Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-10 Thread Markus Schulze

Dear James Gilmour,

you wrote (10 July 2008):

 If you are going to mess about with MMP to the
 extent that you suggest in the hope of making
 some significant improvements to what is
 basically a very poor voting system, why not
 just adopt STV-PR and do the job properly?

When you promote pure STV in a country that
already uses proportional representation by
party lists, then you will be accused immediately
that you were dishonest and that your real aim
was to increase the effective threshold to gain
representation.

My own experience says that, when you want to
promote STV in a country that already uses
proportional representation by party lists,
then your proposal must contain provisions
to compensate party proportionality on the
national level. Otherwise, your proposal is
a non-starter.

Markus Schulze



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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-10 Thread James Gilmour
Markus Schulze   Sent: Thursday, July 10, 2008 8:45 AM
   If you are going to mess about with MMP to the
   extent that you suggest in the hope of making
   some significant improvements to what is
   basically a very poor voting system, why not
   just adopt STV-PR and do the job properly?
 
 When you promote pure STV in a country that
 already uses proportional representation by
 party lists, then you will be accused immediately
 that you were dishonest and that your real aim
 was to increase the effective threshold to gain
 representation.
 
 My own experience says that, when you want to
 promote STV in a country that already uses
 proportional representation by party lists,
 then your proposal must contain provisions
 to compensate party proportionality on the
 national level. Otherwise, your proposal is
 a non-starter.

Markus, you make a very valid point which I, as a practical reformer, fully 
appreciate.  Any reform proposal, and the campaign to
support it, must be wholly appropriate to the local political circumstances.

It would certainly not be part of my agenda to increase the representation 
threshold for any political purpose, but I do recognise
the political problems that can be created by very low effective thresholds 
(e.g. Israel).  It must, however, be accepted that many
party list systems (including MMP systems) have imposed thresholds and that 
these thresholds are completely arbitrary, e.g. 5% of
the party list vote nationally  -  but why not 4% or 6%? . If you are going to 
impose such an arbitrary threshold, why go the bother
of summing the votes nationally?  Why not just use the effective thresholds 
that would result from the underlying regional structure
that exists in many countries and is built into in their voting systems (e.g. 
where parties present lists on a regional basis)?

It must also be appreciated that the effective threshold to gain representation 
in STV-PR is lower than a simple analysis based on
dividing the national first preference vote by the average quota would suggest, 
for two reasons.

In STV, the vote transfers are extremely important and when these are taken 
into account, the effect on small parties and
candidates with less support can change the perspective very dramatically.  For 
example, in the 2007 local government elections in
Scotland (3 and 4-member districts) the lowest proportions of quotas secured by 
winning candidates of the five main parties were:
0.32, 0.42, 0.42, 0.46, 0.48,   Malta shows the dangers of getting hung up on 
first preference votes when the main feature of the
STV voting system is that the votes are transferable.   It is also an unsafe 
assumption that every first preference vote for a
particular candidate is a party vote for that candidate's party.

Parties and candidates (usually) respond to the characteristics of whatever 
voting system is in use.  Thus the approach adopted by
smaller parties where it is STV-PR, is to concentrate their resources where 
their support is strongest and so achieve the local
threshold.  That's how the Northern Ireland Women's Coalition, with about 2% of 
the first preference votes province-wide, won 2% of
the seats overall in the Northern Ireland Assembly (1998) when the district 
magnitude was only 6 (Droop quota threshold = 14.3%).

There is always a trade-off between guaranteed local representation (small 
districts) and proportionality (large districts),
whatever the voting system.  While STV-PR, as normally implemented, might 
reduce the effective threshold to gain representation for
parties nationally, that loss has to be set against the gains for the voters of 
more localised representation and of shifting the
balance of power and accountability from the parties to the voters.  How that 
balance is best presented depends on local politics.
No matter how enthusiastic the electors may be, such a change will nearly 
always be opposed by the larger political parties and
their backers!!

James

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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-09 Thread Rob LeGrand
Kristofer Munsterhjelm wrote:
 You use movie site data for your AAR-DSV examples. Does AAR-DSV
 manipulability mean that a movie site that uses it would face
 difficulty telling users which movie is the most popular or highest
 rated? The manipulability proofs wouldn't harm them as strongly (since
 very few users rate all of the movies), but they would in principle
 remain, unless I'm missing something...

