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

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

by Alan D. Taylor
     
 

ISBN-10: 0387943919

ISBN-13: 9780387943916

Pub. Date: 03/01/1995

Publisher: Springer New York

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…  See more details below

Overview

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.

Product Details

ISBN-13:
9780387943916
Publisher:
Springer New York
Publication date:
03/01/1995
Series:
Textbooks in Mathematical Sciences
Edition description:
Older Edition
Pages:
284
Product dimensions:
6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Preface
1Escalation
1.2Game-Tree Analyses3
1.3Limitations and Back-of-the-Envelope Calculations10
1.4Statement of O'Neill's Theorem14
2Conflict
2.2Dominant Strategies and Nash Equilibria25
2.3Prisoner's Dilemma26
2.4A Game-Theoretic Model of the Arms Race29
2.5Chicken31
2.6Game-Theoretic Models of the Cuban Missile Crisis33
3Yes-No Voting
3.2Swap Robustness and the Nonweightedness of the Federal System51
3.3Trade Robustness and the Nonweightedness of the Procedure to Amend the Canadian Constitution54
3.4Statement of the Characterization Theorem57
4Political Power
4.2The Shapley-Shubik Index of Power65
4.3Calculations for the European Economic Community71
4.4A Theorem on Voting Blocs75
4.5The Banzhaf Index of Power78
4.6Two Methods of Computing Banzhaf Power80
4.7Ordinal Power: Incomparability85
5Social Choice
5.2Five Examples of Social Choice Procedures100
5.3Four Desirable Properties of Social Choice Procedures105
5.4Positive Results - Proofs108
5.5Negative Results - Proofs113
5.6The Condorcet Voting Paradox121
5.7A Glimpse of Impossibility123
6More Escalation
6.2Statement of the Strong Version of O'Neill's Theorem135
6.3Proof (by Mathematical Induction) of the Strong Version of O'Neill's Theorem141
6.4Vickrey Auctions143
6.5Vickrey Auctions as a Generalized Prisoner's Dilemma147
7More Conflict
7.2The Yom Kippur War156
7.3The Theory of Moves158
7.4Models of Deterrence166
7.5A Probabilistic Model of Deterrence171
7.6Two-Person Zero-Sum Games176
8More Yes-No Voting
8.2A Magic Square Voting System189
8.3Dimension Theory and the U.S. Federal System192
8.4Vector-Weighted Voting Systems196
9More Political Power
9.2The Johnston Index of Power206
9.3The Deegan-Packel Index of Power209
9.4The Power of the President211
9.5Ordinal Power: Comparability224
9.6The Chair's Paradox231
10More Social Choice
10.2Social Welfare Functions242
10.3May's Theorem for Two Alternatives245
10.4Arrow's Impossibility Theorem248
10.5Single Peakedness - Theorems of Black and Sen259
Attributions273
References277
Index281

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