The MathTrek blog from Science News has a brief article that provides a good quick overview of problems with election methods. It's called Spoil-Proofing Elections:
Complaints about the obscure Electoral College system are common, but the mathematicians' objection is even more basic. Presidential elections in the United States are decided using a variation of a method known as plurality voting: each person votes for one candidate, and the candidate with the most votes wins.
Seems like the obvious approach—but obvious doesn't always mean effective. "The plurality vote is pretty much the worst voting system there is," says Donald Saari, a mathematician at the University of California, Irvine.
One more interesting excerpt: "69 percent of the time, an election result can be changed by changing the voting rules." The problem is that it's not clear which set of rules produce a "true" result. They all produce results that reflect the voters' wishes as defined in some fashion. The argument is about which definition best serves the purpose of the election in the first place.