[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.



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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