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

[Warren Smith]

I'm trying only to post on the election science foundation re this
topic, so please look there:
http://groups.google.com/group/electionsciencefoundation

There are a lot of developments there.

However since I see a bunch of comments built up at electorama, I will
try to process them now a bit and post (atypically) to both places:

Michael Allan:
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.

WDS REPLY: The idea of the Nash fix was not as an actual proposed
modification and "improvement" to a voting system.  (Indeed it seems
to me it makes it a slightly worse voting system.) It was instead to
make the Nash MODEL of strategic behavior within that voting system,
and the Nash CONCLUSIONS (i.e. the location of the equilibria) be more
realistic and useful.  I.e. one equilibrium is a useful thing to know
about.   10^10000 "equilibria" are a useless thing to know about.
This agrees with Allan, I guess.

> Raphfrk: 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.

--well, my Nash fix quantifies that. The "value" is it makes winning more likely
(even if only by a tiny amount) in the real world of random errors in
each vote caused
by cosmic rays affecting voter brains etc.   This gets quantified
and not ignored.  Even a tiny addition of this suffices to break the
logjam of exact equality that was causing Nash to look idiotic.
Just vague words like
"their side's number of votes" are however inadequate for general
abstract voting systems because they have no meaning.  But the Nash
fixes are precisely defined always (or can be).

> Michael Allan:
We could look at the real reasons for voting.
(Why do people keep doing it?  What do they hope for?)

--I think that is a separate topic.  (A related question is: why do
people vote honestly?)
Nevertheless, I do have a theory about it, based on group selection in
Darwinian evolution, tribe-wide utility not individual utility, see
   http://rangevoting.org/OmoUtil.html

Oddly enough my theory seems to coincide with Terry Bouricius's theory
in his post,
albeit I'm being much more nerdly about it.

Yet another question is, why do a lot more people vote a lot more
honestly, in some voting systems than others?  It appears
experimentally looking at how humans behave that voting in plurality
and IRV and Borda is highly dishonest, but in range voting is
substantially more honest.  I have some theories about that too... see
the "nursery effect" for a partial discussion:
   http://rangevoting.org/NurserySumm.html

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html