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Mathematics + Elections = Concerns and Lawsuits

The Presidential Election almost is on us...an opportune time to explore some discrete mathematics related to the election. In this regard, Donald Saari's book Chaotic Elections! A Mathematician Looks at Voting is a fun guide in this exploration.

According to the book's advertising blurb, this book "should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing...." Plus, despite being a AMS publication, the mathematics-level is at the high school level (for the most part).

The book covers these fundamental ideas:

  • Defines and compares various voting schemes
  • Discusses and gives examples of paradoxes associated with voting
  • Full comparison of the Borda Count and Approval Voting
  • The quite-large probability of "dubious" election results
  • The author's personal take on the theories underlying strategic voting, positive use of symmetry, and "chaos"
  • Throughout the book, the author provides tons of examples applying and illustrating the above ideas...and of course, analyzes the 2000 Presidential election. You can see parts of the book via Google Book Search.