It all depends on what we assume the voters would be trying to do.  If
each voter is trying to move the overall rating of each movie as close as
possible to his/her ideal rating of that movie, without any regard to how
the other movies are rated, then AAR DSV is completely nonmanipulable.
On the other hand, if a voter is trying to affect which movie ends up
with the highest rating, voting insincerely may sometimes give an
advantage.

--
Rob LeGrand, psephologist
[EMAIL PROTECTED]
Citizens for Approval Voting
http://www.approvalvoting.org/


  

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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-09 Thread James Gilmour
Kristofer Munsterhjelm  Sent: Tuesday, July 08, 2008 1:25 PM
 I don't doubt that the problem exists. After all, the term decoy list 
 (lista civetta) comes from the Italian abuse of the system. 
 Do you know of any countries that do have overhang provisions to 
 ameliorate the problem?

While I am sure it was not introduced for this purpose (combating lista 
civetta), an overhang correction (in various forms at
different times) has been used in elections to the German Bundestag.  The 
Wikipedia page on this says a similar correction is
applied in elections to the National Assembly of Venezuela, but I have not 
checked that.   MMP elections to the New Zealand House of
Representatives can produce am overhang of constituency (electorate) seats, but 
no correction is applied.  There is no provision for
overhang seats in MMP elections to the Scottish Parliament or the National 
Assembly of Wales, both of which use regionalised
versions of MMP.

 
   Basically, MMP is a rotten voting system, with or without the
  'overhang' correction, and it should be replaced by a better system of 
  proportional representation.
 
 Even though I think multiwinner methods should be  party-neutral, I can 
 see the appeal of MMP: parties are guaranteed to get their share of the 
 vote, even if the constituency vote is disproportional.

Surely the fundamental requirement of any voting system for a representative 
assembly should be to ensure that the VOTERS get
proportional representation of what they, the VOTERS, want, as expressed 
through their responses to the candidates who offer
themselves for election.  To the extent that the voters vote by party, they 
will get party PR.

The undoubted attraction of MMP is that it appears to retain the alleged 
benefits of single-member districts while giving party PR.
Thus MMP has proved attractive in countries that have suffered the appalling 
British legacy of FPTP elections in single-member
districts.  In fact, research has shown that the alleged benefits of 
single-member districts (the elector-member link) are mostly
illusory, and experience has shown that greater accountability of the elected 
members to the local voters can be obtained in
multi-member districts  -  provided the correct voting system is used.  MMP 
also creates its own problems, especially in electing
two different types of member.  For more details see the Fairshare submission 
to the Arbuthnott Commission which reviewed the voting
system for the Scottish Parliament (PDF, 45 KB):
  
http://www.fairsharevoting.org/Fairshare%20Submission%20Arbuthnott%20Commission%2022%20Mar%2005.pdf


 Thus they can't 
 say that they were robbed of seats because of the quirks of  the system. 
 While in reality such complaints would be infrequent (because those who 
 have power in a very disproportional system are those where the 
 disproportionality swung their way), why have disproportionality when it 
 can be avoided?
 
 If we generalize this, the list part of MMP is a patch to the 
 disproportionality of the constituency method, to take advantage of 
 explicitly-known properties (like party allegiance). That suggests that 
 we use a proportional multiwinner method (like STV) for larger 
 constituencies, and then award list seats (of a much smaller share than 
 half the parliament) to patch up whatever disproportionality still 
 exists - even if the multiwinner method is perfect, rounding errors 
 regarding district size would introduce some disproportionality.
 
 At that point, the generalized MMP with STV sounds a lot like 
 Schulze's suggestion for Berlin.

If you are going to mess about with MMP to the extent that you suggest in the 
hope of making some significant improvements to what
is basically a very poor voting system, why not just adopt STV-PR and  do the 
job properly?

James Gilmour


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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-08 Thread Kristofer Munsterhjelm

James Gilmour wrote:

Kristofer Munsterhjelm  Sent: Sunday, July 06, 2008 12:10 AM
Second, I've been reading about the decoy list problem in mixed member 
proportionality. The strategy exists because the method can't do 
anything when a party doesn't have any list votes to compensate for 
constituency disproportionality. Thus, cloning (or should it be called 
splitting?) a party into two parties, one for the constituency 
candidates, and one for the list, pays off. But is it possible to make a 
sort of MMP where that strategy doesn't work?


