[EM] Multiwinner Condorcet generalization on 1D politics

[Kristofer Munsterhjelm]

Diego Santos wrote:
> 2009/2/15 Dan Bishop <danbishop04 at gmail.com <mailto:danbishop04 at gmail.com>>
> 
>     STV-CLE just happens to work the best when the political spectrum is
>     one-dimensional: Candidates are eliminated at the ends of the
>     spectrum until someone has a quota, and the process continues until
>     candidates are neatly spaced a quota apart.
> 
>     But with multiple dimensions, the CLs' votes get split among
>     multiple candidates, so you have to eliminate more candidates until
>     someone meets quota.  This creates a much stronger centrist bias
>     than the 1-dimensional case.
> 
> 
> The flaw in STV-CLE I see is that the candidate elimination heuristics 
> is based in a majoritarian criterion in a PR method. I think that a good 
> heuristic to eliminate a candidate should be based a PR quota, like 
> Newland-Britton. Some months ago I desgined the "Bucklin elimination 
> STV" (I don't have a definite name for it). When no candidate reaches a 
> quota, then later preferences are added until some candidadate reaches 
> the quota. But, instead of this candidate is considered elected, the 
> candidate with the least sum is eliminated. Some examples with this 
> method has generated good outcomes.

What's so tricky about PR is that in some respects it's majoritarian and 
in others not. For instance, in a situation where you have candidates 
A1..An and a Condorcet type method elects A1, then if duplicate all 
ballots, only changing A1 to B1, A2 to B2, etc, so that one "faction" of 
half the electorate votes as before, and the other faction votes the 
same way but with B* instead of A*, then A1 and B1 should win. That's 
both non-majoritarian (recognizing the factions) and majoritarian 
(within the factions).

Your method may be nonmonotonic, since many elimination methods are. 
Have you tried the other Bucklin generalization, where one elects the 
candidate that exceeds the quota and then does a reweighting? I suppose 
elimination gets you out of having to reweight.

Perhaps that idea could be used for my "weighted positional STV" method 
where I never got reweighting to work properly.