Sorry for the (old) repeat, but Arrow's Impossibility Theorem came up
at last Friam, so I thought I'd resend the past post.
The conversation relating to AIT included noting that the US two
party scheme does not escape the issue, due to the primaries
basically being a tournament run off amongst 3 or more candidates,
and that the parties themselves are built from several coalitions,
thus are greater than a 2-choice vote/game.
One thought I had on the matter was:
- Let everyone vote in both primaries
- Hold all primaries on the same day
BTW: Since this was written, Robert Holmes discussed with several of
us one of the fair voting schemes in the UK. I forget the details,
but the aim was to insure the individual voters maximized their input
into the vote. Robert -- do you know where that scheme fits into AIT?
I would like to add that AIT is germane to ABM: may of the models
have agents voting amongst each other for access to resources, and
similarly, voting within themselves for behavior rules, often with
knowledge of the community's preferences. Both are within AIT, I'd
guess.
We may want to put our heads together at an upcoming wedtech to see
if we understand this, and its impact on our work.
-- Owen
Begin forwarded message:
From: Owen Densmore [EMAIL PROTECTED]
Date: December 18, 2003 10:20:05 AM MST
To: The Friday Morning Complexity Coffee Group friam@redfish.com
Subject: [FRIAM] Arrow's Impossibility Theorem
Reply-To: The Friday Morning Complexity Coffee Group
Friam@redfish.com
During the last Friam, we got talking about voting and Arrow's
Impossibility Theorem came up. It basically discusses anomalies in
voting when there are more than two choices being voted upon.
The result depends strongly on how the votes are tallied. So for
example, in our last election, due to having three candidates, we
entered the Arrow regime. But spoilers like Ralph are not the
only weirdness.
The html references below have interesting examples, and the pdf
reference is a paper by SFI's John Geanakoplos who gave a public
lecture last year.
Fair voting schemes are getting some air-time now a-days. There
are several forms, but the most popular I think is that you
basically rank your candidates in order of preference, the top-
most being your current vote. There are several run-offs which
eliminate the poorest performer and let you vote again, now with
the highest of your ranks still available. This insures you always
have a vote if you want one. This would have won the election here
for Gore, for example, presuming the Nader votes would favor Gore.
Various web pages with examples:
http://www.udel.edu/johnmack/frec444/444voting.html
https://econ.gsia.cmu.edu/Freshman_Seminar/notes_on_arrow.htm
http://www.personal.psu.edu/staff/m/j/mjd1/
arrowimpossibilitytheorem.htm
http://www.sjsu.edu/faculty/watkins/arrow.htm
Three proofs by John Geanakoplos
http://cowles.econ.yale.edu/P/cd/d11a/d1123-r.pdf
Owen Densmore 908 Camino Santander Santa Fe, NM 87505
[EMAIL PROTECTED]Cell: 505-570-0168 Home: 505-988-3787
AIM:owendensmore http://complexityworkshop.com http://
backspaces.net
FRIAM Applied Complexity Group listserv
Meets Fridays 9AM @ Jane's Cafe
Lecture schedule, archives, unsubscribe, etc.:
http://www.friam.org
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
