will be more 
taut in the less-than direction (because the women-prefering voters 
would have no problem with a superproportional allocation of women), but 
it wouldn't be absolute since the other 90% don't seem to care, making 
this a less important issue than if, say, 20% preferred women, 10% men, 
and the other 80% had no opinion.


That is true, but such ranking is currently so unusual that I think it 
would be a fair assumption.


Yes, a good guess, but there could be also situations where e.g. some 
district has high concentration of members of some racial group and most 
candidates are from that group. Ranking only members of that group 
should in this case not be taken as an indication to support all the 
members of this group at national level and in all ideological opinion 
groups.


A better estimate would be whether more candidates of a certain group 
are elected than one would expect from a random sample of the community 
or district in question. Even that isn't foolproof, because there may be 
some properties that people who desire to be a part of the political 
process (i.e. candidates) tend to have with greater frequency than those 
who don't.


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Re: [EM] PR favoring racial minorities


Juho wrote:

On Aug 22, 2008, at 12:36 , Kristofer Munsterhjelm wrote:

Juho wrote:

On Aug 18, 2008, at 12:10 , Kristofer Munsterhjelm wrote:


If we are taking about methods that rank the candidates the idea is to 
define a grammar and terminology so that the most common voter opinions 
(orderings or approximations of them) can be expressed using short 
expressions. Bullet votes and tree inheritance is one (very compact) 
option. Giving a complete ordering of the candidates is another 
(complete) option.




That's a good point. Voters probably wouldn't like to rank tens of 
candidates from tens of parties, so to the extent that it would not 
confuse the voters or make the ballot papers too long, there should be 
shortcuts for the most common patterns of voting.


Those shortcuts could be party list, party tree, a ranked ballot on 
parties rather than candidates, or something similar, with an override 
space for the first few preferences (since that's where most of the 
strength lies).


However, the way the ballot's formatted is going to have some influence 
on the voters simply by what it shows to be the path of least 
resistance. The STV ballots in Australia (that are used as a curious 
form of party list by most voters) provide a good, if extreme, example 
of this. In my opinion, parties shouldn't be given a boost or gain an 
advantage for free just because they are parties - this is part of the 
reason that I prefer party-neutral multiwinner methods. Thus one would 
have to be careful when designing the ballot format so that, on one 
hand, the ballots are not too arduous to complete, but on the other, 
they don't obstruct voters that want to submit personal votes.


How such a ballot would be constructed, I don't know. The parameters 
required (how susceptible the voters are to shortcuts, etc) can't be 
arrived at by mere deduction; they depend on the nature of the voters.


For small districts, a ranked ballot like the one used in Ireland is 
probably sufficient. You pay for it by not being able to ensure national 
proportionality by party. The next step up (in fidelity and complexity) 
is the you have two votes form that accompany systems which try to 
correct the disproportionality on the national level.


If the various formats (list, tree, truncated personal vote) should be 
shortcuts rather than the only way to vote, then one needs to use a 
method, or one of a class, that can understand all the formats. I think 
that party-neutral multiwinner systems make up that class of methods. 
The exception is correcting party disproportionality, which it can't do 
by itself.


On the other hand, if you want list (or tree or whatnot) to be the only 
way to fill out the ballot, then you don't need anything as complex as 
PR-STV.


  In order to guarantee proportionality (of any imaginable grouping) at
national level we may need to allow the voters to rank all candidates 
nation wide (as you noted). The next question then is if we allow the 
voters of one district to have a say on which candidates will be elected 
in the other districts. If we allow that then we could simply arrange a 
national level STV election with some further tricks. The trick could be 
e.g. to refuse to nominate any candidates from some district after the 
agreed number of candidates has been elected from that district. (This 
was just one quickly drafted option.)


Another trick related to one that I've referred to before is this: give 
each voter an additional fractional vote where the candidates are ranked 
in order of distance from the voter. Continuous districting, if you 
want. The fraction depends on how much you want locality to matter. 
You'd also have to link the two votes' weight somehow, otherwise it just 
becomes minisum distance, which isn't what we want.


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Re: [EM] PR favoring racial minorities

2008-08-26 Thread Kristofer Munsterhjelm


Juho wrote:

On Aug 26, 2008, at 1:20 , Raph Frank wrote:


Each candidate can register in any number of polling stations covering
at most N seat's worth of population.  (N=5 might be reasonable).


You might want to keep the sizes of the registered areas of each 
candidate about equal (or to balance the situation in some other way).


Well, since we're already talking about logistics-heavy methods, how 
about this: Take the location of the candidate (his home). Then order 
the polling stations by distance from that location. Find the number p 
at which the circle given by the radius drawn from the candidate's home 
to polling station #p on the sorted list (closer first) encompasses more 
than N seats worth of population. Then the candidate is listed on the 
ballot in polling stations 1 to (p-1) on the sorted list, inclusive.


If the politicians have any influence in where the polling stations are 
placed, they would want to put them more or less evenly so that if, for 
instance, all polling stations are to the North of a candidate, one 
would add some to the South too, to get on more ballots.


Strategic house buying would be funny! Perhaps parties would have 
candidate houses, all of which are carefully located so as to maximize 
the effect, and new candidates are given one of them to stay in for as 
long as he's a candidate.


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[EM] A very simple quota method based on Bucklin

2008-08-26 Thread Kristofer Munsterhjelm

As the subject says, this is a very simple multiwinner method that's 
based on Bucklin. I referred to it in another post, and so I think I 
should explain how it works:


Inputs are ranked ballots. Each voter starts with a weight of one. The 
quota is Droop (Hare does much worse).


As in Bucklin, start counting first place votes, then second place, and 
so on. Equal ranks may either count as one vote for each, or as a 
fractional vote for each.


At some point, the counts of one candidate will exceed the quota. That 
candidate is elected. If more than one are above quota, pick the one who 
has the most votes. If they're still tied, break by the first round 
where their numbers differed. If they're still tied, break the tie based 
on a single-winner method, or flip a coin, or somesuch.


For all of those voters that voted for the winner, reweight their 
weights by (new weight = old weight * (votes for winner - quota)/(votes 
for winner)).
Don't alter the quota, but in all other respects, restart the election 
with the winner removed from all ballots, as if he never entered. Keep 
on doing this until enough candidates have been elected.


That's it. For the single-winner case, the method reduces to Bucklin, 
which is monotonic. I'm not sure if the method is monotonic in the 
multiwinner case as well, but I think so.


According to my simulation, the method isn't as proportional as STV.

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Re: [EM] PR favoring racial minorities

2008-08-26 Thread Kristofer Munsterhjelm


Raph Frank wrote:

That's fine.  In fact, if you had 50% local and 50% national seats,
then it can be made to work perfectly.

Just say that an independent must get at least 50% of the constituency
to be elected and if he does, each of his voters have their weights
reduced to

(VA-50%)/100% where VA is his percentage vote share

This gives perfect proportionality.

In effect, it 'costs' 50% of a constituency to win a seat, and the
independent has managed it and so gets a seat.  The candidate's
supporters 'spend' enough votes to elect the candidate and the rest go
to the national count.

IRV could even be used to make it a little fairer to possibly push a
candidate over the 50% mark.  (Exhausted ballots wouldn't affect the
quota, so 50% would be a true majority).  Any ballots which end up
with the independent would be de-weighted if he is elected.  This
would mean that voters would be advised not to rank independents that
they don't actually want to get elected.

Or one could use STV instead, and have more local seats. If I'm not 
wrong, the 50% mark of maximum disenfranchisement would be lowered 
significantly by STV, so fewer list seats would be required.



If there were 50 top-up and 100 local, then the A party would get 100
and the B party would be assigned all of the top-up seats.


Ah, I see now. No amount of reweighting would handle that case for FPTP 
because the 100 seats are already elected. As I said in the other post, 
the logical thing to do at this point is to start deweighting 
A-victories, although the A-voters would complain. In this two-party 
case, this results in a problem, however, since exactly 51 out of 100 
voted for A in every district. Thus, deweighting A would do nothing 
until a certain point where A loses all its seats and B gains them. The 
right thing would be that A retains some of the seats while B gets the 
rest, violating the constituency preferences only enough to get 
proportionality. But if all districts are equal in preferences (51 out 
of 100 for A), then which should get their preferences overridden? That 
would be done either randomly or by ignoring neutrality - for instance 
by picking based on geographical properties so that the overridden 
constituencies are as evenly distributed as possible.



Under some rules, the number of top-up seats can depend on the results
of the election.

One rule is that all parties must get at least 1 seat assigned.  An
independent on 50% of a district wouldn't get assigned any seats until
the number of national and local seats was equal.

