Series Editor's Introduction v Acknowledgments vii Preface ix 1. What is Social Choice Theory 1 The Voter's Paradox 2 The Big Picture 3 An Outline of This Book 7 2. Fundamental Terminology: Discrete Social Choice 9 3. Arrow's Theorem 12 The Social Preference Function 12 Arrow's Possibility Theorem 13 The Meaning of Arrow's Theorem 21 4. Fundamental Terminology: Continuous Sets of Alternatives 31 The Euclidean Spatial Model 31 Utility Functions 32 Continuity and Utility Representations on the Continuum 37 Convexity and Single-Peakedness 41 5. The Unidimensional Spatial Model 49 The Importance of Single-Peaked Preferences 49 The Median Voter Theorem 50 Reversion Points and Take-It-or-Leave-It Offers 53 Unraveling in Democratically Governed Groups 55 6. The Multidimensional Spatial Model 60 The Importance of Convexity 60 Stability Analysis: Majority Rule in Several Dimensions 64 The Chaos Theorems 77 Addressing the Disequilibrium Problem Structure-Induced Equilibrium 81 Behavioral Sources of Stability 93 7. Conclusion: Looking Backward and Forward 97 References 102 About the Author 109