LEADER 06403nam 22005295 450 001 9910480325503321 005 20200701160933.0 010 $a1-4612-2512-4 024 7 $a10.1007/978-1-4612-2512-6 035 $a(CKB)3400000000089990 035 $a(DE-He213)978-1-4612-2512-6 035 $a(MiAaPQ)EBC3075331 035 $a(PPN)238038076 035 $a(EXLCZ)993400000000089990 100 $a20121227d1995 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematics and Politics$b[electronic resource] $eStrategy, Voting, Power and Proof /$fby Alan D. Taylor 205 $a1st ed. 1995. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1995. 215 $a1 online resource (XIV, 284 p.) 225 1 $aTextbooks in Mathematical Sciences,$x1431-9381 311 $a0-387-94500-8 311 $a0-387-94391-9 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $ainterest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. My experience at Union College has been that there is a real advan­ tage in having students enter the course knowing thatvirtually all the applications will focus on a single discipline-in this case, political science. The level ofpresentation assumes no college-level mathematicalor social science prerequisites. The philosophy underlying the approach we have taken in this book is based on the sense that we (mathemati­ cians)havetendedtomaketwoerrorsinteachingnonsciencestudents: wehaveoverestimatedtheircomfortwithcomputationalmaterial,and we have underestimated their ability to handle conceptual material. Thus, while there is very little algebra (and certainly no calculus) in our presentation, we have included numerous logical arguments that students in the humanitiesand the socialscienceswill find accessible, but not trivial. The book contains five main topics: a m.odel of escalation, game­ theoretic models of international conflict, yes-no voting systems, political power, and social choice. The first partofthe text is made up of a single chapter devoted to each topic. The second part of the text revisits each topic, again with a single chapter devoted to each. The organizationofthe bookisbasedonpedagogicalconsiderations, with the material becoming somewhat more sophisticated as one moves through the ten chapters. On the other hand, within any given chap­ terthere is little reliance on material from earlierchapters, except for those devoted to the same topic. 410 0$aTextbooks in Mathematical Sciences,$x1431-9381 606 $aStatistics  606 $aEconomic theory 606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 606 $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000 606 $aStatistics for Social Sciences, Humanities, Law$3https://scigraph.springernature.com/ontologies/product-market-codes/S17040 615 0$aStatistics . 615 0$aEconomic theory. 615 14$aStatistical Theory and Methods. 615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods. 615 24$aStatistics for Social Sciences, Humanities, Law. 676 $a519.5 700 $aTaylor$b Alan D$4aut$4http://id.loc.gov/vocabulary/relators/aut$0133075 906 $aBOOK 912 $a9910480325503321 996 $aMathematics and politics$9925836 997 $aUNINA