[EM] Re: Election-methods digest, Vol 1 #146 - 9 msgs

John B. Hodges jbhodges at usit.net
Mon Jul 7 16:25:04 PDT 2003

Bart Ingles wrote:
>Date: Sun, 06 Jul 2003 19:01:45 -0700
>From: Bart Ingles <bartman at netgate.net>
>Subject: Re: [EM] request for reading matter
>"John B. Hodges" wrote:
>  > I've read a book by Donald Saari, CHAOTIC ELECTIONS, in which Saari
>>  finds 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
>(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
>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 

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 
John B. Hodges, jbhodges@   @usit.net
The two-party system is obsolete and dysfunctional.
Better forms of democracy: www.fairvote.org

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