(Fwd) Condorcet counter-example (fwd)
seppley at alumni.caltech.edu
Fri Apr 5 19:53:47 PST 1996
(Rob, did you intentionally remove the [EM] subject prefix, or did
eskimo.com do that accidentally?)
Mike Ossipoff wrote:
>Weighted Voting, where voters assign point scores to
>the alternatives, and the alternative getting the most points wins,
>may meet IIAC, which Saari referred to as the Twins Test, but it
>fails the Majority Winner Criterion: Only the points systems can
>fail to elect an alternative that is the favorite of a majority
>of the voters, and which those voters indicate on their ballots
>as their favorite (as by giving the highest point score to, or
>by ranking 1st).
I think Saari would say the Majority Winner Criterion is
inappropriate in the example he provided. I asked him about a less
extreme example, where the apple lovers don't love chocolate almost
as much as apple:
| ,---------------- chocolate
+99 50 apple lovers
-50 99 chocoholics
I had presumed he'd say chocolate is the group preference here too,
but he replied he wouldn't say that either one is the preference.
I've asked him to let me know where the dividing line is.
>Aside from that, I don't understand what Saari's criticism is, in
>this example. Condorcet picks Chocolate, which only has 55% against
>it. Weighted voting also picks chocolate, if people vote sincerely,
>since the Apple people have no problem with Chocolate, and the
>Chocolate people despise Apple.
>So Condorcet picks the same alternative as Saari's proposal, Weighted
>Voting, in that example.
Saari's criticism wasn't ideally expressed, the way he worded his
example. It would look stronger if he'd turned it around: Start
with three variants of apple, which "fratricide" to elect chocolate.
Then the apples collude in a backroom: two drop out of the race and
an apple "steals" the election.
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