Date: Sun, 06 Jul 2003 19:01:45 -0700 From: Bart Ingles <[EMAIL PROTECTED]> Subject: Re: [EM] request for reading matter
"John B. Hodges" wrote: > I've read a book by Donald Saari, CHAOTIC ELECTIONS, in which Saarifinds unique virtues in the Borda Count and many weaknesses in> Approval. (snip) Can y'all recommend some text that > replies to Saari regarding Approval?
Try the following four-article debate in Public Choice http://www.kluweronline.com/issn/0048-5829 (I recommend checking your university library for these):
(1) The problem of indeterminacy in approval, multiple, and truncated voting systems Donald G. Saari and Jill Van Newenhizen Public Choice 59: 101-120 (1988) (c) Kluwer Academic Publishers
(2) The responsiveness of approval voting: Comments on Saari and Van Newenhizen Steven J. Brams, Peter C. Fishburn, Samuel Merrill III Public Choice 59: 121-131 (1988)
(3) Is approval voting an 'unmitigated evil'?: A response to Brams, Fishburn, and Merrill Saari, Van Newenhizen Public Choice 59:133-147
(4) Rejoinder to Saari and Van Newenhizen Brams, Fishburn, Merrill Public Choice 59:149
JBH here- I read the journal articles above. (Shelved under H35 P8X ) I'll have to read them again, but my first impression is that Saari wiped the floor with Brams&company. Their final rejoinder is that he missed the point of their first rejoinder, and I'll have to reread the whole exchange to judge that.
The essence of his argument is in the math, the theorems he claims to prove and his interpretation of what they mean. Isolated examples and "nightmare scenarios" don't really prove anything, because no voting system is perfect. But I'll pass on one of the two examples he gives, as an "approval voting nightmare". You have a town of 10,000 people, choosing a Mayor. 9,999 people regard A as excellent, B as mediocre but passably competent, and C as a disaster. One voter (possibly C himself) regards C as excellent, B as passably competent, and A as a disaster. Everyone follows the recommended strategy for Approval voting of voting for all candidates that offer "above average" utility for the three candidates; so everyone votes for their top two. Tally is C gets one vote, A gets
9,999 votes, and B gets 10,000 and wins.
Saari uses the above example to illustrate that to avoid indeterminacy under Approval voting you have to have essential unanimity among the voters; an army of voter clones. The slightest departure from unanimity introduces a degree of indeterminacy. His general point about indeterminacy under Approval voting (and a class of other voting systems) is that WHATEVER your preferred rule may be for what the "correct" social choice may be, given a profile of voter preferences, an indeterminate voting rule offers you no reason to think you will get the correct choice. And, he argues, Approval voting is considerably more indeterminate, over a much wider range of possible voter preference profiles, than almost any other voting procedure.
Brams&Co argued that the indeterminacy of AV was not a fatal flaw but instead a great virtue, because it gave voters the chance to express their cardinal utilities in a way that determinate systems based on ordinal rankings did not. Saari argues that this is true only under very restrictive assumptions, essentially only when all voters divide the candidates into "the good guys" and "the bad guys" and are indifferent between members of each group. I'll have to reread (and read other people's commentary also) before I can form an opinion on that.
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John B. Hodges, jbhodges@ @usit.net
The two-party system is obsolete and dysfunctional.
Better forms of democracy: www.fairvote.org
REAL CHOICES, NEW VOICES, by Douglas J. Amy
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