[EM] Multiwinner Condorcet generalization on 1D politics

[Kathy Dopp]

Diego,

Regardless of other possible flaws, your method is going to need to
recalculate the quota after each round because otherwise you could end
up with more winners than seats that need to be filled in a round.

Kathy

> Date: Tue, 17 Feb 2009 20:55:39 -0300
> From: Diego Santos <diego.renato at gmail.com>
> Subject: Re: [EM] Multiwinner Condorcet generalization on 1D politics
>
>> 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.
>
>