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

[Michael Allan]

Warren, Jameson and Kristofer,

> > For my part, I argue that Nash can *never* be applied within the
> > context of voting.  The reality as evidenced by the empirical data
> > (in vivo) invalidates the basic assumptions of Nash.  Individual
> > voters are *not* attempting to affect the outcome of elections.
> > As this reality contradicts Nash, we cannot turn around and look
> > back at it through the lenses of Nash.

Warren Smith wrote:
> ... I think you are pretty much right... But I think there is a
> deeper truth....  First of all, as I said in the ESF thread quoting
> Selten, it is interesting to consider the consequences of
> maximally-rational behavior, even if humans aren't it.  Second,
> there is the also-interesting issue of what humans actually do.  And
> hopefully there is some relation between them.

Precisely that hope is without foundation.  There can be no useful
relation between a model that assumes a maximum of purposive
rationality and a reality that demonstrates none.  No voter ever
attempts to improve her standing in the electoral "game", because no
single vote ever affects the outcome of a typical election.

Nash's model may still be useful for analyzing current voting methods,
as you suggest, but I believe those methods are (in a deeper sense)
wrong.  In this sense, it is not the voter's behaviour that is
irrational, but rather our electoral practices. (more below)

Jameson Quinn wrote:
> I agree with your premises, but not your conclusions. Voters are not
> purposive-rational, it's true. But that doesn't invalidate the
> conclusions of a Nash analysis, it just makes them tentative. Voters
> DO think of themselves as being purposive, even when they clearly
> aren't...

I'm not so sure.  Imagine a voter saying: "It's a good thing I voted
today, or the other side would have won the election!"

> > More generally (I argue) purposive-rational models of ego-centric
> > behaviour are unlikely to be made serviceable for voting theory...

Kristofer Munsterhjelm wrote:
> Whether or not that is the case for individual voters, one could
> still use purposive-rational models for political parties. This
> would be useful in considering what sort of "how to vote"
> instructions a party might provide to their voters in order to
> strategize on a wide scale...

Right.  When it comes to elections, a party is naturally self-seeking
and goal-oriented.  If we model the party as a human player, it
definitely "wants" to win.  Usually it also has the means of affecting
the outcome.

But I think that individual voters must also have a place in any
overall theory of voting.  Consider two facts (a,c) that such a theory
(b) must explain:

  a) The institutional fact of current electoral practices,
     procedures, voting methods, and so forth.

  b) Theory to explain the rationality of both (a) and (c), and how
     they interrelate.  Why do we have *these* particular electoral
     practices?  Why does the voter participate in them?

  c) The behavioural fact of the individual's voting to no selfish
     end, in pursuit of no personal interest.

Both (a) and (c) are facts of considerable weight and relevance.  If
(b) is to be useful as a theory, then we might expect it to explain
both.  Warren and Raph suggested the Nash model (for sake of a), but
it is contradicted by (c).  You suggest retargetting the model such
that individual parties (not voters) are the players in the electoral
game.  This may be valid as far as it goes, but it still leaves (c)
unexplained.

Maybe no single theory can explain both facts?  The only way forward,
then, would be to reject one of the facts as being (in some sense)
wrong.  If we accept (a) current practice and (b) the body of mostly
purposive-rational theory that informs it, then a question mark is
left hanging over the individual votes.  Every vote cast in a mass
election is difficult to explain, and apparently irrational.

On the other hand, if we accept (c) voting for non-instrumental and
social reasons in the light of (b) a theory that can explain such
forms of rationality (Habermas for example), then doubt shifts to our
current electoral practices.  Something in our elections or voting
methods is wrong, or something is missing, because from the
perspective of the socially motivated voter, they are extremely
anti-social.

-- 
Michael Allan

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