Another option would be saying that if any independent gets elected,
the number of top-up seats must be equal to the number local seats.

A less severe version would be to activate the rule if more than x%
(say 5%) of the legislature are independents.  This would still cause
slight imbalances, but shouldn't be major.  It would also prevent a
major party using the decoy list strategy as if they did, it would
trigger the rule and thus cancel out the effect, as there would be
enough seats to completely compensate.


In general, one should be careful with a variable size assembly, since 
the size can go beyond all reason if the disproportionality is driven to 
be severe enough.


Decoy lists don't have to be on independents, though. The strategy that 
was used in Italy was that they had constituency parties and list 
parties. Voters would elect the constituency party for the constituency 
and the list party for the top-up. Because there were no list proportion 
for the constituency party, it could not be balanced in that direction, 
nor could it be balanced in the list direction because nobody voted for 
the list party in any constituency.


Schulze's STV-MMP method suggests that, in this case (party overhang), 
some voters who voted for party A in the constituency and party B for 
the lists, are set so that a fraction of their list votes go to A instead.



My issues is that there are 2 types of candidates

- party candidates

If a party candidate wins a seat, they get 100% of the representation
for that constituency.  However, this is compensated by the fact that
they count as 1 seat won for the party.

This votes budget for that district is

Winner won a local seat
+ 1 local seat for the party

Winner counts as a party member
- 1 national seat for the party

All party votes added to party list totals as normal (1 person, 1 vote = fair)

By assigning the seat to the local winner, the winner's party loses a
seat at the national level, so it is neutral.

- independents

Winner won a seat
+1 seat for the independent

Candidate doesn't count as a member of any party
No effect on national vote

All party votes added to party list as normal (1 person, 1 vote)

Here, despite the winner winning a seat, all of his supporters still
get full effect at the national level.

Even if their votes were not eligible for the national count, it still
isn't fair as it hasn't cancelled a full seats worth of votes.


I

Re: [EM] PRfavoringracialminorities

2008-08-27 Thread Kristofer Munsterhjelm

Raph Frank wrote:

On 8/26/08, Kristofer Munsterhjelm [EMAIL PROTECTED] wrote:

No, it uses logarithmic and exponential functions to find the divisor
that corrects the bias that arises with certain assumptions about the
distribution of voters. See
http://rangevoting.org/NewAppo.html . Warren
refers to states and total population, but it works for parties as well
- the state population is the number of voters that voted for the
party in question, and the total population is the total number of
voters -- or for scored single-winner methods, the score for the party
and the total score, respectively.

Ahh, I think I had read that page before.

Anyway, his conclusion is that his parameter should be set to
d=0.495211255149063832...

Webster's sets d to 0.5, so I think that would be easier to use that.

The difference is thus pretty slight and thus the benefit (if any) is
also pretty low.

True. I just gave it as an option for the perfectionists who aren't
satisfied with Webster, or for the case where the election system is so
complex that adding the calculation wouldn't be noticed in theg rand
scheme of things (and where every little bit helps).

Yes. In the same vein, for single-winner methods, a NOTA that actually
does something is preferrable to one that has no influence apart from
showing that people dislike all the candidates.

Yeah. It could be argued that it is a leave the seat vacant/hold
another election vote.

With IRV, it could even be a ranked option.

You can rank NOTA as your lowest option.

In the last round, if the winner doesn't have a majority including
NOTA votes, then the election is declared to have failed and a new one
called or the office left vacant.

For any ranked method, you could have a new election option, being
shorthand for I'd rather have a new election with the status quo going
on in the meantime, than elect any of those listed below this option.
Then, in the social ordering, if this option ranks first, there's a new
election (and all the candidates of the previous election are barred
from participating in the next one). If it doesn't rank first, whoever
wins wins.

For multiwinner elections, you could either redo the entire election, or
if one of the seats go to new election, give those who were elected
prior to this their seats and then elect the remaining seats anew. The
latter option would be very complex, however, because you'd make sure
that it retains proportionality. The obvious way to do so is to retain
weights, but then you have to match those up with the voters, and doing
that while keeping the secret ballot secret would be very difficult indeed.

If we can fix the adjustment for multiple seats, it could be used with
methods that don't reduce to IRV or other nonmonotonic single-winner
methods. Reweighted Range Voting is monotonic, as are all additively
reweighted methods based on monotonic single-winner methods. However, these
don't do very well in my simulation - the best one is reweighted
plurality, which is just plurality, or in other words, SNTV.

RRV still would need the local constituencies to announce a complex
list of results. To work out the winner, you need to know how many
voters voted A, B, C ... and also A+B, A+C, A+D, B+C ... and so on
(and that is assuming everyone votes approval style).

Actually, it is even more complex, I think for RRV you might need the
individual ballot list.

Almost all party-neutral proportional representation methods are
nonsummable. I say almost all because Warren claims that Forest solved
this (that is, made a summable PR method), but I don't have the
rangevoting.org password and I don't want to join, at least not yet.

What I found of Forest discussing summability in 2007 was this:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-April/020081.html
. It seems to say, in essence, that since voters first k preferences are
what count (for some small k), you can store them and average out the
rest to make standard ballots that won't lose much from reality.

I think this may be iffy; there are no hard rules for how much
proportionality you lose, and if there are more than k seats, the
averaging could upset things.

The only way to get transfers to work would be if there was a very
simple way to handle them.

I really don't like PR-SNTV, but it would work.

It works *if* all parties run what is in essence vote management: they
have to divide votes so that no allied candidate gets too many nor too
few votes. The same careful allocation has to happen within each party,
and this can encourage hierarchical systems where those high up
apportion votes in the direction of a candidate in return for the
candidate allying with the higher levels (both inside and outside of
parties).

But at least it's proportional if parties do this. Majoritarian Borda or
Condorcet (elect the first n in the social ordering) isn't even that.

Another, possibly better

Re: [EM] A very simple quota method based on Bucklin

2008-08-27 Thread Kristofer Munsterhjelm


Raph Frank wrote:

On 8/26/08, Kristofer Munsterhjelm [EMAIL PROTECTED] wrote:

 Inputs are ranked ballots. Each voter starts with a weight of one. The
quota is Droop (Hare does much worse).


Can a voter skip ranks and also is there a limited number of ranks?

If you allow rank skipping, then a voter can distinguish between

ABC
and
ABC

E.g.
A:1
B:2
C:10

and

A:1
B:9
C:10

In the second case, the voter will only compromise and vote for B if A
can't get elected even after 9 rounds.




In fact, the notation could include the number of skipped ranks

AB

This means
A:1
B:4

i.e.

A(empty)(empty)B


That would cause exhaustion. Here's an example with six candidates, 
single winner.


10: AD
10: BE
10: CF

The quota is 50% + 1, or 16. However, none of the candidates get more 
than 10 votes.


If the ballots are fully specified, then by pigeonhole, once all ranks 
have been included, each candidate must have got one vote per voter. 
Thus some candidate will be above quota.


One could perhaps fix this by equal-ranking all remaining candidates 
last, below any specified rank.



 For all of those voters that voted for the winner, reweight their weights
by (new weight = old weight * (votes for winner - quota)/(votes for
winner)).
 Don't alter the quota, but in all other respects, restart the election with
the winner removed from all ballots, as if he never entered. Keep on doing
this until enough candidates have been elected.


It might be worth recalculating the quota based on exhausted ballots.
Otherwise, your method might end without electing enough candidates.

You can just recalculate the Droop quota using the new seat total and
the reweighted number of votes.

For example, assuming 100 voters and 4 seats

Q = 100/(4+1) = 20

After round 1, your reweigting will decrease the effective number of
ballots by 20 and seats to 3.  This has no effect on the quota
(assuming no exhausted ballots)

Q = 80/(3+1) = 20

This means that you can just keep recalculating the quota to take
account of exhausted ballots.


It should have no effect on ballots that aren't exhausted, since the 
reweighting reduces the nominator by a quota, and the election of a seat 
reduces the denominator by one, thus canceling out.


Say there are k votes for the winner, and all weights are 1. The quota 
is Q  k. Then the sum of the new weights is k * (k - Q) / k. Cancel out 
the  factor of k and we get (k-Q). Call the number of those who didn't 
vote for the winner r. Then the quota was (r + k)/(numseats + 1). 
Afterwards, we have


(r + k - Q) / (numseats),

which has reduced the numerator by a quota, and the denominator by one, 
which was what we wanted.



Another option for weightings is to weight each ballot at

w = 1/(candidates elected + 1)

If the ballot was voting for a candidate who gets elected, its
'candidates elected' count goes up by 1.

