Mathematics and Politics

Why would anyone bid $3. 25 in an auction where the prize is a single dollar bill? Can one “game” explain the apparent irrationality behind both the arms race of the 1980s and the libretto of Puccini’s opera Tosca? How can one calculation suggest the president has 4 percent of the power in the United States federal system while another s- gests that he or she controls 77 percent? Is democracy (in the sense of re?ecting the will of the people) impossible? Questionslikethesequitesurprisinglyprovideaveryniceforumfor some fundamental mathematical activities: symbolic representation and manipulation, model–theoretic analysis, quantitative represen- tionandcalculation,anddeductionasembodiedinthepresentationof mathematical proof as convincing argument. We believe that an ex- sure to aspects of mathematics such as these should be an integral part of a liberal arts education. Our hope is that this book will serve as a text for freshman-sophomore level courses, aimed primarily at students in the humanities and social sciences, that will provide this sort of exposure. A number of colleges and universities already have interdisciplinary freshman seminars where this could take place. Most mathematics texts for nonscience majors try to show that mathematics can be applied to many different disciplines. A student’s viii PREFACE interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. Our experience at Union College and Williams College has been that there is a real advantage in having students enter the course knowing that virtually all the applications will focus on a single discipline—in this case, political science.

“This book is well written and has much math of interest. While it is pitched at a non-math audience there is material here that will be new and interesting to the readers...-Sigact News”

From the reviews of the second edition:

“Mathematics and Politics is the fruit of undergraduate mathematics courses taught by the authors. The primary audience is political and social science majors. … The writing style is appropriate for the intended audience with the understanding that the students/readers have some familiarity with political science economics or sociology. … Overall the book serves as a useful quantitative introduction to several of the covered topics. … Faculty in the social sciences should strongly consider Mathematics and Politics as a resource/reference.” (J. Douglas Barrett, Technometrics, Vol. 53 (1), February, 2011)

“It is intended to serve as a text for social science and humanities students that will highlight the power and utility of mathematics. … if you are considering a course as described above, this textbook deserves to be the one that will entice you into taking the plunge. And if you simply want to educate yourself in areas of social science mathematics that have only recently started to get the attention they deserve, Mathematics and Politics deserves your strong consideration.” (Edward W. Packel, SIAM Review, Vol. 52 (4), 2010)

Alan Taylor is professor of history at the University of California at Davis. He is the author of "William Cooper's Town: Power and Persuasion on the Frontier of the Early American Republic," which won the 1996 Pulitzer Prize for History and the Bancroft Prize in American history.
Eric Foner is DeWitt Clinton Professor of History at Columbia University. He has been awarded the Bancroft Prize, Parkman Prize, and a "Los Angeles Times" Book Award, among other honors.

Mathematics and Politics requires no prerequisites in either subject. The underlying philosophy involves minimizing algebraic computations while focusing on the conceptual aspects of mathematics in the context of real-world questions in political science. This new addition has an added co-author, Allison Pacelli, and covers six major topics: social choice, yes-no voting systems, political power, game-theoretic models of international conflict, fairness, and escalation. In addition to having two new chapters (treating apportionment and conflict resolution), the text has been extensively reorganized and the number of exercises increased to over 300. EXCERPTS FROM REVIEWS OF THE FIRST EDITION "Taylor has done a remarkable job of showing the power of deductive reasoning in ... the strategic choices actors make in conflict situations ... a penetrating analysis of both real-life and hypothetical situations." -- Steven Brams, New York University Alan Taylor's book is carefully crafted. He is ever aware of his audience, but relentlessly presses the beginning student to understand more and more." -- Samuel Merrill III, American Mathematical Monthly This book is a unique and valuable source ... Coverage is thorough and extensive; ideas are explained clearly and at an appropriate mathematical level." -- Ed Packel, Lake Forest College "... Mathematics and Politics is a nearly perfect solution, either for classes or for the serious professional who wants to retool. ... The writing is crisp, and the sense of excitement about learning mathematics is seductive." -- Michael Munger, Chance " I like this book. It's nice mathematics with serious applications." -- John Ewing, Indiana University "Now we have, in Alan Taylor's book, an introduction to these ideas that is delightfully lucid and requires almost no mathematical prerequisites." -- Phillip D. Straffin, College Mathematics Journal "[The book] breaks new ground and could stand as the definitive undergraduate textbook in this area for quite some time." -- Stan Wagon, Macalester College

Why would anyone bid $3. 25 in an auction where the prize is a single dollar bill? Can one "game" explain the apparent irrationality behind both the arms race of the 1980s and the libretto of Puccini's opera Tosca? How can one calculation suggest the president has 4 percent of the power in the United States federal system while another s- gests that he or she controls 77 percent? Is democracy (in the sense of re'ecting the will of the people) impossible? Questionslikethesequitesurprisinglyprovideaveryniceforumfor some fundamental mathematical activities: symbolic representation and manipulation, model-theoretic analysis, quantitative represen- tionandcalculation,anddeductionasembodiedinthepresentationof mathematical proof as convincing argument. We believe that an ex- sure to aspects of mathematics such as these should be an integral part of a liberal arts education. Our hope is that this book will serve as a text for freshman-sophomore level courses, aimed primarily at students in the humanities and social sciences, that will provide this sort of exposure. A number of colleges and universities already have interdisciplinary freshman seminars where this could take place. Most mathematics texts for nonscience majors try to show that mathematics can be applied to many different disciplines. A student's viii PREFACE interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. Our experience at Union College and Williams College has been that there is a real advantage in having students enter the course knowing that virtually all the applications will focus on a single discipline--in this case, political science.

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