[EM] New Voting mailing list: Politicians and Polytopes

[Markus Schulze]

Dear Craig,

you wrote (7 Apr 2000):
> Mr Schulze could tell us of the light and merit of modern
> publications on voting theory, e.g. as offset against a
> simple desire to get the single candidate whose name is
> there on the paper, into government.

You will never win a prize for discovering the relativity
theory a second time even if you can prove that you have
never heard of Einstein. Therefore -if you have a problem-
it makes sense to browse through the literature to see
whether this problem has already been solved by some other
persons.

For example, Woodall has proven that no election method can
meet the following four criteria simultaneously:

1) Monotonicity.

2) Later preferences must neither help nor hinder earlier
   preferences.

3) If no second preferences are expressed and candidate A
   has a plurality of first preferences, then candidate A
   must be elected.

4) If more than half of the voters strictly prefer candidate
   A and candidate B to every other candidate, then either
   candidate A or candidate B must be elected.

[Douglas R. Woodall, "An impossibility theorem for electoral
systems," Discrete Mathematics, vol. 66, p. 209-211, 1987]

Therefore the question is: What are you willing to sacrifice
to get monotonicity?

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de