This also achieves proportionality.  It works like proportional approval voting.


Does that pass Droop proportionality? It looks like D'Hondt.


 That's it. For the single-winner case, the method reduces to Bucklin, which
is monotonic. I'm not sure if the method is monotonic in the multiwinner
case as well, but I think so.

 According to my simulation, the method isn't as proportional as STV.


What does this mean?  It looks like the method meets Droop
proportionality, so should be proportional.


It means that if voters and candidates have binary opinion profiles and 
vote in order of Hamming distance (number of opinions where they 
disagree) to each candidate, ranking those with greater Hamming distance 
lower and breaking ties randomly, then the difference of the proportion 
that hold the yes stance on some issue or issues in the assembly 
differ more from that proportion in the population, on average, than 
would be the case for an assembly elected using STV.


The simulation shows different scores even among methods that satisfy 
Droop proportionality. QPQ does best, then STV, then this.



If sims are showing non-proportional effects, it probably means that
votes are 'bleeding' over into other parties.

If I vote

A1A2B1

I could end up helping party B get seats instead of my favourite
party.  A better vote (from my point of view) would be

A1A2

This means none of my vote bleeds over into party B.


That makes sense. Bucklin passes Later-no-help while failing 
Later-no-harm, thus producing an incentive to truncate ballots. IRV (and 
thus STV) passes both, but pays for it by being nonmonotonic.


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Re: [EM] PR favoring racial minorities

2008-08-28 Thread Kristofer Munsterhjelm


Juho wrote:
Yes, security might force us to use simpler solutions like ballots to be 
similar, votes to be shorter (e.g. only two or three rankings allowed), 
and even to reduce the number of candidates. The latter two 
simplifications are already vote buying / coercion oriented.


Security might also force us to more complex solutions like having 
districts to limit the number of available candidates. Otherwise the 
voter might be asked to vote for some candidate from the other side of 
the country that nobody is expected to vote.


One more approach to semi-computerized voting. A computer displays the 
personal alternatives and then prints a ballot. This solution hides the 
personalized nature of the ballot and still avoids the problem of voter 
voting for candidates that he/she should not vote.


One could augment the semi-computerized voting by making it print all 
candidates, but randomly order (last behind all others) the ones that 
are not applicable to the districts. Then the ballots would have to be 
examined more closely in order to figure out what house is its center.


That's not to say it would make it impervious to such attacks: the 
random ordering might easily have ...  DistantCommunistA  
DistantRightWingerA  DistantCommunistB  ... because the randomizer 
doesn't know (and can't know) what's reasonable. Filling out the 
random-last with a Markov simulation of other ballots would be more 
reasonable, but that'd require a postprocessing step and it might mess 
with the proportionality, so I don't think that would be worth it.


However we look at it, we return to the problem that ranked ballots can 
be fingerprinted. The only solution I can see for that is to have a 
summable system and add the individual ballot in matrix (or array) 
format instead of ballot format. But most PR methods are not summable! 
Are there other ways of preventing ranked ballot fingerprinting?


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Re: [EM] PR favoring racial minorities

2008-08-28 Thread Kristofer Munsterhjelm


Juho wrote:
The idea of an appropriate size circle around candidates home (or home 
district) sounds like a pretty safe and simple approach. That gives also 
the voters a natural explanation to why some of the familiar candidates 
are on the list and some not.


Dynamic districts may also be seen to fix something important. If the 
district borders are considered artificial the circle based approach 
moves the borders further away, and as a result also the problem of 
artificial borders (in the sense that one can not vote for and be 
represented by one's neighbour) may mostly fade away.


One more approach to this would be to provide perfect continuous 
geographical proportionality. One would guarantee political and 
geographical proportionality at the same time. One would try to minimize 
the distance to the closest representative from each voter and make the 
number of represented voters equal to all representatives. In short, 
distribution of representatives would be close to the distribution of 
the voters (while still maintaining also political proportionality).


There would, of course, be limits to the guarantee of having both 
political and geographical proportionality at the same time. If your 
immediate vicinity have candidates whose opinion you completely disagree 
with, one of geographical proportionality and political proportionality 
will have to sacrifice part of itself for the other. As I've said 
before, in that case I think political proportionality is more 
important. In the long run, the effect might self-stabilize, if for no 
other reason that if there are many Y-ists in an area, one of them is 
going to notice and want to become a candidate.


I'm not quite sure how to do perfectly continuous geographical 
proportionality. My two linked ballots idea would probably work, but I 
think we can do better by using the distance information directly. Just 
how, though, I'm not sure.


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Re: [EM] Geographically proportional ballots

2008-08-29 Thread Kristofer Munsterhjelm


Juho wrote:

On Aug 28, 2008, at 11:36 , Kristofer Munsterhjelm wrote:

One more approach to semi-computerized voting. A computer displays 
the personal alternatives and then prints a ballot. This solution 
hides the personalized nature of the ballot and still avoids the 
problem of voter voting for candidates that he/she should not vote.


One could augment the semi-computerized voting by making it print all 
candidates


That could be thousands, so maybe a subset in many cases.


Just enough to hide the data. One could print out to the nearest 
candidate that's, say, a tenth of the population away from the voter.


Here I say that a candidate is N voters away from a voter if it's not 
possible to make a compact region that includes both the voter and the 
candidate, yet has fewer than N voters in it. For simplicity, the region 
might be a circle.


, but randomly order (last behind all others) the ones that are not 
applicable to the districts.


I guess one would need to know the district (or the person if the 
candidate lists are personal) to decipher the vote in the calculation 
process. That information could help also the malicious readers. Or did 
you mean that the random data would be part of the vote but would be 
just noise since different ballots would cancel the effect of each others.


The latter. The idea is to append a ballot with noise so that a voter 
that votes A  B  C  rest, with the first of the rest being (randomly) 
D cannot be distinguished from a voter somewhat closer to A, B, C, and 
D, voting A  B  C  D  rest, except probabilistically with a 
resolution too low to discern individual voters.


Voter would have also have to trust that the printed ballot is what it 
should be.


True, that's a problem, and it's not even possible to know whether the 
printed ballot has some hidden information in it. For instance, the 
voting machine might have been tampered with so that it encodes a 
timestamp (or copy of the first few ranked votes) into the random-last 
votes, encrypted so that it's indistinguishable from the noise a good 
random process would produce.


The technique that I proposed above would work best with bullet votes 
(e.g. with open lists). Also short votes (that list only few candidates) 
are quite ok (some risk if one votes for the most distant candidates in 
all directions).


Yes; and also large virtual districts.

However we look at it, we return to the problem that ranked ballots 
can be fingerprinted. The only solution I can see for that is to have 
a summable system and add the individual ballot in matrix (or array) 
format instead of ballot format. But most PR methods are not summable! 
Are there other ways of preventing ranked ballot fingerprinting?


One could break a Condorcet ballot ABC to separate pairwise 
preferences AB, AC and BC (is this what you meant with the matrix 
format?). If there are also many other candidates (tied at bottom) one 
could use e.g. A*, B*, C*, cancel BA, cancel CA, cancel CB. That 
information could be derived also from a more understandable (= easier 
for the voter to check) set of opinion fragments A, B, C, AB, AC, BC.


That's what I mean, but not restricted to Condorcet matrices. If you 
want to use the ballot data for any sort of positional system (as well 
as those where the positional scores change over time, like Bucklin), 
you'd use an n*n matrix where candidate[0] is the number of times the 
candidate got first place, candidate[1] is the number of times the 
candidate got second place, and so on. Counting a particular positional 
rule requires only an array (one-dimensional matrix), and so on; but all 
of this is made all that more difficult by that no PR method I know of 
is summable without doing quantization on the ballots (like Forest's 
patch does).


I don't know how to capture that formally - perhaps that I know of no 
summable party-neutral PR method that's responsive, if I understand 
responsivity correctly (if there's a tie in the social order, a single 
vote must always be able to resolve that tie). But even that doesn't 
quite get it, for say that some candidate ranked (n+1)th in the 
quantization method has a tie with another. Then a ballot that ranks 
this candidate first would be accepted and resolve the tie (assuming the 
underlying method is responsive, too).


IRV ballots are trickier. Raph Frank already mentioned the idea of 
truncation and combination of this with candidate given preference lists.


An interesting corollary of this is that if the quantization method is 
acceptable, then the IRV is not summable complaints can be effectively 
countered. Just apply the patch to IRV and then you can sum up the ballots.


