[EM] Cabal equilibria in voting
Jameson Quinn
jameson.quinn at gmail.com
Tue Jan 26 20:22:50 PST 2010
2010/1/26 Peter de Blanc <peter at spaceandgames.com>
> Hi,
>
> I've been doing some analysis of strategic voting - specifically, looking
> for equilibrium strategies. Nash equilibria are of course not very useful
> for elections, because almost anything is a Nash equilibrium. So I've
> defined a less inclusive type of equilibrium called a cabal equilibrium.
>
Interesting. I like the idea of cabal equilibrium, it's useful in voting
analysis.
>
> The very short version of the result is that most popular voting methods
> (plurality, approval, Condorcet, IRV) have a cabal equilibrium iff there's a
> Condorcet winner, and a cabal equilibrium always elects a Condorcet winner.
>
You can add Range to that list, of course. However, you have NOT shown the
conditions for honest voting to be a cabal equilibrium in any of these
systems. To me, an interesting question would be: which Condorcet
tie-breaker has the smallest set of possible true preferences for N voters
for which honest voting is not a cabal equilibrium? In other words, which
Condorcet system has the least possibility for strategy? If there's no
closed formula or logical proof of the result, one could still answer the
question empirically, exhaustively enumerating all classes of possibilities
for some reasonable N.
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