[EM] Naming equilibria and approval strategy

Alex Small alex_small2002 at yahoo.com
Thu Nov 25 21:14:12 PST 2004

OK, so there are many different ways to generalize/extend/apply/whatever the concept of Nash equilibrium to voting, and my preferred formalism is hardly the only way to do it.  I am no longer interested in the issue of who gave what name to what.  Whenever I wish to discuss a particular sort of equilibrium, I will simply specify the conditions for the equilibrium under consideration and go from there.
I will, however, observe that it is probably not a good idea to apply the name "Nash" to an equilibrium that doesn't always exist.  One of the beautiful things about Nash's result is that his equilibria always exist as long as some fairly non-restrictive conditions are met.  The ubiquity of his equilibria is what makes his concept so broadly applicable and important.  If one uses the word "Nash" in the name for an equilibrium condition that can't always be met, it deviates from the original spirit of the term.
However, that is purely a matter of taste, and not something that I have any more desire to argue over.  I've said what I have to say on that.
And, as long as I'm issuing mea culpas, I was incorrect to say that cardinal preferences aren't a factor in Approval strategy.  I was talking about the context of people with adequate information (usually after-the-fact) but I failed to make that clear, and so my statement as originally made was incorrect.  I still maintain, however, that when people have adequate information their _ordinal_ preferences are all that matter.  If you and I both think that A>B>C, and we have adequate information to predict the consequences of our actions, we will vote the same way.  (Assuming that our only goal is to elect the best possible candidate from the set {A, B, C}.  Of course, if we have other goals, such as sending messages to influence parties over the long term, then obviously things become more complicated.)
Anyway, I hope that straightens things out.

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