I don't know about making it not work, but the 'overhang' provisions in some versions of MMP would, 
at least partly, address this problem.  The version of MMP used for 

elections to the Scottish Parliament
(no overhang correction) is wide open to this abuse, and we already have two registered political parties 
that could make very effective use of it IF they so wanted.  The Labour Party and the Co-operative Party 
jointly nominate candidates in some constituencies.  The Co-operative Party does not nominate any
constituency candidates nor does it contest the regional votes.  


I don't doubt that the problem exists. After all, the term decoy list 
(lista civetta) comes from the Italian abuse of the system. Do you know 
of any countries that do have overhang provisions to ameliorate the problem?


 Basically, MMP is a rotten voting system, with or without the

'overhang' correction, and it should be replaced by a better system of 
proportional representation.


Even though I think multiwinner methods should be party-neutral, I can 
see the appeal of MMP: parties are guaranteed to get their share of the 
vote, even if the constituency vote is disproportional. Thus they can't 
say that they were robbed of seats because of the quirks of the system. 
While in reality such complaints would be infrequent (because those who 
have power in a very disproportional system are those where the 
disproportionality swung their way), why have disproportionality when it 
can be avoided?


If we generalize this, the list part of MMP is a patch to the 
disproportionality of the constituency method, to take advantage of 
explicitly-known properties (like party allegiance). That suggests that 
we use a proportional multiwinner method (like STV) for larger 
constituencies, and then award list seats (of a much smaller share than 
half the parliament) to patch up whatever disproportionality still 
exists - even if the multiwinner method is perfect, rounding errors 
regarding district size would introduce some disproportionality.


At that point, the generalized MMP with STV sounds a lot like Schulze's 
suggestion for Berlin.



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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-08 Thread Kristofer Munsterhjelm

Rob LeGrand wrote:

Kristofer Munsterhjelm wrote:

(On a related note, has anyone tried to use Range with LeGrand's
Equilibrium Average instead of plain average?)


I don't recommend using Equilibrium Average (which I usually call AAR
DSV, for Average-Approval-Rating DSV) to elect winner(s) from a finite
number of candidates.  AAR DSV is nonmanipulable when selecting a single
outcome from a one-dimensional range, just as median (if implemented
carefully) is, but it is manipulable when used as a scoring function in
a way similar to how Balinski and Laraki proposed using median:

http://rangevoting.org/MedianVrange.html


You use movie site data for your AAR-DSV examples. Does AAR-DSV 
manipulability mean that a movie site that uses it would face difficulty 
telling users which movie is the most popular or highest rated? The 
manipulability proofs wouldn't harm them as strongly (since very few 
users rate all of the movies), but they would in principle remain, 
unless I'm missing something...


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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-08 Thread raphfrk

 
 Kristofer said:
 
That could be an interesting way to solve the indecisive parliament or 

 frequent government change problem where these exist. In order to 

 recall the executive, they have to vote for a new coalition at the same 

 time. 

They have kinda that rule in Germany.? The only way to remove their
Chancellor is to nominate a replacement.

There is a proposed alternative to MMP called Fair majority voting that
solves some of its problems.? It has the same single winner + national party
proportional vote system.? It has some problems of its own though.

http://www.mathaware.org/mam/08/EliminateGerrymandering.pdf

Basically, each voter votes for a party and candidate.? In each
district, plurality is used to work out the winner (I think approval 
could also work).

The fair number of seats for each party is worked out based on the party
vote and a set of multiplers are determined so that each party gets the 
right number of seats.

These multipliers are multiplied by the vote total of each candidate in the 
party.
A party which got to few seats would be given a higher multipler.

In effect, it flips the results where the margin of victory was small in order
to bring all parties to their proportional totals.

I am not sure what the best way to do the task that matrix voting tries to 
accomplish.

Normally positions on the executive are not equal in value.

There are free riding issues with selection of major posts.? For example, if 
you rank 
your party leader first choice as PM, you use up some of your vote for the other
positions.? The solution could be to kick out anyone in the party who doesn't 
rank
their own leader first choice, so all equally share the cost.

In Northern Ireland, they use the d'Hondt system for allocating seats on the 
executive.
This gives the larger parties an advantage as they get to pick first.? Also, 
the largest
2 parties get 1 seat each for free.

Another option would be a fair division protocol.? If you had 2 equally sized 
parties,
one party leader could split the executive positions into 2 and then the other 
party
leader could pick one group.? This should mean that both groups have roughly 
equal 
value.

