[EM] PR for ethnically polarized electorates (Forest Simmons)

[Toby Pereira]

A few months ago, Forest Simmons made a series of interesting posts on this subject. I was thinking about it again recently, and on further reflection have a few further questions. Forest's quotes here come from more than one post.

From: Forest Simmons <fsimmons at pcc.edu>

>Suppose that there are two extreme groups A and B supported by two individual ethnicities, as well as a more moderate group M >with preferences like

>10 A(100)
>30 A(100)>M(80)
>45 B(100)>M(80)
>15 B(100)

>(The numbers in parentheses represent voter expectations of relative benefits.)

>In ordinary party list PR methods the parliament would be formed by 40 representatives from A and 60 representatives from B.  >The moderate party would be shut out entirely.

>Here are my questions:

>1. What method(s) would take this information and elect a parliament with respective party strengths of  10, 15, and 75  for A, B, >and M?

>2.  What election method could possibly get the two middle factions to honestly convey this information via their ballots?  In other >words, how to keep the two middle factions from defecting from their common interest?

[snip]

>The simplest answer to question one that I know of is based on an idea that Martin Harper came up with 12 years ago as a way of >showing that ordinary Approval satisfies "one voter one vote" in the same strict sense that IRV does (through vote transfer):

>First list the candidates in order of most approval to least approval.  Then on each ballot transfer the entire support of the voter to >the highest candidate on the list that is approved on the ballot.  In other words, the voter's one and only vote is for the candidate >she approves that is most approved by other voters.  As Martin pointed out, this assignment of votes still elects the ordinary >Approval winner in the single winner case.  (Half a dozen years later Jobst pointed out that this same idea can be used to assign >probabilities in a single winner lottery method.)

Is this definitely the best system? If you have these approval ballots:

2: A
10: A, B
1: B, C
9: C

Then the approvals are A=12, B=11, C=10. If I've understood what you said correctly, this would transfer to A=12, B=1, C=9. Would it be better to do it sequentially? So A has the most approvals and takes all its voters, and this leaves us with:

1: B, C
9: C

Applying the same procedure again gives us A=12, C=10 leaving B with nothing. Leaving B with one seems wasteful since B is unlikely to get a seat like this.

[snip]

>In our last post we showed that direct approval voting for parties does not yield a satisfactory answer to question two, i.e. there are >strategic incentives against directly approving the moderate party, even when many of the voters consider it almost as good as >their favorite extreme party.

>The solution to this problem comes from Jobst Heitzig, in an idea which he came up with in the context of lottery methods, but >which applies equally well in this PR context.  Let's call the idea "Conditional Approval."

>The idea is to give the voters a way of saying "I'll cooperate if they will cooperate, and I'll defect if they defect."  In other words, "Put >me down for approving M (the moderate compromise party) as long as there are 74 other voters who are willing to do the same, >otherwise no."

>Now suppose that all 75 voters in the middle two factions indicate this conditional approval of M on their conditional approval >ballots (along with unconditional approval of their favorites).  I claim that this position is a strategic equilibrium, because this >position makes impossible the pesky unilateral defections we had to deal with in our direct approval approach.  If any of the 75 >voters from the two middle factions defect, then the deal is off, and the payoffs jump from the (cooperate, cooperate) corner of the >(old) payoff matrix to the (defect, defect) corner, resulting in a loss for both of the middle factions.

This may work in this case, but I'm unsure as to how the voters would have any clue in advance how many other voters their approval of M should be conditional upon. Where does the number 74 come from other than a calculation with knowledge of the final result?

Could you take a score ballot and instead of using the scores as scores in a normal way, take them as approvals that are conditional upon the right number of other people also approving/conditionally approving the right candidates? So the calculation process works out the conditional number for them. Would there be a simple way of calculating how it should be done that would avoid or ameliorate against strategic incentives against giving the moderate party an honest score?

Toby
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