This is almost identical with the final version of CD that I posted
before, at EM.
At that time, I meant "CD" to stand for "Co-operation/Defection". But
it was pointed out that "Chicken-Dilemma is the accepted name for the
problem. Also (and I knew this at the time, but missed its
importance), there are other co-operation/defection problems than the
chicken dilemma--or at least there's one other one, called "the
prisoner's dilemma". The prisoner's dilemma is much worse than the
chicken dilemma. Anyway, so now I mean "CD" to stand for Chicken
Dilemma. The name of this criterion is the Chicken Dilemma Criterion.
By the way, of course, unless it's Approval with only a few voters,
the voting chicken dilemma isn't as bad as the classic chicken
dilemma, in which you either co-operate or defect. In the voting
chicken dilemma, if, with Approval there are many voters, or if the
method is Score, you have non-probabilistic inbetween strategies. It's
as if, in the car-chicken-dilemma, you could tell the other driver, "I
am going to move halfway out of a head-on collision. The other half is
up to you. Suit yourself."
When there are few voters, and the method is Approval, then it's like
the classic chicken dilemma, where it's either an asymmetry that makes
it clear who has more right or motivation to defect, or else "mixed
strategy" (probabilistic choice between the two choices). But of
course, even in that situation described in this paragraph, you'd be
unlikely to actually need probabilistic choice, "mixed strategy". If
the rival-compromise is disgusting, or the conduct of hir voters is
inexcusable, then you'd just defect. Likewise if they defected last
time. So I don't know if, with voting, it would ever come to mixed
strategy in the situation described in this paragraph.
Of course, with Approval, with many voters, probabilistic voting is an
effective way to emulate Score's fractional ratings, and that's
something that I and others would often do in a chicken dilemma with
Approval with many voters, or with Score.
Anyway, I've only made a few small changes to CD. Here it is:
The Chicken Dilemma Criterion (CD):
Supporting definitions:
1. The A voters are the voters who prefer candidate A to every other
candidate. The B voters are the voters who prefer candidate B to every
other candidate.
2. The "other candidates" are the candidates other than A and B.
3. A particular voter votes sincerely if s/he doesn't falsify a
preference, or fail to vote a felt preference that the balloting
system in use would have allowed hir to vote in addition to the
preferences that s/he actually votes.
Premise:
1. The A voters and the B voters, combined, add up to more than half
of the voters in the election.
2. The A voters and the B voters all prefer both A and B to the other
candidates.
3. The A voters are more numerous than are the B voters.
4. Voting is sincere, except that the B voters refuse to vote A over anyone.
5. Candidate A would be the unique winner under sincere voting (...in
other words, if the B voters voted sincerely, as do all the other
voters).
Requirement:
B doesn't win.
[end of CD definition]
Mike Ossipoff
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