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

[Michael Allan]

Jameson Quinn wrote:
> > This is a great idea at its heart, but I can see a couple of
> > problems which need fixing. ...

I will argue the opposite, that Raph and Warren's attempt to redeem
Nash is itself unredeemable.

> > To be clear: in the Gandhi/Hitler case, the situation where 100%
> > vote Hitler somehow against their will, is [no longer] a Nash
> > equilibrium, because each voter sees that there is some finite ...
> > probability that a poisson distribution around 1 will be greater
> > than a poisson distribution around the 99,999 other voters still
> > voting Hitler.
 
Raph Frank replies:
> Right, it adds a possibility for each vote to affect the result.

It's also an indication of the problem.  Consider these two facts:

 1. Current voting methods lack the Nash-redeeming addition.  In a
    typical election, no individual vote has any effect on the result.
    The effect is exactly zero.

 2. Voters nevertheless turn out in large numbers.

It follows that the individual voter is *not* attempting to affect the
results.  If we grant him/her a degree of competence and foresight, we
must conclude that voting is not a purposive-rational situation, and
we have little to gain from applying Nash's purposive-rational theory
to it.  Warren was right in the first place: "Nash says almost nothing
about voting.  It is worthless."  (But that's the end of it.)

People vote for social reasons.  In particular, voting appears to have
a largely communicative rationality behind it.  People like to express
themselves.  They also see it as their social duty, and so they feel
bound try their best (despite the hurdles we sometimes put in their
way).  Much follows from this, including a need to improve our voting
methods (big hurdle).  But wow! you guys are headed in exactly the
wrong direction!

Or am I wrong?
-- 
Michael Allan

Toronto, +1 647-436-4521
http://zelea.com/