The Theory of Voting
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Voting theory has recently become a popular topic in mathematics courses aimed at nonmathematicians—liberal arts majors, for example—and has a natural home in discrete mathematics courses.
The chapter begins with a discussion of basic methods, such as plurality versus majority voting, sequential voting, and point-count methods. Condorcet’s method is described. The second section treats multiple elections where several candidates are elected for each position, and the generalized Hare method and approval voting are described.
The fairness of elections is discussed in Section 10.3, together with techniques to manipulate the result, and amendments. The chapter concludes with a discussion of the problems inherent in electoral systems, and concludes with Arrow’s Impossibility Theorem.