[EM] PR for ethnically polarized electorates

[Juho Laatu]

Good questions.

My first easy answer is bicameralism. That's at least a clear start for discussing how one could reach some ideal distribution of representatives. Traditional proportional methods are good in picking the 40/60 representatives. That would be chamber number one ("proportional"). One (but not the only one) straight forward approach for the second ("compromise") chamber is to use single seat districts and some Condorcet method. (That gives us also local representation, that was not requested, but that could be one possible approach anyway.) The two chambers could be separate and have different duties, or could be combined into one "mixed" chamber.

On 25 Jun 2014, at 03:21, Forest Simmons <fsimmons at pcc.edu> wrote:
> 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?

With the given distribution of voter opinions it is possible that in the second chamber most representatives would come from M.  The bicameral approach would be balanced so that the respective sizes of the two chambers would be 10+15 and 75.

It is however possible that the distribution of the opinions is regional. In that case the second chamber could in an extreme situation consist of A and B representatives only. 40% of the districts could have a clear A majority, and 60% of the districts could have a clear B majority. Note however that if many of the single seat districts have also a meaningful minority of the other large group, the elected representatives would tend to be moderate, although representing one of the two major groupings.

One could balance this kind of (but milder) tendencies (that reduce the number of M representatives) by increasing the size of the second chamber. Another approach would be to give more power (e.g. some veto power) to the second chamber (I'll skip discussion on those possibilities and their possible problems in this mail). A third approach would be to use one nation wide multiseat district (or few multiseat districts) instead of numerous single seat districts in the second chamber. (The first chamber could have smaller districts than the second chamber in this approach.) Maybe something like using Condorcet to pick the first representative, then use some STV style approach to reduce the weight of those votes that supported this candidate, then pick the next representative etc. You could use this third approach also in a unicameral system to get the intended mix of A, B and M representatives at one go.

One could use a weight reduction algorithm where one reduces the weight of each vote in the pairwise comparisons (separately for each comparison) if that vote already has a representative that is ranked higher than both compared candidates.

> 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?

The proportional+Condorcet bicameral approach could have two separate ballots. Or if the districts and candidates are the same in both elections, one could use the first candidate of the ranked ballot in the first chamber election, and all the ranked candidates in the second chamber.

Let's assume that all the 45 B>M voters will defect and they will vote 45 B instead. If the second chamber uses single seat districts and Condorcet, truncation would be about as stupid as in Condorcet in general. Those voters would give up their ability to elect M representatives instead of A representatives in districts where B does not have majority.

The strategic questions become more interesting if the second chamber (or single chamber) has multiseat districts and uses the Condorcet + STV style approach to reduce the weight of the votes. If all voters bullet vote, the resulting balance could be 40/60. If A faction will not truncate, they will get some more M representatives instead of A representatives. I'll skip any more detailed analysis of what the balance will be in the discussed algoritms.

I guess that's enough to convey my first impressions and first simple arpproaches to covering this kind of compromise seeking needs. I'll reserve the right to change my opinions and tune the algorithms a bit further after giving them some more thought :-).

Juho