[EM] Nash equilibrium for voting?

[MIKE OSSIPOFF]

When I brought up Nash equilibrium here, I suggested that, for
public elections, the following is a straightforward definition,
in keeping with the intent of the usual definition:

For a particular situation (configuration of candidates, voters,
and voters' utilities for the candidates), a voting Nash equilibrium
is a configuration of votes such that no group of voters have the
same candidate-utilities, and who have voted in the same way, can
improve the outcome for themselves by changing their voting strategy
in the same way.

[end of definition]

Blake posted a different definition, in which (if I've got it right
without looking it up) a Nash equilibrium is a configuration of votes
such that no group of voters can improve the outcome for themselves
by changing their voting strategy.

I'm bringing this up now because it might not be completely obvious
what is the most useful way to define Nash equilibrium for voting.
But it seems to me that Blake's definition violates the intent
of the usual definition, which speaks of one player _unilaterally_
changing his strategy.

The familiar definition of Nash equilbrium seems interested in
what a player can gain for himself without being sure that anyone
else is changing their strategy. The natural public election extension
of that is what a faction can gain for itself without any assumtion
that other factions will vote differently.

So I'm going to keep the definition that I posted before, the
1st one in this message.  But, as I said, I bring this up now to
find out if anyone else has an opinion about what definition of
Nash equilibrium for voting would be most useful or meaningful.

I know that Richard questioned the meaningfulness of that
equilibrium, because it sounds like bloc voting. I replied that
in any case, an outcome that a faction can improve on for themselves
isn't a stable outcome, and Plurality, IRV, and the margins methods
can have, and will often have, situations in which the only outcomes
that aren't unstable in that way are ones in which people are
defensively order-reversing. That can't be gotten around. You can
kiss the margins methods goodbye as a proposal for public elections.

Mike Ossipoff



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