If you allow me I'd like to advertise trees once more. Trees (= 
hierarchical open lists) can be seen as very truncated ranked votes. 
Bullet vote to one candidate is inherited by his/her nearest group and 
so on. When the tree is formed one can expect all common thinking 
patterns to get

Re: [EM] PRfavoringracialminorities

2008-08-29 Thread Kristofer Munsterhjelm

Raph Frank wrote:

On Wed, Aug 27, 2008 at 7:59 PM, Kristofer Munsterhjelm
[EMAIL PROTECTED] wrote:

True. I just gave it as an option for the perfectionists who aren't
satisfied with Webster, or for the case where the election system is so
complex that adding the calculation wouldn't be noticed in theg rand scheme
of things (and where every little bit helps).

Someone would probably call you on it :). You would have to justify
what the particular method is best.

Well, yes, but I meant something like that if you're switching from Meek
(numerical solution for nonlinear systems) to an election system with a
divisor component, then a single exponential equation might seem simple
in comparison. Of course you would have to explain it, but the society
would already be used to the idea that voting systems may have to be
complex to give good results, and thus would accept it (if they accepted
the explanation, or trusted those who accepted the explanation) more
readily than those who were not used to that.

For any ranked method, you could have a new election option, being
shorthand for I'd rather have a new election with the status quo going on
in the meantime, than elect any of those listed below this option. Then, in
the social ordering, if this option ranks first, there's a new election (and
all the candidates of the previous election are barred from participating in
the next one). If it doesn't rank first, whoever wins wins.

Well, I guess it depends on the method. However, if it was IRV, I
think there is a reasonable case for making the NOTA option not be
subject to elimination.

For multiwinner elections, you could either redo the entire election, or if
one of the seats go to new election, give those who were elected prior to
this their seats and then elect the remaining seats anew. The latter option
would be very complex, however, because you'd make sure that it retains
proportionality. The obvious way to do so is to retain weights, but then you
have to match those up with the voters, and doing that while keeping the
secret ballot secret would be very difficult indeed.

One option is to use Asset voting for that situation.

Your vote can designate a named candidate as responsible for voting
for you if a NOTA option wins a seat.

This might be a separate column. You rank the candidates in one
column and then mark one of them as your NOTA delegate.

That could work. However, the NOTA list would have to be longer than the
ordinary list, I think, because in situations where NOTA ranks first,
that means that the candidates below NOTA are not considered good
enough, and thus by implication would not be considered good enough to
give one's vote (as an asset) to. The same argument, if weakened, could
be used where all but one is below NOTA - presumably only those who gave
the above-NOTA candidate the asset vote would consider him good enough,
and so all those who gave below-NOTA candidates the asset would be left
out in the cold.

What I found of Forest discussing summability in 2007 was this:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-April/020081.html
. It seems to say, in essence, that since voters first k preferences are
what count (for some small k), you can store them and average out the rest
to make standard ballots that won't lose much from reality.

I think this may be iffy; there are no hard rules for how much
proportionality you lose, and if there are more than k seats, the averaging
could upset things.

Hmm, this looks like a more general case. However, I think you would
maintain proportionality as long as you meet the Droop criteria.

If all voters from a group vote for their candidate first choice, then
they are guaranteed a seat (assuming the group has a Droop quota).

The only effect is on lower rankings.

One issue is that if a party expects to get more than 3 seats, then
there could be issues. However, even then it mightn't be a major
problem.

Abuse would require that the abusers vote 1,2,3 for the party and then
try to mess up their 4th rank. I think that this is likely to
increase the number of votes received by that faction rather than
decrease it.

I don't even think it needs to be malicious. If voters have sufficiently
many opinions they compare the candidates on, that might cause honest
differences in the 4th rank and below. Averaging, by necessity, throws
away some of this data.

I really don't like PR-SNTV, but it would work.

It works *if* all parties run what is in essence vote management:

Yes. However, vote management strips voters of their power to choose.
They can't bottom rank a disliked party candidate (without the party
losing a seat).

True, and I don't think you could make a summable SNTV DSV method.

The election system here in Norway is somewhat like this. In the national
election, you vote for a party (closed list PR). For each district,
candidates are allocated to the parliament according

Re: [EM] A computationally feasible method (algorithmic redistricting)

2008-09-01 Thread Kristofer Munsterhjelm


Michael Rouse wrote:


There was a discussion of district-drawing algorithms on the 
election-methods list a few years back. I've always thought that taking 
centroidal Voronoi cells with equal populations was an elegant way to do 
it. Here's an example of standard Voronoi cells and the centroidal 
version I pulled off of Google:

http://www.mrl.nyu.edu/~ajsecord/npar2002/html/stipples-node2.html


To find the district centers (centroids), you have to do what's 
effectively vector quantization. The voters make up the points, and you 
want to choose n codebook points so that the average distance to the 
closest codebook point, for all points, is minimized.


To my knowledge, optimal vector quantization is NP-hard. The good news 
is that there are approximation methods that have proven worst-case time 
complexity. However, they'll not give you the absolutely best possible 
arrangement.


One such algorithm is described here: 
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.3529


A simpler algorithm, though one that doesn't give any worst-case bounds, 
is Lloyd's algorithm. Start with random center points, then calculate 
the centroids for the current Voronoi cells. Move the center points 
towards the centroid (shifting the Voronoi cell somewhat) and repeat. Do 
so until they settle. This can get stuck in a local optimum.


The other possibility I liked was allowing voters to vote for the 
districts they wanted -- either for the next election, or more 
entertainingly, the current one. People have a pretty good feel for what 
mapping is compact and reasonable, and which ones are ridiculous, 
especially if they can compare them. You could have certain criteria 
that must be met -- like all districts must be contiguous  -- and sort 
the maps by some metric, like from shortest to longest aggregate 
perimeter. You could have all qualifying parties submit a map, as well 
as any group that gets above a certain number of signatures in a petition.


Those maps could be pruned so that only the Pareto front remains. That 
is, if there's some map that's worse on all metrics with regards to some 
other map, then that first map isn't included. As long as there are 
enough metrics to give a reasonable choice on the Pareto front, this 
should exclude the worst of the gerrymandered proposals and keep the 
voters from being swamped with millions of frivolous proposals.


I don't think it's necessary to make it that complex, though. If you 
favor actual people doing the final choice, an independent commission 
(like the redistribution commissions of Canada and Australia) could make 
the choice of which nondominated map to use.


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Re: [EM] language/framing quibble

2008-09-01 Thread Kristofer Munsterhjelm


rob brown wrote:
On Mon, Sep 1, 2008 at 3:20 AM, Kristofer Munsterhjelm 
[EMAIL PROTECTED] mailto:[EMAIL PROTECTED] wrote:


Consider Condorcet. One of the greater problems with plurality is
vote-splitting, which favors minorities since it destroys a center
that many think is good but only a few think is great. Thus,
adopting Condorcet would help the majority, not minorities at the
expense of the majority, ...

 
First, I think you are misusing the words majority and minority here 
(as is common).  Personally I think they have no meaning unless there 
are only two candidates (and there were never any other potential 
candidates).


I'd say that one could generalize the above to coalitions. Then a method 
favors a majority if it gives more power to a coalition supported by a 
majority, and favors a minority if it gives more power to a coalition 
supported by a minority.


One example I would use to argue that Plurality can swing in the 
direction of a minority is the 1987 South Korean election. The two 
democratic groups split the vote, giving the election to the general who 
supported an earlier coup.


I'll grant that if we use your definition, that example isn't applicable 
- since there were three parties in all.


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Re: [EM] Geographically proportional ballots

2008-09-02 Thread Kristofer Munsterhjelm


Juho wrote:

On Aug 29, 2008, at 15:51 , Kristofer Munsterhjelm wrote:

One more approach to semi-computerized voting. A computer displays 
the personal alternatives and then prints a ballot. This solution 
hides the personalized nature of the ballot and still avoids the 
problem of voter voting for candidates that he/she should not vote.


One could augment the semi-computerized voting by making it print 
all candidates

That could be thousands, so maybe a subset in many cases.


Just enough to hide the data. One could print out to the nearest 
candidate that's, say, a tenth of the population away from the voter.


Here I say that a candidate is N voters away from a voter if it's not 
possible to make a compact region that includes both the voter and the 
candidate, yet has fewer than N voters in it. For simplicity, the 
region might be a circle.


One should maybe avoid the possibility of someone deriving the location 
of the voter based on the distribution of all the candidates on the 
ballot. (Also picking fully random candidates may reveal the location 
since there will be one concentration of nearby candidates.)


This could happen if the voter has a compact region significantly 
different from the rest. For instance, vote-buyers may (theoretically) 
advertise that they're just in range to candidate x, so that x will be 
on his ballot whereas x won't be on all the others in his region.


