Election Methods list: Many introductory math textbooks, and the webpage <[EMAIL PROTECTED]> 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: [EMAIL PROTECTED] > To: [EMAIL PROTECTED] > Subject: [EM] math 103 website > > http://www.ctl.ua.edu/math103/ > > has some info about the math of voting. > BCC: SS, Saari ===== "Democracy"?: http://www1.umn.edu/irp/images/postcardAd2.jpg AR-NewsWI, a news service for Wisconsin animal advocates: http://groups.yahoo.com/group/AR-NewsWI/ __________________________________________________ Do You Yahoo!? Yahoo! GeoCities - quick and easy web site hosting, just $8.95/month. http://geocities.yahoo.com/ps/info1
