[EM] How to fix the flawed "Nash equilibrium" concept for voting-theory purposes

[Raph Frank]

On Tue, Apr 13, 2010 at 5:02 PM, Jameson Quinn <jameson.quinn at gmail.com> wrote:
> This is a great idea at its heart, but I can see a couple of problems which need fixing. For one thing, you didn't specify that the sum of the means for all vote types must be 1.

Actually, it would probably be better to require 1 ballot type to have
a mean of 1 and the rest have a mean of zero.

Otherwise, it isn't the same voting system.

> For another, as stated, this raises the possibility of negative totals for certain vote
> types - something which many voting systems couldn't handle. For a third, if you
> keep the variance for each vote type constant, then total variance in "where my
> vote goes" depends on the square root of the number of vote types - especially
> problematic for Range voting, which has an unmanageably large number of
> vote types, even for few candidates.

My proposal resolves most of those issues, after the votes are case,
each ballot has a probability of p to be excluded from the count.

However, for most of the theorems that that this would depend on, the
variance wouldn't actually matter.  You could set it that the variance
is 1 part in a billion.

This would create the slope to prevent the (meta-stable) equilibria.

> To be clear: in the Gandhi/Hitler case, the situation where 100% vote Hitler somehow against their will, is not a Nash equilibrium, because each voter sees that there is some finite (though smaller than the number of atoms in the visible universe) probability that a poisson distribution around 1 will be greater than a poisson distribution around the 99,999 other voters still voting Hitler.

Right, it adds a possibility for each vote to affect the result.

> However, I actually think that this distribution is not realistic.

OTOH, it is also unrealistic that voters would only care about the outcome.

Most people would prefer a situation where their favourite loses 55-45
than one where they lose 70-30.