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Topic: Borda count
Replies: 9   Last Post: Nov 17, 2000 3:13 PM

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Posts: 1,815
Registered: 12/6/04
Re: Borda count
Posted: Nov 16, 2000 5:14 PM
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Guy Brandenburg wrote:

> My souces for this lesson were, more or less, the COMAP book For All
> Practical purposes, which is an interesting source of ideas; columns I
> had read a long time ago in Scientific American by Martin Gardner and I
> suspect others on Kenneth Arrow's apparent proof that the only type of
> election procedure that actually follows a few apparently simple axioms
> is a dictatorship; and a much more recent article on voting theory by a
> person whose name I cannot recall right now because I forgot to bookmark
> it and instead simply printed out and took to school. He contradicts
> Arrow. I will attempt to find this citation on Monday.

I went through Arrow's work not long ago. The original paper is quite hard to
read, because Arrow uses terminology that is very unfamiliar to people whose
mathematical background is more modern. A very readable modern work on the
subject is Alan D. Taylor's book *Mathematics and Politics: Strategy, Voting,
Power and Proof*, Springer-Verlag, New York, 1995, ISBN 0-387-94391-9.

I doubt that the other author you mentioned contradicts Arrow, whose work seems
correct to me. However, Arrow's Theorem depends on some carefully stated
definitions, and it may be the case that the other author used somewhat
different definitions which don't support Arrow's reasoning or his conclusions.

--Lou Talman
Department of Mathematical and Computer Sciences
Campus Box 38
Metropolitan State College of Denver
PO Box 173362
Denver CO 80217-3362

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