I am definitely not intending an argument but once again
we've hit upon how slippery the language can be without proper
context.
In physical sciences, "there are 11 equilibria" would be
expressed as there is no "equilibrium but there are 11 stable solutions to the
system." Perhaps "never the twain shall meet", but it would be nice if the
vocabulary were cross-discipline.
The way Nash defined a "Nash equilibrium" there can be more
than one, which is part and parcel of the difficulties social scientists have.
Chemists faced with a reaction that beuatifully changes the container of a flask
from blue-on-top and red-on-bottom to red-on-top and blue-on-bottom describe an
"oscillating equilibrium". Mathemations would call it a
bifurcation.
I think my point (if I had one) was that we should be
careful about how we use terms. A "Nash equilibrium" is defined in terms of
strategies and counter-strategies. It is not an inherent attribute of any voting
method. By Nash's definitions if there are well-defined game-players voting as
blocs then one or more Nash equilibria can be established regardless of the
counting method (I think it has been written here that someone has proven
that).
Thanks for the wishes, and the same to
all!
On 12/24/05, Paul Kislanko <[EMAIL PROTECTED]> wrote:
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of rob brown
Sent: Saturday, December 24, 2005 4:11 PM
To: Paul Kislanko
Cc: [email protected]
Subject: Re: [EM] Approval Voting elections don't always have an equilibriumRob Brown wrote: I'm a little curious, since you seem to talk about multiple voters switching their vote together....maybe this really represents a situation where there are multiple equilibriums, as opposed to no equilibriums?"On the surface, "multiple equilibria" is kind of an oxymoron, but the notion may be made precise.
Hmmm, aside from my glaring error in pluralizing "equilibrium" :) .... I'm pretty sure that the concept of equilibrium allows there to be more than one.
For instance Nash's famous proof is that there is *at least* one Nash equilibrium for certain well defined types of games:
In this article they give an example where there are 11 equilibria:
http://en.wikipedia.org/wiki/Nash_equilibriumAnyway, as we approach the end of another Western calendar year, may I take this opportunity to wish everyone well.
Likewise, and have a Merry Christmas as well if you celebrate such a thing. :)
-rob
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