I wonder what your goal is in reducing the number of Nash equilibria in
an election. If you're trying to use the modified election method as a
model for studying the old method, then you might also look at some
alternative types of equilibria which are more restrictive than the Nash
equilibrium. The "trembling hand" equilibrium randomizes player actions,
but it uses infinitesimal probabilities. I've done some analysis of
elections using a new type of equilibrium called a Cabal equilibrium,
but it didn't get much attention when I posted it here. (If you want to
read about it: http://www.spaceandgames.com/?p=106
http://www.spaceandgames.com/?p=134 )
My other guess is that your goal is to increase voter turnout by
increasing a voter's probability of changing the election outcome.
However, I think changing this probability from 0 to 10^-10,000 is
inconsequential.
- Peter de Blanc
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