[EM] Multiwinner Condorcet generalization on 1D politics

[Diego Santos]

2009/2/17 Kristofer Munsterhjelm <km-elmet at broadpark.no>

> 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.


Yes, this method probably violates monotonicity.


> 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.


I tried a method that after I discovered identical to Benham's Generalized
Bucklin PR 2.3.

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

Maybe monotonicity failure can be avoided if instead of eliminate some
candidate, just collapse the ballots where this candidate is in first with
its next preferences.

-- 
________________________________
Diego Renato dos Santos
Mestrando em Ciência da Computação
COPIN - UFCG
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