Alternatively, one of the leaders could give each position a value and the 
other 
party leader can pick any group of positions such that the total adds up to 
less than half.
If the first leader undervalues a position, the 2nd leader gets a powerful 
position for a 
low cost.? Likewise, if he overvalues a position, the 2nd leader will just not 
take it, giving
him a larger share of the other positions.

I am not such if this can be expanded to multiple parties of differing sizes.

Also, there is the issue that there would be no coherent national policy on 
anything.? You
could have one minister taking actions which cancel out the actions of another 
minister.
(and both spending money doing it).? Ofc, this creates an incentive for them to 
work together
and find a compromise.

Also, budgets could be an issue.? One option would be to share tax income out 
proportionally.
Each member of the legislature could decide what ministries their share is 
allocated to.


 
Tax cuts/raises are an even bigger issue.? 



Raphfrk

Interesting site
what if anyone could modify the laws

www.wikocracy.com

 


 



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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-08 Thread Juho

On Jul 8, 2008, at 15:24 , Kristofer Munsterhjelm wrote:

Even though I think multiwinner methods should be party-neutral, I  
can see the appeal of MMP: parties are guaranteed to get their  
share of the vote, even if the constituency vote is disproportional.



use a proportional multiwinner method (like STV) for larger  
constituencies, and then award list seats (of a much smaller share  
than half the parliament) to patch up whatever disproportionality  
still exists - even if the multiwinner method is perfect, rounding  
errors regarding district size would introduce some  
disproportionality.


I assume you want to have some level of regional representation. =  
At least large districts with multiple seats.


You said you want the method to be party-neutral. = Maybe STV will  
do (I assume all party-like list (or tree) based methods would not be  
ok).


If you use large districts and STV in each of them (separate  
candidates for each district) that should give you already quite  
accurate political proportionality (only some rounding errors left).  
If the size of the districts is small that would cut out some small  
parties (or not give them fully proportional number of seats). (Some  
tricks could be used to fix also the remaining rounding errors if  
needed.)


My point is that if you are happy with large districts the MMP  
part (and separation of two different kind of representatives) is  
not necessarily needed.


Juho






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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-06 Thread Markus Schulze

Dear Kristofer,

you wrote (6 July 2008):

 I've been reading about the decoy list problem in mixed
 member proportionality. The strategy exists because
 the method can't do anything when a party doesn't
 have any list votes to compensate for constituency
 disproportionality. Thus, cloning (or should it be
 called splitting?) a party into two parties, one for the
 constituency candidates, and one for the list, pays off.
 But is it possible to make a sort of MMP where that
 strategy doesn't work?

 That MMP method would have to use some kind of reweighting
 for those voters who got their way with regards to the
 constituency members, I think, because if the method
 just tries to find correlated parties, the party could
 theoretically execute the strategy by running all the
 constituency candidates as independents. What kind of
 reweighting would that be? One idea would be to have a
 rule that says those with say x about the constituency
 vote gets 1-x in the list vote. Then vary x until the
 point of party proportionality is found. No matter what
 party someone who makes a difference with regards to the
 constituency candidate chooses, his vote loses power
 proportionally, and thus decoy lists wouldn't work.

Wow, that's exactly what I have proposed recently for
an STV-MMP system in Berlin. Please read these papers:

http://m-schulze.webhop.net/schulze4.pdf
http://m-schulze.webhop.net/schulze5.pdf

Read especially page 3 of paper schulze5.pdf.

Markus Schulze



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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-06 Thread Stéphane Rouillon

Dear Kristofer,

if your goal to issue a smaller group representing  the same opinions 
and debates than the larger group
I think maintaining proportortionality is a good characteristic to make 
sure most positions of
these debates survive the attrition.  The reduction in size should 
facilitate the oral exchanges.
I have a tendancy to view any election as an attempt to build a 
microcosm of a larger group

in order to facilitate debates...

For your second point, there is one way to enforce coherency (using a 
mathematical definition)
within an MMP election. If one uses the same results to elect the 
individual representatives
and to determine the corrected proportion obtained after electing list 
members. The simple way to enforce
such coherence between these two proportions is to use a single ballot 
MMP, where voting
for an individual is considered too as giving support in favor of this 
candate party list.
From what I know two german landers use this system. Otherwise you have 
to relie on cultural

honesty of the parties or electorate to avoid the decoy problem.

