Mathematics and Voting
نویسنده
چکیده
T he 2008 annual Math Awareness Month theme features the unusual combination of “Mathematics and Voting”. The importance of voting is obvious; indeed, with the United States election season hard upon us, discussions about voting are seemingly nonstop. More generally, on almost any day of any year the news media reports on some consequential election going on somewhere in the world. But what does mathematics have to do with any of this? Actually, a lot. In fact, mathematics has been central to this area since 1770, when the mathematician JeanCharlesdeBorda challengedwhether the French Academy’s elections for new members accurately reflected the views of the voters: Borda blamed their voting rule, the plurality vote. It is this concern, whether an election rule can faithfully produce outcomes capturing “the will of the voters”, that requires serious mathematical attention. Consider the consequences; as it is well understood, electing the “wrong leader” can cause serious, lasting problems. Butwhile themathematical study of this topic is more than a couple of centuries old, there remain more mysteries than answers, and the mathematical development of this area is in its early stages. To illustrate what can happen, suppose the voter preferences among candidates {A,B, C} in
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