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MATHEMATICS AND POLITICS Strategy, Voting, Power and Proof Second Edition Alan D. Taylor Department of Mathematics Union College Schenectady, NY and Allison M. Pacelli Department of Mathematics Williams College Williamstown, MA ABC.
Preface Whywouldanyonebid$3.25inanauctionwheretheprizeisasingle 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 sug- geststhatheorshecontrols77percent?Isdemocracy(inthesenseof reﬂectingthewillofthepeople)impossible? Questionslikethesequitesurprisinglyprovideaveryniceforumfor some fundamental mathematical activities: symbolic representation andmanipulation, model–theoretic analysis, quantitative representa- tionandcalculation,anddeductionasembodiedinthepresentationof mathematicalproofasconvincingargument.Webelievethatanexpo- 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 interdisciplinaryfreshmanseminarswherethiscouldtakeplace.
Preface ix two new chapters on fairness, we have introduced a new section to twoofthetopicsintheﬁrsteditionofthebook,andupdatedmaterial in a number of places. We also increased the number of exercises by roughlyﬁftypercent,andcorrectedacoupleofglitchesbroughttoour attentionbyreadersoftheﬁrstedition.