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

[Michael Allan]

> > ... 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...
 
Raph Frank wrote:
> Another way of phrasing it would be that people see value in
> increasing their side's total number of votes... Thus, each vote
> does in fact count.

You may say that, but it does not follow from the facts.  The fact of
a particular effect does not reveal the purpose of the act.  A vote
may have any number of particular and general effects, including the
shifting of a digit or two in a register somewhere (as you suggest),
but no single one of them (nor even the sum) need be of importance to
the voter.

What does follow is a conclusion from the counterfact.  Where a given
effect is *not* present, and where no rational actor could expect it,
we may safely conclude that it was *not* the purpose of the act.
Therefore the facts *do* support this conclusion:

  The individual voter is *not* attempting to affect the results of
  the election.

> Also, each person's vote might make a difference.

In actuality, however, it makes no difference to the election.  Do you
not agree?  Time and time again the voter casts her vote, and never
once does it have an effect on the results.  Yet, come the next
election, there she is, once again, casting her vote.

Negative implications of this: Nash's theorem (with or without fuzzy
logic) is inapplicable.  More generally, purposive-rational models of
ego-centric behaviour are unlikely to be made serviceable for voting
theory.

Positive implications: We could look at the real reasons for voting.
(Why do people keep doing it?  What do they hope for?)  We could
re-build our theories and re-design our voting methods accordingly.

-- 
Michael Allan

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