[EM] [OT] Kenneth Arrow theory... anyone?

Sampo Syreeni decoy at iki.fi
Fri Nov 21 13:55:03 PST 2003

On 2003-11-21, Joseph Malkevitch uttered:

>If one can order the alternatives being voted on (candidates) on a linear
>scale so that all of the alternatives are "single peaked" (using ordinal
>ranking ballots) then if there are an odd number of voters the Condorcet
>method will always choose a winner. (This result is due to Duncan Black.)

Hadn't heard of it before, but it seems proper after reading Buchanan and
Tullock's writing. They use single-peakedness to assure acyclicity, but I
don't think they go as deep as to worry about the problems with
discreteness. Rather they present the solution in a continuum-limit form.

>In fact if there are n alternatives and rankings are done without ties
>then at most 2 to the nth power can be single peaked while there might be
>as many as n! rankings.

How do you derive the exponential for single-peaked preferences?
Sampo Syreeni, aka decoy - mailto:decoy at iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
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