[EM] math 103 website - Arrow & Saari

[Steve Barney]

Election Methods list:

Many introductory math textbooks, and the webpage <DEMOREP1 at aol.com> referred
us to in a recent message, draw too strong a conclusion from Arrow's Theorem.
The assertion that:

"Mathematical economist Kenneth Arrow proved (in 1952) that there is NO
consistent method of making a fair choice among three or more candidates. This
remarkable result assures us that there is no single election procedure that
can always fairly decide the outcome of an election that involves more than two
candidates or alternatives"
--http://www.ctl.ua.edu/math103/Voting/overvw1.htm#Introduction


is not quite true. His theorem only proves that there is no method which can
satisfy all of his fairness criteria. In other words, Arrow proved that his
criteria are inconsistent with one another. We must remember that "fairness" is
not a strictly objective thing. It necessarily involves an evaluative judgment,
and is based on questionable intuitions. Fairness goes outside of the realm of
factual truth and falsity, and into the realm of the good and bad. The realm of
the good and bad is not a matter of mere mechanics. Fairness cannot be
mathematically proven one way or the other. Arrow's Theorem may be interpreted
as providing a good reason to subject his fairness criteria to further
scrutiny, to try to understand why his particular criteria are inconsistent
with each other, and to come up with more satisfactory results with other
elementary fairness criteria or axioms.
	I recommend reading Donald Saari's new book, 

		_Decisions and Elections_
		Cambridge University Press
		October 2001
		http://www.cup.org/


in which he interprets and scrutinizes Arrow's Theorem in exactly this way, and
comes up with more satisfying results. Among other things, he finds that, if
Arrow's "binary independence" condition is slightly modified so as to require a
procedure to pay attention to the strength of a voters preferences (he calls
his version the "intensity of binary independence" condition), then the Borda
Count procedure solves the problem and satisfies the theorem. 
	I am no professional voting theorist, but I have studied this subject and his
work in some depth, and I think this is a very important book. I wouldn't be
surprised if Saari is rewarded with a Noble Prize in Economics for his work -
at least two other ground breaking voting theorists, Sen and Arrow, have
received them.

Steve Barney, student
University of Wisconsin Oshkosh

> Date: Sat, 24 Nov 2001 20:14:51 EST
> From: DEMOREP1 at aol.com
> To: election-methods-list at eskimo.com
> Subject: [EM] math 103 website
> 
> http://www.ctl.ua.edu/math103/
> 
> has some info about the math of voting.
> 

BCC: SS, Saari


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