Salutations,
Stéphane

Kristofer Munsterhjelm a écrit :
I thought I could ask a few questions while otherwise being busy 
making my next simulator version :-) So here goes..


First, when a group elects a smaller group (as a parliament might do 
with a government, although real parliaments don't do it this way), 
should the method used to elect the smaller group be proportional?


I think one could make a majoritarian version with cardinal 
ratings/Range. It'd work this way: for n positions, each voter submits 
n rated ballots. Then, with k candidates, make a k*n matrix, where 
position (a,b) is the sum of the ratings the voter assigned candidate 
a in the ballot for position b.


We've now reduced the problem of picking (candidate, position) values 
so that the sum is maximized. The constraints on the problem are: only 
one value can be selected from each row (can't have the same candidate 
for two positions), and only one value can be selected from each 
column (can't have two candidates for the same position). I think 
that's solvable in polynomial time, but I haven't worked out the details.


That's for majoritarian matrix votes with cardinal ratings (or Range - 
could also be median or whatever as long as the scores are 
commensurable).


(On a related note, has anyone tried to use Range with LeGrand's 
Equilibrium Average instead of plain average?)


Perhaps the same pick-the-best-sum reasoning could be extended to a 
Condorcetian matrix vote, using Kemeny score for the Condorcet matrix 
for the position in question instead of ratings sums/averages. But as 
far as I remember, Kemeny scores relate to social orderings, not just 
candidate choices, so maybe the Dodgson score instead -- but that may 
not be comparable in cases where different candidates are Condorcet 
winners in different elections, since those would all have Dodgson 
scores of 0 (no swapping required).


In any case, the reduction above won't work if matrix voting methods 
ought to be proportional. I'm not sure whether it should be 
majoritarian or proportional, and one could argue for either - 
majoritarianism in that that's how real world parliamentary 
governments are formed (negotiations notwithstanding), and 
proportionality because some group may be very good at distinguishing 
suitable foreign ministers while some other, slightly larger group, 
might not do very well at that task but be good at distinguish 
suitable ministers of interior.



Second, I've been reading about the decoy list problem in mixed 
member proportionality. The strategy exists because the method can't 
do anything when a party doesn't have any list votes to compensate for 
constituency disproportionality. Thus, cloning (or should it be 
called splitting?) a party into two parties, one for the constituency 
candidates, and one for the list, pays off. But is it possible to make 
a sort of MMP where that strategy doesn't work?


That MMP method would have to use some kind of reweighting for those 
voters who got their way with regards to the constituency members, I 
think, because if the method just tries to find correlated parties, 
the party could theoretically execute the strategy by running all the 
constituency candidates as independents.
What kind of reweighting would that be? One idea would be to have a 
rule that says those with say x about the constituency vote gets 1-x 
in the list vote. Then vary x until the point of party 
proportionality is found. No matter what party someone who makes a 
difference with regards to the constituency candidate chooses, his 
vote loses power proportionally, and thus decoy lists wouldn't work.


No concrete methods here, but maybe someone else will add to them... 
or find flaws in my reasoning and correct them :-)


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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-06 Thread James Gilmour
Stéphane Rouillon  Sent: Sunday, July 06, 2008 6:02 PM
 For your second point, there is one way to enforce coherency (using a 
 mathematical definition)
 within an MMP election. If one uses the same results to elect the individual 
 representatives
 and to determine the corrected proportion obtained after electing list 
 members. The simple way to enforce
 such coherence between these two proportions is to use a single ballot MMP, 
 where voting
 for an individual is considered too as giving support in favor of this 
 candidate party list.
  From what I know two German landers use this system. 

I am aware that some German Lander use single ballot MMP, but it is a 
fundamentally flawed system and should not be recommended.
The problem is that the candidate votes (cast in single-member districts) do 
not provide an accurate reflection of the voters'
overall support for the political parties because the candidate votes are 
distorted by local tactical voting.  If you must use MMP
(a poor voting system), it should always be a two-vote version.

James



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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-06 Thread Rob LeGrand
Kristofer Munsterhjelm wrote:
 (On a related note, has anyone tried to use Range with LeGrand's
 Equilibrium Average instead of plain average?)

