Mathematics and Voting

As this article by Donald Saari in the April 2008 issue of the Notices of the American Mathematical Society eloquently discusses, one can uses mathematics to examine the arbitrary brokenness of voting rules.

Here is the abstract: The mathematical analysis of voting systems, and of aggregation rules in general, shows that they can yield paradoxes as well as preferences. In this article, featured here for Mathematics Awareness Month, the author explains what kind of problems can arise and how they can be mathematically understood.

Saari has written numerous articles and multiple books on the topic, and this particular expository piece is a good place to start. (Notice that I'm a bit late in writing this post... )