``A Mathematical Look at Politics” by E. Arthur Robinson, Jr., Daniel H. Ullman

Jacek W. Mercik

Mathematica Applicanda, Tome 41 (2013) no. 2, pp. 209-213.

Résumé

The 460-page book “A Mathematical Look at Politics” (E. Arthur Robinson, Jr. and Daniel H. Ull-man. A mathematical look at politics. CRC Press–Taylor and Francis Group, Boca Raton, FL, 2011. ISBN: 978-1-4398-1983-8) written by Arthur Robinson and Daniel Ullman [1] consists of four chapters (the descriptions of the chapters are given in parenthesis): I --- Voting (the two candidate case, social choice functions, criteria for social choice, which methods are good?, Arrow’s theorem, variations on a theme), II --- Apportionment (Hamilton’s Method, Divisor Methods, Criteria and Impossibility, the Method of Balinski and Young, Choosing a Divisor Method, History of Apportionment in the United States), III --- Conflict (Strategies and Outcomes, Chance and Expectation, Solving Zero-Sum Games, Conflict, Nash Equilibria, the Prisoner’s Dilemma) and chapter IV --- the Electoral College (Weighted Voting and Privileges). At the end of each chapter there are problems and exercises. Finally, solutions to the exercises and problems, bibliography and index are at the end. Recommendations for instructors are also presented at the end of the preface. In the preface, one may find the declaration of the Authors that this book focuses on mathematical reasoning about politics rather than on mathematics:-- Is there a good way to choose winners of elections?-- Is there a good way to apportion congressional seats?-- Is there a good way to make decisions in situations of conflict and uncertainty?The book offers an alternative textbook to the usual mathematics courses for liberal arts students seeking to meet a general education requirement in mathematics or quantitative reasoning. What makes this book mathematical is not numbers or formulas, but rather reasoning. The book requires rather little background in mathematics or political science. Some experience with the American system of government is assumed.

Détail

DOI : 10.14708/ma.v41i2.461

Classification : 91-01, 91A05, 91B12, 91B14, 91F10
Mots-clés : voting procedures, social choice function, divisor methods, game, conflict, Nash equilibrium, weighting voting, privileges