[EM] Nanson and Borda

[Joseph Malkevitch]

If one uses preferential ballots where there is no indifference allowed 
in ranking the candidates, and if one gives points to the candidates 
where the number of points that candidate i gets for a particular ballot 
is the number of candidates ranked below candidate i on that ballot, 
then this is what I will mean by the Borda Count. If one "sequentially" 
eliminates candidates based on currently having the lowest Borda count, 
and eliminates that candidate from the ballots and recomputes the Borda 
Count until one obtains a winner, this is what I will mean by Nanson's 
Method.

Borda, J-C, Memoire sur les elections au Scrutin, Memoires of the Royal 
Academy of Sciences (1781)

Nanson, E., Methods of Election, Trans. Proc. Royal Society of Victoria 
18 (1882) 197-240.

(See also, I. McLean and A. Urken, Classics of Social Choice, U. 
Michigan Press, 1995).

It turns out that if there is a Condorcet winner for the original 
ballots that Nanson's method will select this Condorcet winner.

Cheers,

Joe

--
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
Phone: 718-262-2551
Web page: http://www.york.cuny.edu/~malk
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