But if that's not the case, then the only way your deduction will work 
is statistically, and when doing so, it'll be hard to separate a single 
person from the rest of the mass you know is in the close vicinity. If 
you tell A to rank yourself in first place, and you then find out that 
one of the ballots from this area has yourself in first place, you still 
don't know if it's A or not (absent intentional ballot fingerprinting by 
the voter).


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Re: [EM] A computationally feasible method (algorithmic redistricting)


Raph Frank wrote:

On Tue, Sep 2, 2008 at 11:00 PM, Kristofer Munsterhjelm
[EMAIL PROTECTED] wrote:

The reasonable thing to use would be Euclidean distance, since that makes
sense, given the geometric nature of the districting problem. If you want to
be even more accurate, you can use great circle distance instead to reflect
that the districts are on the (near-)spherical Earth, but at the scales
involved, the difference would be slight (and so it would be another
dotting the i-s refinement :-)


My splitline software used a sphere (and gnomonic projection for the
lines).  However, I think it wasn't necessary, but wanted it to be as
accurate as possible.

OTOH, I think that it might be better to define the map as a 2d map
using Mercator projection.  The problem with the sphere is that each
point is a real number.

If the data is presented as (longitude, latitude), then the numbers
that are input into the algorithm are rational numbers as they are
given with a certain number of digits after the decimal point.  This
allows an exact solution to be found.  However, with reals, different
precisions could give different answers.  Also, if there is a tie, it
may not be possible to determine that one occurs.  This is less of a
problem if a specific algorithm for determining the result is used.

I think splitline can be solved exactly if the map is 2-d and all
coordinates in the input data are rational numbers.


If you use a Mercator projected map, you're just hiding the 
quantization. All maps have some distortion, and since the map 
projection uses trigonometric functions, you can just use the Haversine 
distance directly. If you need the precision and an exact measurement of 
error, you could use a rational number class with sine and cosine 
approximation tables (or Taylor series), but I think real error like the 
Earth not being perfectly spherical will get you before the rounding 
errors do.



Back to to the Voronoi diagrams, I think you may have misunderstood
what I meant.

The issue here is that ordinarily, it doesn't matter what power you use.

If you colour each pixel the colour of the nearest point, then you get
a standard Voronoi  diagram.

Likewise, if you say that you colour each pixel the colour of the
point with the lowest (distance)^2, then you get the same diagram.

If you square all the distances, then the lowest distance is still the lowest.

All cells will have straight lines as their edges.

However, if I say that you should colour the pixel the colour of the
nearest point, but that the distance to point 1 is to be decreased by
100km, then you would expect that the cell with point 1 as its centre
would be increased in size as some pixels which went to other cells,
would now go to point 1's cell (as its distance has been decreased).

If you look at the results, then you would see that cell 1 no longer
has straight lines as its boundary.

Now, if instead, you assign the pixels to the cell with the nearest
distance squared and apply an offset to point 1, then you still
maintain straight line edges.

Also, it has the nice feature that you can work out the square distance as

(x0-x1)^2 + (y0-y1)^2 + Cn

You save a square root which takes a long time to calculate.


I see. I thought you were talking about how to calculate the distance in 
the first place. Since squaring and square roots are monotonic, if you 
have squared distance = (x0-x1)^2 + (y0-y1)^2, picking the maximum or 
minimum distance would be the same as picking the maximum or minimum 
squared distance. Weighting would differ, of course, as you note.


Power diagrams on Euclidean distance are still convex polyhedra, though, 
to my knowledge.



That last one might be ideal for districting.  It would allow a city
to be a circle which surrounded by a rural district.


The surrounding district would score pretty badly on the all-pairs 
distance measure, and also on a similar convexity measure (given as the 
probability of the line between two random points being entirely inside 
the district, or where it is outside of the district, being so only over 
water or outside of the state).



For example, if you had a State with 2 cities and 3 seats, it might be
best to split the state into 2 circle districts centred on the cities
and 1 rural district which is everyone else.

Most other methods can't handle having one district as an island
contained in another.


If it's best, the earlier measures are not adequate to discover it.


Also note that it's possible to find the borders of the Voronoi cells (for
the Euclidean metric, at least) much quicker than doing a nearest-neighbor
search on every single pixel. Quantization brought on by the varying sizes
of census blocks may complicate matters, though.


Yeah, most of the automatic methods assume that the 'population' is
uniform density.

What is nice about the reweighted version is that you can expand and
contract a region without having to move the points.

If you increase a region's weight

Re: [EM] Using gerrymandering to achive PR


Raph Frank wrote:

1) Every odd year, an 'election' is held but voters vote for parties

2) based 1), seats are distributed using d'Hondt between the parties


If you're going to have D'Hondt, or PR in general, why bother with the 
districting? Just use open list or a party-neutral proportional 
representation method like STV.


It's not impossible to introduce STV; it has been used in many places in 
the US, like New York's experiment with PR from 1937 to 1945. What seems 
to be more difficult is to keep PR in the face of compounding opposition 
from the established parties (though in the aforementioned New York 
case, they got a lot of help from the Cold War situation along with the 
election of Communists; they could then link communism and PR).



Also, if a party cannot be gerrymandered any seats, maybe it should be
eliminated, to allow its supporters votes to be useful.

Another question, would it be illegal to restrict candidates so that
they must come from the designated party?  This would allow each party
to run 2 candidates in their district, thus improving choice.


I suppose that if you want to steer democracy, you could redistrict so 
that a certain fraction (changing for each election) have narrow 
margins. The question would be one of stability on one hand and 
responsive changes on the other (analogous to feedback damping), but 
again, who's to say where the optimum is? That is, if one should steer 
democracy in the first place.


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Re: [EM] Free riding


Jonathan Lundell wrote:

On Sep 3, 2008, at 12:28 AM, Juho wrote:

I hope this speculation provided something useful. And I hope I got 
the Meek's method dynamics right.


Meek completely fixes Woodall free riding. That strategy takes advantage 
of the fact that most STV methods (to the extent we're in a STV/Meek/etc 
context) are sensitive to elimination order in how they distribute 
surpluses. In most other STV methods, if I vote for my first and second 
preferences AB first, and A has a surplus, then only a fraction of my 
vote (or a probabilistic whole) transfers to B. But if I rank hopeless 
candidate Z first: ZAB, then (hopefully) A gets elected before Z is 
eliminated, and my whole vote goes to B. If Z gets eliminated first, no 
harm done, I'm left with AB. The hazard, of course, is that so many 
voters do this that Z gets elected and/or AB eliminated.


Meek cures this entirely via its principle that when Z is eliminated, 
the ballots are counted *as if Z had never run*. There's no advantage to 
me in ranking Z first.


In general then, any method that acts like Z had never run (when Z is 
eliminated) would be resistant to Woodall free-riding.


Hylland is another kettle of fish. Here, I vote BA instead of my sincere 
AB, because I know that A will be elected without my help, and I can 
afford to spend my entire vote on B.


This is only useful, of course, if I'm competing with other A supporters 
who have some second choice, say AC voters. They will have only a 
fraction of their votes transfer to C, while I will have my entire vote 
counted for B because I didn't bother to rank A first, even though A is 
my first choice (I'd better be very confident).



There's a risk to the Hylland strategy, of course, if I make a mistake 
in judging that A will be elected without my help. Other than that, 
though, I don't offhand see a way of defending against Hylland free riding.


Hmm.. what could be done here? We could try to find out methods that 
resist Hylland free-riding, or find methods where there are few honest 
reasons to use the vote management version.


For the latter, I think PR methods that deal with equally ranked 
candidates as if they were symmetrically completed would have an 
advantage. For a party that expects very few personal votes, equal 
ranking would spread the voting power to a much larger extent than they 
could by running a vote management strategy. For instance, for a 6 
candidate case, there's no way the party could arrange 720 different 
pseudo-bailiwicks. Hopefully, parties that say don't equal rank would 
appear dishonest. There's nothing stopping them from doing so, 
technically, though, and the equal-rank property would make it easier 
for those who actually want to do vote management to do so, as they can 
get the majority to equal rank and then just have a small subgroup vote 
opposite the ordering of the personal voters.


For the former, I think that Approval methods would have some inherent 
safety against this (simply because you can't reorder the candidates). I 
might be wrong (I don't know enough about it), since Plurality doesn't 
let you reorder the candidates either, but SNTV basically requires 
vote-management to work at all.


One could also have a PR method that uses relative information about the 
ranking of strong winners as little as possible. Schulze's STV is one 
example of such a method. Perhaps one could make a method based on DSC 
or DAC in a similar vein (but not PSC-CLE, it scores badly in my 
simulations), since DAC/DSC works based on sets of candidates.


