I did some checking, and I found out that plotting candidates on the triangle ABC *did* violate IIA. Worse yet, it violates the majority criterion. For example, if you had 50.1% in the triangle ACB and 49.9% in the triangle CBA, the center of mass would be somewhere in CAB (the center of mass moves through that triangle as the votes shift from ACB to CBA).
I then decided it might be more consistent (and violate fewer criteria) to take the surface of a cube rather than a triangle. If you define the following cube faces for a three candidate election: Top: C>A>B Bottom: B>A>C Left: A>C>B Right: B>C>A Front: A>B>C Back: C>B>A Weight each face by how many votes matches it. For things like bullet-voting A, you'd put half of a vote in A>B>C and half in A>C>B, and if you had an A=B>C vote, you'd put a half of a vote apiece in A>B>C and B>A>C. Each option covers a pyramidal volume defined by the square face as the base and the center of the cube as the apex. Once all of the weights have been assigned, find the center of mass. The pyramid it lies in will give the rank order. The nice thing about this compared to the triangle version is that it doesn't appear to violate the majority criterion. Now I just need to find out what previously-defined voting method this corresponds to, and what *other* voting properties it violates. :D Michael Rouse [EMAIL PROTECTED] ---- election-methods mailing list - see http://electorama.com/em for list info
