{"title":"Alan D Taylor","description":null,"products":[{"product_id":"mathematics-and-politics-book-alan-d-taylor-9780387776439","title":"Mathematics and Politics","description":"The author is a recognized expert in applying ideas in modern mathematics to problems in international conflict resolution. Intended for non-specialists and requiring only introductory mathematics, the quantitative methods are presented in strongly applied settings for political science and the social sciences.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49728589791505,"sku":"NGR9780387776439","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":50350286373137,"sku":"CIN0387776435G","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50351089221905,"sku":"CIN0387776435VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52592114106641,"sku":"NLS9780387776439","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387776435.jpg?v=1750813464"},{"product_id":"mathematics-and-politics-book-alan-d-taylor-9780387943916","title":"Mathematics and Politics","description":"1 Escalation.- 1.1. Introduction.- 1.2. Game-Tree Analyses.- 1.3. Limitations and Back-of-the-Envelope Calculations.- 1.4. Statement of O'Neill's Theorem.- 1.5. Conclusions.- Exercises.- 2 Conflict.- 2.1. Introduction.- 2.2. Dominant Strategies and Nash Equilibria.- 2.3. Prisoner's Dilemma.- 2.4. A Game-Theoretic Model of the Arms Race.- 2.5. Chicken.- 2.6. Game-Theoretic Models of the Cuban Missile Crisis.- 2.7. Conclusions.- Exercises.- 3 Yes-No Voting.- 3.1. Introduction.- 3.2. Swap Robustness and the Nonweightedness of the Federal System.- 3.3. Trade Robustness and the Nonweightedness of the Procedure to Amend the Canadian Constitution.- 3.4. Statement of the Characterization Theorem.- 3.5. Conclusions.- Exercises.- 4 Political Power.- 4.1. Introduction.- 4.2. The Shapley-Shubik Index of Power.- 4.3. Calculations for the European Economic Community.- 4.4. A Theorem on Voting Blocs.- 4.5. The Banzhaf Index of Power.- 4.6. Two Methods of Computing Banzhaf Power.- 4.7. Ordinal Power: Incomparability.- 4.8. Conclusions.- Exercises.- 5 Social Choice.- 5.1. Introduction.- 5.2. Five Examples of Social Choice Procedures.- 5.3. Four Desirable Properties of Social Choice Procedures.- 5.4. Positive Results-Proofs.- 5.5. Negative Results-Proofs.- 5.6. The Condorcet Voting Paradox.- 5.7. A Glimpse of Impossibility.- 5.8. Conclusions.- Exercises.- 6 More Escalation.- 6.1. Introduction.- 6.2. Statement of the Strong Version of O'Neill's Theorem.- 6.3. Proof (by Mathematical Induction) of the Strong Version of O'Neill's Theorem.- 6.4. Vickrey Auctions.- 6.5. Vickrey Auctions as a Generalized Prisoner's Dilemma.- 6.6. Conclusions.- Exercises.- 7 More Conflict.- 7.1. Introduction.- 7.2. The Yom Kippur War.- 7.3. The Theory of Moves.- 7.4. Models of Deterrence.- 7.5. A Probabilistic Model of Deterrence.- 7.6. Two-Person Zero-Sum Games.- 7.7. Conclusions.- Exercises.- 8 More Yes-No Voting.- 8.1. Introduction.- 8.2. A Magic Square Voting System.- 8.3. Dimension Theory and the U.S. Federal System.- 8.4. Vector-Weighted Voting Systems.- 8.5. Conclusions.- Exercises.- 9 More Political Power.- 9.1. Introduction.- 9.2. The Johnston Index of Power.- 9.3. The Deegan-Packel Index of Power.- 9.4. The Power of the President.- 9.5. Ordinal Power: Comparability.- 9.6. The Chair's Paradox.- 9.7. Conclusions.- Exercises.- 10 More Social Choice.- 10.1. Introduction.- 10.2. Social Welfare Functions.- 10.3. May's Theorem for Two Alternatives.- 10.4. Arrow's Impossibility Theorem.- 10.5. Single Peakedness-Theorems of Black and Sen.- 10.6. Conclusions.- Exercises.- Attributions.- References.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50351277867281,"sku":"CIN0387943919G","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50406848102673,"sku":"CIN0387943919VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52139222270225,"sku":"NLS9780387943916","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387943919.jpg?v=1751325277"},{"product_id":"mathematics-and-politics-book-alan-d-taylor-9781441926616","title":"Mathematics and Politics","description":"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.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50375263060241,"sku":"CIN1441926615G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51123219530001,"sku":"NIN9781441926616","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52434370494737,"sku":"NLS9781441926616","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1441926615.jpg?v=1750794765"},{"product_id":"social-choice-and-the-mathematics-of-manipulation-book-alan-d-taylor-9780521008839","title":"Social Choice and the Mathematics of Manipulation","description":"Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This 2005 book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52339801587985,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52339802013969,"sku":"NLS9780521008839","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521008839.jpg?v=1758170164"},{"product_id":"social-choice-and-the-mathematics-of-manipulation-book-alan-d-taylor-9780521810524","title":"Social Choice and the Mathematics of Manipulation","description":"Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This 2005 book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. 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