I don't recommend using Equilibrium Average (which I usually call AAR
DSV, for Average-Approval-Rating DSV) to elect winner(s) from a finite
number of candidates.  AAR DSV is nonmanipulable when selecting a single
outcome from a one-dimensional range, just as median (if implemented
carefully) is, but it is manipulable when used as a scoring function in
a way similar to how Balinski and Laraki proposed using median:

http://rangevoting.org/MedianVrange.html

For more on AAR DSV, please see chapter 3 of my now-completed
dissertation:

http://www.cse.wustl.edu/~legrand/dissertation.pdf

--
Rob LeGrand, psephologist
[EMAIL PROTECTED]
Citizens for Approval Voting
http://www.approvalvoting.org/


  

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Re: [Election-Methods] Matrix voting and cloneproof MMP questions

2008-07-06 Thread Terry Bouricius
On the question of whether electing a subgroup should be proportional or 
majoritarian...I often make a distinction on two factors: 1) Is the 
association voluntary (in which dissatisfied minorities can easily 
withdraw to join or form a different association), and 2) Is the function 
of the association directional or goal oriented, vs. service, maintenance 
or regulatory-oriented (a political party that wants to move society in a 
direction, vs. an alumni association).

Voluntary associations that have a directional goals (such as  a platform) 
can sometimes be best served by majoritarian or centrist internal election 
method, such as electing party leaders, Whereas compulsory associations 
that are engaged in maintenance (a government) are best served by 
proportional methods.

Terry

- Original Message - 
From: Kristofer Munsterhjelm [EMAIL PROTECTED]
To: EM election-methods@lists.electorama.com
Sent: Saturday, July 05, 2008 7:09 PM
Subject: [Election-Methods] Matrix voting and cloneproof MMP questions


I thought I could ask a few questions while otherwise being busy making
my next simulator version :-) So here goes..

First, when a group elects a smaller group (as a parliament might do
with a government, although real parliaments don't do it this way),
should the method used to elect the smaller group be proportional?

I think one could make a majoritarian version with cardinal
ratings/Range. It'd work this way: for n positions, each voter submits n
rated ballots. Then, with k candidates, make a k*n matrix, where
position (a,b) is the sum of the ratings the voter assigned candidate a
in the ballot for position b.

We've now reduced the problem of picking (candidate, position) values so
that the sum is maximized. The constraints on the problem are: only one
value can be selected from each row (can't have the same candidate for
two positions), and only one value can be selected from each column
(can't have two candidates for the same position). I think that's
solvable in polynomial time, but I haven't worked out the details.

That's for majoritarian matrix votes with cardinal ratings (or Range -
could also be median or whatever as long as the scores are commensurable).

(On a related note, has anyone tried to use Range with LeGrand's
Equilibrium Average instead of plain average?)

Perhaps the same pick-the-best-sum reasoning could be extended to a
Condorcetian matrix vote, using Kemeny score for the Condorcet matrix
for the position in question instead of ratings sums/averages. But as
far as I remember, Kemeny scores relate to social orderings, not just
candidate choices, so maybe the Dodgson score instead -- but that may
not be comparable in cases where different candidates are Condorcet
winners in different elections, since those would all have Dodgson
scores of 0 (no swapping required).

In any case, the reduction above won't work if matrix voting methods
ought to be proportional. I'm not sure whether it should be majoritarian
or proportional, and one could argue for either - majoritarianism in
that that's how real world parliamentary governments are formed
(negotiations notwithstanding), and proportionality because some group
may be very good at distinguishing suitable foreign ministers while some
other, slightly larger group, might not do very well at that task but be
good at distinguish suitable ministers of interior.


Second, I've been reading about the decoy list problem in mixed member
proportionality. The strategy exists because the method can't do
anything when a party doesn't have any list votes to compensate for
constituency disproportionality. Thus, cloning (or should it be called
splitting?) a party into two parties, one for the constituency
candidates, and one for the list, pays off. But is it possible to make a
sort of MMP where that strategy doesn't work?

That MMP method would have to use some kind of reweighting for those
voters who got their way with regards to the constituency members, I
think, because if the method just tries to find correlated parties, the
party could theoretically execute the strategy by running all the
constituency candidates as independents.
What kind of reweighting would that be? One idea would be to have a rule
that says those with say x about the constituency vote gets 1-x in the
list vote. Then vary x until the point of party proportionality is
found. No matter what party someone who makes a difference with regards
to the constituency candidate chooses, his vote loses power
proportionally, and thus decoy lists wouldn't work.

No concrete methods here, but maybe someone else will add to them... or
find flaws in my reasoning and correct them :-)

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