[EM] Voting geometry, with interactive examples

[mrouse1 at mrouse.com]

While googling around this morning, I found a web page on voting geometry,
complete with Flash examples you could play with, on the following
website:

http://mathdl.maa.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=1195&pf=1

I did have a question on it, though. In the representation triangle, if
you took the center of mass for each of the smaller preference triangles
(with the weight depending on how many voters picked that order) and found
the point of balance for the entire triangle, what voting method would
that be equivalent to?

For instance, taking the Milk-Soda-Juice example, you have
6 Milk>Soda>Juice (6 A>B>C)
5 Soda>Juice>Milk (5 B>C>A)
4 Juice>Soda>Milk (4 C>B>A)

If you put a mass of 6 at the centroid of the A>B>C triangle, a mass of 5
in the B>C>A triangle, and a mass of 4 in the C>B>A triangle, which voting
method would correspond to finding the center of mass for the complete
A-B-C triangle?

I hope others find the site interesting, and if anyone knows the answer to
my question just let me know. Thanks!

Michael Rouse
mrouse1 at mrouse.com