[EM]

[Alex Small]

Adam wrote:

>It seems clear that only the Condorcet winner (if one exists) will produce
>a Nash equilibrium.

Are you suggesting that if there is no Condorcet winner there is no Nash
equilibrium, or that if there is a Condorcet winner all of the Nash
equilibria will elect the Condorcet winner, or both?

The first option is false from what I understand (I thought Nash got his
prize and movie for proving that there is always at least one equilibrium,
given some very general assumptions).

The second seems attractive, and would be a powerful counter-argument to
many AV criticisms if true, but I'm not convinced of its veracity.

>Although certain dogmatic approaches in approval voting adjustment can
>produce a cycle, this doesn't mean a Nash equilibrium does not exist.

I understand that there will still be a Nash equilibrium in the presence of
a cycle (under certain polling assumptions).  I was wondering what the
general conditions are (making certain assumptions about voter behavior in
the presence of repeated polling) for equilibria where additional polls do
not change the outcome.

Those equilibria may or may not also be Nash equilibria, since the polling
assumptions that I've seen usually assume that people distinguish between
the top 2 in revising their strategies.  That does not encompass all
possible strategic adjustments, however, so it is not entirely clear to me
that repeated polling will always find the Nash equilibrium and/or
Condorcet winner.  I'd like to hope so, however.  Anyway, it's an
interesting question to explore.

Alex