[EM] PR for ethnically polarized electorates

Wed Jun 25 16:29:56 PDT 2014

Now let's take up question 2 which, in view of our tentative answer to
question one, can be reformulated in the following way:

Given honest benefit expectations

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

from the parties A, B, and M,

how to elicit the approvals that we needed as input to our answer to
question one?

The input approvals for our Martin Harper inspired method were

10 A
30 A, M
45 B, M
15 B

There is a pretty good case that these would be sincere approvals, so why
not just instruct the voters to list the parties that they approve of?

The trouble is that under direct approval voting the above approvals would
not form a Nash equilibrium.  In particular the third faction would have a
great incentive to defect from this position.

to see this let's compare the expected benefit of the third faction members
before and after unilateral defection :

Before:  10*0+30*80+45*80+15*100 = 7500
After:     10*0+30*80+45*100+15*100 = 8400

Their expectation difference is 45*(100-80)=900

Here's the full payoff matrix for the respective middle factions:

                        defect                       cooperate

defect .............(4000, 6000)...............(7600, 5100)

cooperate.........(3400, 8400)..............(7000, 7500)

In other words, we are dealing with a game of "prisoner's dilemma" which
has the greatest total payoff when neither player defects, but the only
equilibrium is the position of both players defecting, which has the worst
total payoff.

In summary, our analysis has revealed two things:  (1) It shows that direct
approval voting gives strong game theoretic incentives for disapproving M
in the two middle factions. (2) It shows that best over-all expectation is
the case in which the two middle factions do approve M.  This second point
is the "dispassionate" response that I promised to Toby's question about
the desirability of M getting the full middle 75 percent.

In the next installment I will explainn how to solve this dilemma.

Forest

Date: Wed, 25 Jun 2014 15:15:44 -0700
> From: Forest Simmons <fsimmons at pcc.edu>
> To: Toby Pereira <tdp201b at yahoo.co.uk>
> Cc: EM <election-methods at lists.electorama.com>
> Subject: Re: [EM] PR for ethnically polarized electorates
> Message-ID:
>         <CAP29oneWAh9dhh3YoOtcJ=
> 1Qbv2cCM6RLLbeyn8VTYeNGuzW_A at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Thanks to Juho and Toby for their insights.
>
> It is true, as they suggest, that question 2 is the harder one.
>
> 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.)
>
> I am now pointing out that Martin Harper's vote transfer scheme is a simple
> way of designing a PR method (based on approval ballots) that solves
> problem one. In the given example let us assume that the truncations are
> reliable indicators of disapproval.  Then the approval ballots are
>
> 10 A
> 30 A, M
> 45 B, M
> 15 B
>
> The approval order is M>B>A
>
> The first faction ballots all count for A.  The last faction ballots all
> count for B, and the other 75 ballots all count for M, yielding the desired
> quotas of 10, 15, and 75 respectively.
>
> Toby asks the question of why this M heavy proportion is so desirable.
>
> One answer is that in these polarized countries (the ones that inspired
> this thread in the first place) the fewer extremists in power the better.
> But in my next post, the one addressing question two, I will give a more
> dispassionate answer to that question.
>
> Forest
>
>
>
> On Wed, Jun 25, 2014 at 12:23 PM, Toby Pereira <tdp201b at yahoo.co.uk>
> wrote:
>
> > At first glance it seems that 10, 15 and 75 for A, B, M respectively
> seems
> > a little optimistic from a voting system. It's not just that party list
> PR
> > would shut out M - I can't see any system calling itself PR could award
> the
> > seats in those proportions. Something like reweighted range voting or the
> > score PR system I detailed a couple of weeks ago would stop M being shut
> > out with honest voting, but they would go nowhere near as far as you are
> > suggesting.
> >
> > Regarding voter honesty, it may be difficult to ensure it anyway with a
> > normal score-based PR method, but I can't see how you could get it to
> work
> > given that you would want the middle two factions' support for A and B to
> > be effectively ignored. To be clear, 10, 15, 75 are the proportions
> > you'd expect if the 75 people who gave a positive score to M completely
> > lost all their support for A/B and raised M to from 80 to 100.
> >
> >    *From:* Forest Simmons <fsimmons at pcc.edu>
> > *To:* EM <election-methods at lists.electorama.com>
> > *Sent:* Wednesday, 25 June 2014, 1:21
> > *Subject:* [EM] PR for ethnically polarized electorates
> >
> > In Rwanda it was the Hutu and the Tutsi tribal division.  In Iraq the
> > Sunni, Shia, and Kurds.  In the former Yugoslavia it was the Serbs Croats
> > and Bosnians.  There are similar divisions today in the Ukraine, Israel,
> > Syria, Bolivia, etc.
> >
> > What do they have in common?  A need for electing a representative body
> > that has as many moderates and as much consensus as possible so that
> > minorities are not so desperate for separation, i.e. to prevent the
> scourge
> > of Balkanization that seems to be spreading like a plague.
> >
> > 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?
> >
> > Forest
> >
> >
> > ----
>
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