[EM] math 103 website - Arrow & Saari

[Joseph Malkevitch]

The insight that some of the mathematics that has been done in political science gives is
that part of the reason there is so much dispute about elections, apportionment, etc. is
that there are no methods that meet all the fairness criteria that one would like. Since
there is no "perfect" method people no argue over which of the criteria one might like
are the most important. Based on this subset of fairness properties they assert that one
method is the best, but people who believe another subset of fairness properties are
better arrive at a different method to endorse.

Regards,

Joe

Steve Barney wrote:

> 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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>
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--
Joseph Malkevitch    |
Mathematics Dept.    |
York College(CUNY)   |
Jamaica, NY 11451

Phone: 718-262-2551
Web page:
http://www.york.cuny.edu/~malk