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

[Toby Pereira]

I just want to return to this again. I've quoted below the relevant bit. When deciding which of the their approved candidates to assign to a voter, I don't think the method Forest suggested or my sequential method necessarily always give the best results. I've already given an example for Forest's suggestion (which I think originally came from Martin Harper), but I can change the example slightly to show that the sequential system is also lacking.

2: A
10: AB
3: BC
9: C

The approvals are A=12, B=13, C=12. This means we lock in B=13. This leaves:

2: A
9:C

This would give a final result of A=2, B=13, C=9. But looking a the approvals, you could have A=12, C=12, which looks better. But then what is the measure we're trying to optimise? I would argue that it's to maximise the average number of voters in a voter's group. For example if we compared groups of size 3 and 1 with groups of size 2 and 2, both have an average group size of 2. But that's not what we're measuring. It's average per voter group size. So with groups of 3 and 1, you have (3*3 + 1*1)/4 = 2.5. With groups of 2 and 2, this average is still 2. So group sizes of 3 and 1 are better. This would also mean that A=12, C=12 is the optimal result in the above example.


>________________________________
> From: Toby Pereira <tdp201b at yahoo.co.uk>
>To: Forest Simmons <fsimmons at pcc.edu>; EM <election-methods at lists.electorama.com> 
>Sent: Sunday, 9 November 2014, 18:48
>Subject: Re: [EM] PR for ethnically polarized electorates (Forest Simmons)
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>>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):
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>>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.)
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>Is this definitely the best system? If you have these approval ballots:
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>2: A
>10: A, B
>1: B, C
>9: C
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>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:
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>1: B, C
>9: C
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>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.
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