Social Choice Theory is the branch of mathematics dealing with the making of group decisions based on individual preferences. It analyses voting systems and shows how they may have anomalous or unfair consqeuences.
Perhaps the most significant result of social choice theory is ArrowsParadox. In a nutshell, this proves that there is no fair voting system which does not produce anomalous results. See VotingAnomalies? for examples of such anomalies in existing voting systems.
Interesting Links
Voting Systems - 
http://www.wikipedia.org/wiki/Voting_system : The WikiPedia? entry on voting systems is quite comprehensive.
The Voting Systems FAQ - http://pl.atyp.us/misc/votefaq.txt :
A catalogue of different voting systems used worldwide.