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

[Jameson Quinn]

2010/4/14 Raph Frank <raphfrk at gmail.com>

> On Wed, Apr 14, 2010 at 11:06 AM, Michael Allan <mike at zelea.com> wrote:
> > 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.)
>
> 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.
>
> Also, each person's vote might make a difference.
>
>
This is, of course, true. Public voting is more a ritual process for
communicating, building community, and/or transferring sovereignty, than it
is a purposive-rational act. Nevertheless, its ritual power comes from the
fact that it superficially *appears* to be rational. People want their votes
to bring their preferred candidate(s) apparently "closer" to winning, so
they can feel that they "contributed" in some sense towards a rational goal.

Thus, it is still productive to search for an electoral system that is, at
the least, monotonic, and also as strategy-free as possible (without
neglecting goals such as simplicity and transparency). Since by the
strictest definitions, no system is strategy-free, it is worthwhile to
search for definitions which help in sorting "better" systems from "worse"
ones. I think that the trembling-hand Nash equilibrium is one such
definition. Still, there are details of it's implementation and implications
that haven't been publicly worked out, and that's exactly what this list is
for.

JQ
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