Mathematics and Politics: Strategy, Voting, Power and Proof / Edition 1

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This book teaches humanities majors the accessibility and beauty of discrete and deductive mathematics. It assumes no prior knowledge of either college-level mathematics or political science, and could be offered at the freshman or sophomore level. The book devotes one chapter each to a model of escalation, game-theoretic models of international conflict, political power, and social choice. The material progresses in level of difficulty as the book progresses.
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Product Details

  • ISBN-13: 9780387943916
  • Publisher: Springer New York
  • Publication date: 3/1/1995
  • Series: Textbooks in Mathematical Sciences
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 284
  • Product dimensions: 6.13 (w) x 9.22 (h) x 0.58 (d)

Table of Contents

1 Escalation
1.2 Game-Tree Analyses 3
1.3 Limitations and Back-of-the-Envelope Calculations 10
1.4 Statement of O'Neill's Theorem 14
2 Conflict
2.2 Dominant Strategies and Nash Equilibria 25
2.3 Prisoner's Dilemma 26
2.4 A Game-Theoretic Model of the Arms Race 29
2.5 Chicken 31
2.6 Game-Theoretic Models of the Cuban Missile Crisis 33
3 Yes-No Voting
3.2 Swap Robustness and the Nonweightedness of the Federal System 51
3.3 Trade Robustness and the Nonweightedness of the Procedure to Amend the Canadian Constitution 54
3.4 Statement of the Characterization Theorem 57
4 Political Power
4.2 The Shapley-Shubik Index of Power 65
4.3 Calculations for the European Economic Community 71
4.4 A Theorem on Voting Blocs 75
4.5 The Banzhaf Index of Power 78
4.6 Two Methods of Computing Banzhaf Power 80
4.7 Ordinal Power: Incomparability 85
5 Social Choice
5.2 Five Examples of Social Choice Procedures 100
5.3 Four Desirable Properties of Social Choice Procedures 105
5.4 Positive Results - Proofs 108
5.5 Negative Results - Proofs 113
5.6 The Condorcet Voting Paradox 121
5.7 A Glimpse of Impossibility 123
6 More Escalation
6.2 Statement of the Strong Version of O'Neill's Theorem 135
6.3 Proof (by Mathematical Induction) of the Strong Version of O'Neill's Theorem 141
6.4 Vickrey Auctions 143
6.5 Vickrey Auctions as a Generalized Prisoner's Dilemma 147
7 More Conflict
7.2 The Yom Kippur War 156
7.3 The Theory of Moves 158
7.4 Models of Deterrence 166
7.5 A Probabilistic Model of Deterrence 171
7.6 Two-Person Zero-Sum Games 176
8 More Yes-No Voting
8.2 A Magic Square Voting System 189
8.3 Dimension Theory and the U.S. Federal System 192
8.4 Vector-Weighted Voting Systems 196
9 More Political Power
9.2 The Johnston Index of Power 206
9.3 The Deegan-Packel Index of Power 209
9.4 The Power of the President 211
9.5 Ordinal Power: Comparability 224
9.6 The Chair's Paradox 231
10 More Social Choice
10.2 Social Welfare Functions 242
10.3 May's Theorem for Two Alternatives 245
10.4 Arrow's Impossibility Theorem 248
10.5 Single Peakedness - Theorems of Black and Sen 259
Attributions 273
References 277
Index 281
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