[EM] [OT] Kenneth Arrow theory... anyone?
Joseph Malkevitch
joeyc at cunyvm.cuny.edu
Fri Nov 21 14:44:02 PST 2003
Dear Sampa,
The exact result is that when there are n alternatives there are at most
2^(n-1) ballots which can form a single-peaked set, and the proof is a
geometric argument using mathematical induction based on the number of
ways to draw the single-peaked schedules in an nxn array of lattice
points. In fact, one can milk the geometry argument for a bit more in
the way of combinatorial observations, such as how many different
candidates can be ranked 1st, etc. in a maximal single peaked set. I
published some expository remarks about this in an article about
elections that appeared in the volume published by the New York Academy
of Sciences called Mathematical Vistas.
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
More information about the Election-Methods
mailing list