The theme for Mathematics Awareness Month 2008 is Math and Voting

[Dr. Strange]

I haven't been terribly impressed with the themes for the past few years. But I'm excited about this one!
http://www.mathaware.org/index.html

[izquierdista]

1. One interesting mathematical result

is that there is no "fair" system of voting, one that will pick a clear winner, when more than two choices are present. Any algorithm that tries to allocate minor candidate votes to one of the two 'major' candidates will show some amount of bias.

[Dr. Strange]

2. That's true (if voters are asked to rank the candidates).

I'm curious about the mathematics of approval voting. I wonder if it avoids the problems that arise from "preference ballot style" voting.

[izquierdista]

3. It still has a "bias"

Voting with more than two available choices is akin to the 3-body problem in physics -- not solvable. That doesn't mean you can't make reasonable approximations to a solution, which is what approval voting tries to do. (And you can trisect an angle, just don't tell the Greeks that you used a calculator and cheated.)