[EM] [ESF #939] Re: How to fix the flawed "Nash equilibrium" concept for voting-theory purposes

[Raph Frank]

On Wed, Apr 14, 2010 at 4:11 PM, Warren D. Smith (CRV cofounder,
http://RangeVoting.org) <warren.wds at gmail.com> wrote:
>
>> Clay: I think you're massively overcomplicating this. Just define it to be
>> more optimal to have Hitler win by 1 point than by 2.
>
> --no, you are massively oversimplifying this.

I agree with Warren here, the idea is to come up with a method that
works when applied to any voting method.

> Peter de Blanc apparently knew something I did not.  There is a notion
> of "trembling hand Nash equilibrium" I had not known about. Wikipedia
> says it was invented by Reinhard Selten 1975:
>
> http://en.wikipedia.org/wiki/Trembling_hand_perfect_equilibrium

Cool.  This means that every voter casts their vote with probability p
and a random vote with probability (1-p).  That is pretty close to my
suggestion, but with a non-vote rather than a random vote.

> DEFINITION OF ABSTRACT ALGORITHMIC VOTING SYSTEM:
> "votes" are arbitrary bitstrings and the "voting system" is an
> algorithm that outputs a finish order among the C candidates.  A
> "voting strategy" is an algorithm which
> inputs your honest candidate-utilities and whatever knowledge you have
> about the other voters, and outputs a vote.

Shouldn't there be a requirement that the strategy is reasonably effective?

Though I guess since you show that even this definition is not
possible, adding more restrictions isn't going to suddenly make it
work.

> OBVIOUS THEOREM:
> An all-is-one-honest voting strategy always exists (by the inverse-
> permutation argument mentioned above).

This is subject to the information requirement that you specified before.

Though, I guess you could use the law of large numbers to help.

With plurality, the strategy would be to vote for the candidates
probability that is monotonically decreasing from favourite to least
favourite.
(and lots of other methods)