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
advantage.
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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