A final option would be to have a method where either not running a vote 
management scheme is a stable equilibrium, or where the risks when 
performing vote management are too high. The latter would probably deter 
individual voters more than parties, since parties can coordinate; but 
parties can't perfectly manage votes either.


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Re: [EM] A computationally feasible method (algorithmic redistricting)


Brian Olson wrote:


I guess my time in Computer Science land has left me pretty comfortable 
with the idea that there are lots of problems that are too hard to ever 
reliably get the best solution. I don't know if there's a short-short 
popularizing explanation of how finding a good solution is Hard while 
measuring the quality of a solution is pretty quick.


If anybody asks and it's not the time, place, or audience for discussing 
NP Hard problems, I will wave my hands and say, Hey, look over there! 
Good results, on my one puny computer! With more it'd only get better!


I think puzzles and games make good examples of NP-hard problems. 
Sokoban is PSPACE-complete, and it's not that difficult to show people 
that there are puzzles (like ciphers) where you know if a solution is 
right, but it takes effort to find the solution. That's pretty much the 
point of a puzzle, after all (although not all puzzles are NP-hard; they 
can be fun even if they're not, as long as they do something for which 
it's challenging to find a solution).


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Re: [EM] Free riding

2008-09-04 Thread Kristofer Munsterhjelm


Raph Frank wrote:

On Wed, Sep 3, 2008 at 10:51 PM, Kristofer Munsterhjelm
[EMAIL PROTECTED] wrote:

In general then, any method that acts like Z had never run (when Z is
eliminated) would be resistant to Woodall free-riding.


Right, you can get that benefit from alot of methods.  For example,
you could do hand counted PR-STV with the following changes

- restart the count if someone is eliminated (excluding them from consideration)
- the quota is recalculated at each restart

This gets almost all the benefit from Meek's method.


At the risk of sounding repetitive, I'll say that this is what the 
multi-round tweak to QPQ does. Whenever someone's eliminated, that 
candidate is permanently excluded, and then the method starts from the 
beginning. Presumably it too would be resistant to Woodall free-riding. 
I don't know if the single-round method is as well.



Hmm.. what could be done here? We could try to find out methods that resist
Hylland free-riding, or find methods where there are few honest reasons to
use the vote management version.


Ultimately, the problem is that you cannot meet Droop proportionality
without allowing it to some extent.


The next best thing is what Schulze calls weak invulnerability to 
Hylland free-riding. A method passes WIHFR if it's vulnerable to 
Hylland free-riding only if to not be so would make it violate Droop 
proportionality.


(He then proves an equivalent condition, but the notation is a bit too 
heavy for me to parse. It seems to be if voters reorder strong winners, 
then the outcome should not change, where a strong winner is in all 
stable sets, a stable set being a multiwinner generalization of the 
Smith set.)



For instance, for a 6 candidate case, there's no way the party
could arrange 720 different pseudo-bailiwicks.


I can't imagine them trying in that case, they likely to just try to
manage first choice vote management.  Maybe, more seats would protect
against vote management.


There's one way they could slip this under the radar. The party could 
say that they want all voters to vote A1  A2  A3 instead of A1 = A2 = 
A3, ostensibly to perform the same function as list ordering does in 
party list PR. Then, once the people have become used to not using 
equal-ranking, the party can spice it up by vote-managing.



There's nothing stopping them
from doing so, technically, though, and the equal-rank property would make
it easier for those who actually want to do vote management to do so, as
they can get the majority to equal rank and then just have a small subgroup
vote opposite the ordering of the personal voters.


I think if voters were aware of it, they may react by not giving
personal votes to that party.


Yes. From one point of view, vote-management based on Hylland 
free-riding uses the strength of personal votes to prop up a collective 
(party) ordering that would otherwise collapse. This can be seen by that 
if there are no personal votes, everybody votes by party, and the party 
is indifferent to which candidates within their party actually gets 
their seats, then equal-ranking would have no disadvantages.



For the former, I think that Approval methods would have some inherent
safety against this (simply because you can't reorder the candidates).


You mean proportional approval voting ?

I think that has strategy issues too.


Not necessarily PAV, but a method that's based on Approval and would 
otherwise be as good as STV, if such a beast exists. What kind of 
strategy can be used in PAV?



Schulze's STV is one
example of such a method. Perhaps one could make a method based on DSC or
DAC in a similar vein (but not PSC-CLE, it scores badly in my simulations),
since DAC/DSC works based on sets of candidates.


I wonder if a range ballot would be useful.  The algorithm then
optimally converts it into a ranked ballot.

For example,

1) Each voter submits a range ballot
2) Each voter's algorithm votes for 1 candidate
3) Vote totals are published
4) Repeat step 2,3 say 200 times

Each candidate's score is the sum of votes received in the last 100 rounds.

This allows voters decide if they want to risk it.  If their favourite
is ahead, they might decide to stop voting for him.  However, if they
have rated him much higher than 2nd, they might continue to vote for
that candidate.

I am not sure what algorithms to use in 2), one option is to allow
voters to pick.


Allowing voters to pick the candidate to vote for would be very tedious; 
the algorithm would have to run 200 rounds of voting. If this was a 
single-winner method, you could have used a cardinal ratings (range) 
equivalent of approval strategy A, but I'm not sure how you'd make a 
multiwinner version of that.


More generally, this could be considered DSV. Within the category of 
DSV, one cuold probably make a method that vote-manages on behalf of all 
voters more effectively than any party can. I thought Schulze STV did 
that (because of its mention of strength of vote managements

Re: [EM] language/framing quibble

2008-09-04 Thread Kristofer Munsterhjelm


Fred Gohlke wrote:

Good Afternoon, Kristofer Munsterhjelm

Thank you for your thoughtful comments.  I understand and agree with you 
on plurality and two-party dominion, and their off-shoots, 
gerrymandering and the various forms of corruption.  The difference 
between our views seems to be the focus on finding a 'better way' to 
count votes when (in my opinion) the real problems are the 'who' and the 
'what' we vote for.  Until we enable the people, themselves, to select 
who and what they will vote for, changing the way the votes are counted 
is an exercise in futility.


Although you didn't specifically say so, I take it you do not consider 
the political duopoly right.  Neither do I.  But neither do I see 
wisdom in fragmentation ... replacing the duopoly with a multitude of 
smaller factions ... because it bypasses the vital step of studying the 
nature of partisanship and how it came to dominate politics, right here 
in the birthplace of 'The Noble Experiment':


   When the Founders of the American Republic wrote the U.S.
Constitution in 1787, they did not envision a role for
political parties in the governmental order.  Indeed, they
sought through various constitutional arrangements such as
separation of powers, checks and balances, federalism, and
indirect election of the president by an electoral college to
insulate the new republic from political parties and factions.
Professor John F. Bibby[1]


You are right in your assumption: I do not consider the political 
duopoly right. On the other hand, I don't consider better election 
methods to be mere tweaks. The construction of organizations and their 
interplay in the domain of politics is, I think, more than anything else 
a process. The process is influenced by both external and internal 
constraints: what weakens and what strengthens.


A plurality system serves as a constraint that gives voice to the two 
most likely choices and consequently silences the rest. However noble 
minor parties or groups may be, there is no way that they can compete, 
at least not without displacing a former major group or party (as the 
Republicans did after the Civil War, occupying the empty space left 
after the collapse of the Whigs).


I think that a proper election method can offer the people a much better 
way of picking their leaders, when that is required. Ideally, such 
leaders would not be required, and we'd all be in a minimally 
hierarchical society, but reality intervenes.


Because organization is a process, the change of election methods don't 
just change how the people pick their representatives or leaders, but 
also how those leaders react to the now-differing constraints, and how 
the people in turn respond to those changes, and so on. Using a party 
neutral method (like STV) would also encourage indpendents to run since 
they'd actually have a chance, and thus weaken the partisanship you 
refer to. With Duverger's tendency reversed, the multiple parties would 
keep any one party from gaining such dominance that it could trump 
through policy unopposed, even more so since the opposition of multiple 
parties would be stronger than the opposition of a single party.


If considered desirable, party power could be weakened further by rules 
similar to those of the consensus government used in some Canadian 
territories. One should still be careful not to consider organization 
itself an evil and reason that since dictatorships are the extreme of 
order, the extreme of chaos, on its own, would be ultimate liberation. 
At the least, one should have something with which to replace the old 
party dynamics, or risk that groups make their own rules (rules that 
favor themselves, naturally).


