Mathematics and Politics : Strategy, Voting, Power, and Proof

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.