[EM] Does IRV elect "majority winners?"
km-elmet at broadpark.no
Fri Jan 9 01:57:04 PST 2009
Dave Ketchum wrote:
> On Thu, 08 Jan 2009 11:51:36 +0100 Kristofer Munsterhjelm wrote:
>> The point is that it's an advantage to the voters to express their
>> thoughts in this manner. It's kind of like if Condorcet weighted votes
>> by 1 / (number of ranks specified) so that it made sense to bullet-vote.
> It is a convenience, but no advantage as to power of their votes.
It's a mere convenience to Condorcet voters. To Range voters, voting
Approval style (certain edge cases notwithstanding) is a definite power
Say that the election is so far A: 99.8, B: 99.4, C: 37.4, and your
sincere preference is A: 0.4, B: 0.7, C: 0.2. You'd prefer B to win, so
you say A: 0, B: 1, C: 0.
>>>>> I am still trying to promote series thought as to need for a
>>>>> majority for other than Plurality or Approval.
>>>> A worst-case point of view might be to consider the groups maximally
>>>> different. That is, nobody who voted A > B also voted A > C. From
>>>> that point of view, and a strict interpretation of "majority", one
>>>> would have to have the weakest victory be one of a majority - that
>>>> is, for the candidate X so that the magnitude of the win of A
>>>> against X is least, A must beat X by a majority.
>>> Let me offer bullet voting in Condorcet:
>>> 32 A
>>> 33 B
>>> 34 C
>>> C wins because, with 99 voters, C's 34 makes it CW.
>> That's true. I was talking about Condorcet majorities, though, and
>> none of those would have such a majority.
>> In general, if you have a voting method and everybody bullet-votes,
>> then you pretty much have to reduce to Plurality, since there's no
>> other information available.
> I do not HAVE to reduce Condorcet to Plurality here, for the voters have
> provided valid Condorcet votes.
> However, if bullet voting is common enough in Condorcet elections, it
> could make sense to count as if Plurality until ranking is seen, and
> then adjust and continue counting by Condorcet rules.
What I mean is that if you have some method, and the input is only
bullet-vote ballots, the method pretty much has to act as Plurality
would in that case. That is, the method "reduces" to Plurality in the
case of everybody bullet-voting.
Condorcet reduces to Plurality since if all votes are bullet votes,
they're effectively of the form
A > B = C = D
B > A = C = D
C > A = B = D
meaning that a vote for whoever was bullet-voted is a vote for that
candidate in preference to all other candidates, hence a candidate that
would win Plurality is a CW if everybody bullet-votes.
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