To sum that up, I am saying that first, altering the methods of election 
can lead to favorable results beyond the immediately obvious. Second, 
perhaps partisan politics can be improved upon, but if there'll still be 
elections, there'll still be a need for good election methods; and 
third, further decentralizing changes will be next to impossible to get 
through when the ruling parties are so few and hence so much a central 
power.


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Re: [EM] A computationally feasible method (algorithmic redistricting)

2008-09-04 Thread Kristofer Munsterhjelm


Juho wrote:

On Sep 4, 2008, at 0:59 , Kristofer Munsterhjelm wrote:
I think puzzles and games make good examples of NP-hard problems. 
Sokoban is PSPACE-complete, and it's not that difficult to show people 
that there are puzzles (like ciphers) where you know if a solution is 
right, but it takes effort to find the solution. That's pretty much 
the point of a puzzle, after all (although not all puzzles are 
NP-hard; they can be fun even if they're not, as long as they do 
something for which it's challenging to find a solution).


Puzzles and ciphers are good examples of cases where general 
optimization may typically fail to find even a decent answer (well, in 
these example cases the solution must be 100% good or it is no good at 
all). My assumption was that in the area of voting methods it would be 
typical that general optimization methods are sufficient and will with 
good probability lead to good enough results. Are there and 
counterexamples to this?


That gets harder, since most puzzles are of the right or not quality. 
Games could count, but it muddies the situation because if games are 
*-complete, they're usually PSPACE (because you have to come up with 
something that works for all possible replies).


However, games that have rules governing the dynamics could be used. For 
instance, finding out where to put the pieces in a Tetris game in the 
absolutely best manner possible is NP-complete. Still, people manage to 
play Tetris, because their approximations are good enough (or not, in 
which case they usually lose at higher levels) and because the 
situations aren't critical.


The problem with using these examples is that you lose the explaining 
power. If you tell someone that placing pieces optimally in Tetris is 
NP-complete, he won't get it, since to him Tetris is easy up to a 
certain point (assume this is someone who knows how to play it), and the 
reason he loses at a sufficiently level is because he can't approximate 
fast enough, which probably has very little to do with asymptotic 
complexity and rather much to do with the constants in the term.


So you'd have to use puzzles to explain the all-or-nothing version and 
only then go on to the optimization version.


Note that I fudged my own explanation a bit here: optimal anything isn't 
NP-complete, it's NP-hard. It's decision problem (is there a way of 
doing it better than x by some given measure) that's NP-complete, and 
you can find the optimum (best value of x possible) by doing a binary 
search.


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Re: [EM] No geographical districts

2008-09-05 Thread Kristofer Munsterhjelm


Raph Frank wrote:

On Fri, Sep 5, 2008 at 2:00 AM, Stéphane Rouillon
[EMAIL PROTECTED] wrote:

Hello Juho,

using age, gender or other virtual dimension to build virtual districts
replaces geographic antagonism by generation antagonism.
The idea is to get equivalent sample that are not opposed by intrinsec
construction.


A simple option would be to convert the date of birth into a number,
but have the year the the least significant part..

16-04-82 would become 160,482

The public could then be sorted by those numbers.  In effect, you are
splitting people by the day of the month they are born on, if there is
a tie, you use month and only use year at the end.

This would give a mix of ages, genders and any other measure in each district.

It is pretty much equivalent to just randomly distributing the voters
between the districts, but unlike a random system, it is harder to
corrupt.


It could have a similar result to having alphabetic ranked ballots, only 
with birthdays instead of last names. The selection would be biased in 
the direction of those that are born close to January. It may not 
matter, but it would appear unfair.


If you have computers, you could just sort by SHA512(name concatenated 
with birthdate concatenated with the year of the election). That's 
probably overkill (since even if you could break SHA-512, which would be 
a feat by itself, you'd have to convince the favored member to change 
his name to something suitable), but then there'd be a sufficient margin 
of safety. Randomness without randomness.


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Re: [EM] Free riding

2008-09-06 Thread Kristofer Munsterhjelm


Raph Frank wrote:

I think there is a slight issue.  In PAV, the satisfaction of each
voter is determined by

S(N) = sum(1 + 1/2 + 1/3 + 1/4 +  + 1/N )

Where N is equal to the number of candidates elected.

An approx function could be created that gives S(N) for non-integer N.
 The easiest would be just linear interpolation.  However, log(N) is
pretty close, but has a slight offset.

So maybe:

C(N) = log(N) - S(N)
Creal(x) = linear interpolate C(N)

Sreal(x) = log(x) - C(x)

This gives the right answer at the integers and a smooth curve between
them (maybe to much detail here :) ).


Why not have just linear interpolation, like RRV? Say that you've voted 
for A and B, and these are elected, and your rating was:


A: 0.9
B: 0.6

Then your satisfication is 0.9 + 0.6/2. Voting approval-style (A: 1, B: 
1) would give the familiar 1 + 1/2.


If it's Cardinal-n (limited number of choices), then you would normalize 
by maximum (e.g 8 of 10 becomes 0.8) and sum as above.



N would then be set equal to the sum of the ratings divided by the max
rating.  E.g. if I rate A as 100 and B as 30, and both are in the
result, then that counts as 1.3 candidates elected, so would take 1.3
terms of the above sum.  This would work out as a satisfaction of
around 1.2 with the above formula, which is between a satisfaction of
1.0 for 1 candidate and 1.5 for 2 candidates.


Oh, I see. You're considering a candidate with score 0.3 being not one 
candidate elected at score 0.3, but a third of a candidate elected. 
Let's consider that from basics. In PAV you have a function,


x
f(x) = SUM 1/n
   n=1

defined for integers, so that e.g f(2) = 1/1 + 1/2, which fits. Then, 
the continuous version would be the integral. The integral of 1/x is 
log(x), but that doesn't quite give the same results since 1/1 + 1/2 
just sums up two values, whereas the integral takes the entire curve 
between 1/1 and 1/2. Thus you'd have to adjust it somehow.


If done correctly, you wouldn't need any sort of interpolation, though.

A simple regression gives f(x) = log(e + 1.773 * (x-1)). The middle 
constant there increases very slowly: it's 1.7778 for x=14.


Using 1.773, your 1.3 candidate example would give a satisfaction of 
1.17871.



 The hard part is finding a way of tallying group support. As mentioned,
first preference wouldn't work, because then you'd get return of Woodall
free-riding: parties would say just vote for a friend as a write-in, then
the order we give you.


Wouldn't parties want to have as many FPV as possible?


Oops, I must have been thinking about decoy lists. You're right, so the 
distortion would be in the other direction. Counting party support by 
FPV would discourage personal votes, both in one end (because 
independent  A1  A2 would count for the independent and not at all for 
A) and in the other (because A1  independent  A2 .. would count 
completely for A).



In theory, if there was some way to measure vote management, then a
party could be punished for vote management by being assigned a lower
value in a later election, but that is probably to complex.


If there was a method of counting party support, parties with 
superproportional support could be deweighted the next time around. I 
think it would be too unstable, though.


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Re: [EM] Geographical districts

2008-09-10 Thread Kristofer Munsterhjelm


James Gilmour wrote:

Raph Frank  Sent: Friday, September 05, 2008 12:35 PM



Also, what is optimal for Should we use subsidiarity to make
decisions?.


I don't think this question can be answered as you have asked it.
Perhaps it would be more appropriate to ask Do we want our 
decision-making to be based on the principles of subsidiarity (i.e.

bottom-up)?  There are also problems with regard to optimal. A
benign dictator might make a more optimal decision than any
democratic group, but on the other hand you could say that that could
never be optimal because it was not democratic.  [As Professor Joab
(BBC Brains Trust - long ago!) might have said: It all depends on
what you mean by 'optimal'!!]


By the standard of freedom, (real) subsidiarity seems only logical. If 
you're an individual and you do something that has no impact on the rest 
of the world, there would appear, by that measure, to be little point 
for the rest of the world to interfere. If we make this more general, 
then if you're a group and you do something that has no impact on anyone 
but your group, then there would be little point for those outside to 
interfere.


There are two problems with this, though. Some may use logic similar to 
the potential way of arguing for a temporary regime of enforced equality 
 of minorities or sexes in an assembly: to interfere, if shortly, with 
the dynamics of the system, one can quickly redirect it towards a 
direction that it would naturally find but that would take significantly 
longer had you not interfered.


The second is that, for some actions, it's not easy to say who will be 
influenced. All may be, because we are social animals. Another argument 
I've heard, regarding public services, is that if you do something that 
would usually only affect yourself, but that you need a public service 
because of this, then that's a concern of all. For instance, in a nation 
with public healthcare, some may argue that if you do risky things, that 
concerns society in general since you could end up getting hurt and need 
the public health service, which the entire society maintains.



