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

[Joseph Malkevitch]

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