Social Choice and the Mathematics of Manipulation

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SOCIAL CHOICE AND THE MATHEMATICS OF MANIPULATION by Alan D. Taylor Mathematical Association of America, 2005, 187 pp. ISBN: 978-0-521-00883-9

Since the first time I raised my hand to cast my vote for someone in elementary school, I have been interested in the mathematics of voting and the fairness of voting systems. Like most people, for the longest time I thought voting systems were rather straightforward and fair. Over the years, however, various books as well as elections themselves have demonstrated that this is far from true. Social Choice and the Mathematics of Manipulation provides an in-depth understanding and appreciation of the structures, properties, and analysis of voting and social choice systems. These systems are described in a convenient and logical mathematical framework with precise notation and definitions so that the various systems can be compared and analyzed, and important properties understood. With the help of this informative and constructive book, I now understand these systems much more thoroughly and completely.

Taylor states that the prerequisite for this book is "a certain degree of what is usually called mathematical maturity" and it is "at a suitably accessible level for use in a number of undergraduate courses or graduate courses in mathematics, economics, and political science." However, I am not sure that undergraduates outside of mathematics majors would have the level of mathematics required for this book since many of the mathematical concepts and proofs are demanding. The first three chapters contain exercises, but the six remaining chapters do not. Some of the topics covered include mathematical descriptions of more than 25 voting systems, Arrow's Theorem, a historical synopsis, manipulability, resolute voting rules, nonresolute voting rules, approval voting, and quota systems. …

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