In conclusion, it appears that optimization for any given programmatic 
sense of optimality can just as well expose edge or corner cases that 
one didn't think of, as give what was intended. Still, as long as one 
keeps the above in mind, I think subsidiarity is a good idea.


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Re: [EM] the 'who' and the 'what'

2008-09-10 Thread Kristofer Munsterhjelm


Michael Allan wrote:

What about an alternative electoral system, in parallel?  If voters
really want to see change - if they really want to choose the 'who'
and the 'what' - a parallel system would give them an opportunity to
vote with their feet.  If nothing else, they might be curious to learn
how the results would differ (who would be Mayor, for example) if the
selection wasn't restricted to party candidates.



That's one way to do it. I think that if electoral reform is to work, 
the voters have to recognize that the new option (the better system) 
really is a better system, and also be interested in changing the system 
in the first place.


One way of showing that the new method works better is to work from the 
local level up. Another is, as you state, to have a parallel instance 
where voters can see that it's better. The parallel instance doesn't 
have to be completely identical, it could be as simple as MTV's use of 
Selectricity (Schulze) for its elections, although in that example, it 
may be harder for voters to identify that it's the voting method that 
makes for better results (since the internals are hidden).


If you take the parallel system strategy to its extreme, you'd get a 
parallel organization where (as an example), a group elects a double 
mayor and support him over the real mayor, essentially building a state 
inside the state. I don't think that's very likely to happen, though; as 
hard it may be to alter the nation through voting, it's going to be even 
harder to make a duplicate state from nothing, and that duplicate state 
would still have to abide by the laws of the real state.


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Re: [EM] language/framing quibble


Fred Gohlke wrote:

Good Afternoon, Kristofer

re: This sounds a lot like what I've previously referred to as
'council democracy'.

I hadn't heard that term before or seen the proposal.  I wonder if the 
concepts can be merged, perhaps by an analytical critique of the processes.


I first mentioned it here: 
http://listas.apesol.org/pipermail/election-methods-electorama.com/2008-July/021966.html 
to which Abd replied here: 
http://listas.apesol.org/pipermail/election-methods-electorama.com/2008-July/021968.html 
. I said that I think some unions use this process: they have local 
delegates that form councils that elect regional delegates and so on.



re: The first problem of council democracy is that it magnifies
 opinion in a possibly chaotic manner.

This is, I suspect, a function of the size of the 'council'.  The larger 
it is, the less opportunity each member has to help form its view.


That is, unless we use proportional representation. If the council is of 
size 7, no opinion that holds less than 1/7 of the voters can be 
represented, so if the opinion is spread too thin, it'll be removed from 
the system; but if you have an extreme of a single layer with PR, 
elected nationally, then the number is much lower.


An aspect of this question that troubles me is the backward-looking 
nature of opinion.  Government is (or, at least, ought to be) concerned 
with the present and the future.  We should prize our representatives' 
ability to address contemporary concerns with all the resources at our 
command rather than apply pre-conceived solutions to new, and possibly 
unknown, circumstances.  In other words, opinion must be subject to 
intellect.


Yes, that's true. I'm using opinion mainly as a way to show that 
minority properties can be either attenuated or magnified, based simply 
on how the voters are distributed among the councils. This could apply 
to any preference that may be held by only a minority (or even by a 
majority, as the worst case scenario shows): it could be a preference 
for deliberative or intelligent representatives for that matter.



re: In the very worst case, an opinion held by (2/3)8 = 4% can
 be held by a majority of the last triad.

I lack the expertise to evaluate the math, but I don't understand the 
point for a different reason:  Is 'an opinion ... held by a majority of 
the last triad' not but one of a multitude of such opinions?  Does a 
person's value rest on a single opinion or on the mix of opinions that 
define the person?  Indeed, is their value not better determined by 
their ability to implement whatever mix of opinions we perceive them to 
have?


Again, I use opinions to make the argument simple. Consider it another 
way: each reduction of many triads to one triad has to, by some measure, 
aggregate minority opinion. In the worst case, only the majority counts 
(as this is majority-based and not a consensus mechanism), and the 
minority preference (opinion, share, whatever) gets shaved off. Since 
the reduction is exponential, even more gets shaved off at each 
instance, and these slices may in the end constitute a majority.



re: ... but the point holds: because the comparisons are local,
 disproportionality can accumulate.

I'm not clear on this point.  By 'local', do you mean that the 
participants are from a distinct locality?  That is certainly true at 
the very lowest levels, but the distinction blurs as the levels advance. 
 I'm not sure what will be disproportionate.


Here's an example of size 3 of the effect I'm talking about. I hope my 
(and your) mail software won't mangle this too badly.


For the sake of simplicity, again, we'll consider binary opinion. 
There's a question that has a yes or no answer. The concils are set up 
like this:


L1  YYN YYN NNN
 |   |   |
 Y   Y   N
 |   |   |
 +---+---+
L2  YYN

Here there are four ayes that overrule the five nays, simply because 
they're better positioned. If you look at the second level, it even 
seems like the ayes have 2/3 of the public support, when that is clearly 
not the case.


In an ordinary council democracy, a conspiracy could stack the councils 
in this manner, but in your proposal, because of random selection, that 
would not be possible. Still, it shows a problem of the process by 
showing a true majority getting assigned a minority of the 
representatives and vice versa.


Weighted votes could ameliorate the case, but it wouldn't fix it 
completely, and it may be unwieldy. In the case above: the unanimous N 
would have strength 3 while the Y members have strength 2 each, thus 
giving 58% for the ayes. That's lower than the raw 2/3 ~= 67%, but still 
too high.



re: One could reduce the first problem by having a larger group
 that elects more than one member.

The question of group size is worthy of considerable thought.  Rather 
than extend this message, I will post a message titled 'DELIBERATIVE 
GROUP SIZE and PERSUASION' so we can focus on

Re: [EM] sortition/random legislature Was: Re: language/framing quibble


Raph Frank wrote:

Sorry, pressed reply instead of reply to all

On 9/11/08, Aaron Armitage [EMAIL PROTECTED] wrote:
  It doesn't follow from the fact we choose representatives for ourselves
   that we would lose nothing by being stripped of the means of political
   action. We would lose our citizenship, because citizenship means precisely
   having a share of the right to rule. Registering for a lottery doesn't
   count.


So, any form of randomness is not acceptable?  What about one of the
 the proposed random ballot rules, where if there is consensus, a
 specific candidate wins.  However, if that doesn't work, the winner is
 random.


There's probably a tradeoff here. A completely random legislature would 
have no direct link to the people, except by the people, as a mass, 
changing their opinions. An elected legislature is at the other end of 
the scale: the people can directly influence its composition by 
declining to vote for some candidates and supporting others.


The relative isolation from direct influence is both a random assembly's 
strength and a weakness. It's a strength because, if campaign men can 
influence voters in the wrong direction, then the assembly remains 
impervious to this attack. It's a weakness for the reasons Aaron gives, 
that it severely weakens the voter-representative link.


A random assembly also resists the attack where one corrupts candidates, 
simply because it's not clear who the candidates are going to be. I 
don't know if randomness, or more generally, a weak voter-representative 
link is required for this resistance. It might be, for a single given 
representative, but a method where voters elect groups and some subset 
of each group is taken could also be resistant to this, if it's not 
obvious beforehand which subset is taken.


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Re: [EM] A computationally feasible method (algorithmic redistricting)


Juho wrote:
The traditional algorithm complexity research covers usually only 
finding perfect/optimal result. I'm particularly interested in how the 
value of the result increases as a function of time. It is possible that 
even if it would take 100 years to guarantee that one has found the best 
solution, it is possible that five minutes would be enough to find a 99% 
good solution with 99% probability.


Decrypting ciphered text does not work this way (the results could still 
be worth 0 after 10 years with good probability). But solving e.g. 
CPO-STV may well behave more this way (probably one can find an 80% good 
solution in one minute). Good performance in value/time means that 
general optimization works (and the method can be considered feasible in 
practice despite of being theoretically infeasible).


In computer science, you have something called polynomial time 
approximation schemes (or PTASes). If a problem has a PTAS, then it's 
possible to get within a factor e (epsilon) of being optimal, in 
polynomial time, where the solution time for a fixed e is polynomial 
(but need not be polynomial with respect to e). An approximation scheme 
that runs in time n^(1 + 1/e) is a PTAS, although it's not polynomial 
with respect to e.


The equivalent group for probabilistic algorithms is called polynomial 
time randomized approximation schemes, and give a result within e of 
optimal in polynomial time /with high probability/.


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Re: [EM] the 'who' and the 'what'