On Tue, May 27, 2003 at 10:33:31AM -0400, Andrew Pimlott wrote:
> > Which makes D win, rather than A, B or C.
> Unfortunately, that doesn't mean this is not the best strategy.
Sure it does: if their sincere preferences were "A,B,C > D" in all cases,
(whatever their preferences amongst A, B and C) then they've all got
the worst possible result.
> It could be that the best strategy, applied by everyone, tends to
> produce stalemate. :-/
If that's not what they want, then, by definition it's not the best
possible strategy.
For example, let's suppose you value an outcome of "A" as 100, "B" as 90,
"C" as 20, and "D" as 0. Your sincere preferences are "ABCD". Voting
sincerely gives odds of, say:
A wins: 0.4
B wins: 0.3
C wins: 0.2
D wins: 0.1
with a total score of 71. If voting insincerely gives you odds of:
A wins: 0.5
B wins: 0.1
C wins: 0.1
D wins: 0.3
with a total score of 61, you've had an overall loss and it wouldn't be
strategic to vote that way at all. Obviously it depends on exactly what
values you're going to assign, and what the probabilities really are,
but the strategy of voting your first preference, then the default option
simply doesn't work.
> However, throw in one more ADBC vote, and Concorcet+SSD will declare
> A the winner, whereas the proposed method will be stuck on D.
Huh? If you have:
21 ADBC
20 BDAC
20 CDAB
you still have D beats A by 40:21, D beats B by 41:20, D beats C by 41:20.
Note that if your strategy is "keep rerunning the vote 'til everyone
agrees that A is the best", then your sincere preference really is "ADBC"
-- that is, you really do think further discussion is a better result
than B or C.
Cheers,
aj
--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
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