[EM] Proof Borda Count best in the case of fully ranked preference ballots

[Steve Barney]

Forest and all:

Just so you know, in the case of fully ranked ordinal preference ballots,
Donald Saari has claimed to have proven, mathematically, that the Borda Count
is the optimal procedure in the sense that it produces the smallest number, all
together, of paradoxical outcomes. I am not capable of confirming or refuting
his proof, but this does carry a lot of weight with me. It is obvious that
Saari is a very rigorous and capable mathematician, as is confirmed by some of
my math professors, and an appropriate authority. For me the problem is that I
must fully understand his proof and argument before I can agree or disagree
with it. I have been working on that. In case you are curious, some of Saari's
articles are available on his web site:

http://www.math.nwu.edu/~d_saari/

The final proof is contained in 2 papers published in the January 2000 issue of
the journal _Economic Theory_, which are available in full text in Ebsco Host
(many public libraries offer access to that database).

"Mathematical structure of voting paradoxes: I. Pairwise votes." 
By: Saari, Donald G.; Economic Theory, 01/01/2000, 53p

"Mathematical structure of voting paradoxes: II. Positional voting." 
By: Saari, Donald G.; Economic Theory, 01/01/2000, 48p


Steve Barney
Oshkosh, WI

> Date: Thu, 14 Feb 2002 16:33:31 -0800 (PST)
> From: Forest Simmons <fsimmons at pcc.edu>
> To: Rob LeGrand <honky1998 at yahoo.com>
> CC: election-methods-list at eskimo.com
> Subject: Re: CSSE = Simmons' Method ?
> 
> The more I think about it the more I prefer Borda Seeded Bubble Sort as a
> simple, high utility, hard to manipulate, method satisfying the Condorcet
> Criterion, when limited to pure ranked preference ballots where
> truncation, Yes/No, NOTB, etc. are not allowed or provided for. 
[...]


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