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Kenneth Arrow's pathbreaking ?impossibility theorem" was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence. In this book, Amartya Sen and Eric Maskin explore the implications of Arrow's theorem. Sen considers its ongoing utility, exploring the theorem's value and limitations in relation to recent research on social reasoning, while Maskin discusses how to design a voting rule that gets us closer to the ideal?given

"This book develops John Dewey's broad conception of social conflict as a natural process of discovery and preference adjustment, resolving Kenneth Arrow's famous theorem of the impossibility of ordering diverse preferences through voting. It addresses the nature and resolution of today's urgent problems and political polarization"--

2.3 More Dimensions and 360 Degree Medianhood: Cox's Theorem2.4 Pairwise Symmetry: Plott's Theorem; 2.5 Default Stability and a Side Trip beyond Majority Rule; 2.6 Essential Packaging; 2.7 Contrasts and Limitations, or Purging Preposterous Premises; 2.8 Observable Evidence of Cycles; 3 Social Rationality; 3.1 Choice Functions and Rationality; 3.2 Rationality and the Classical Framework of Social Choice; 3.3 Arrow's Theorem; 3.4 On interpreting and Misinterpreting the Independence of Irrelevant Alternatives; 3.5 Proof of Arrow's Theorem; 3.6 On Not Overstating the Theorem

Front Cover; Social Choice and Welfare; Copyright Page; Introduction to the series; Preface; Table of Contents; List of participants; Introduction; References; PART IA: THE ETHICAL ASPECTS OF SOCIAL CHOICE: THE AGGREGATION PROBLEM; CHAPTER 1. Arrow's theorem: Unusual domains and extended co-domains; 1. Introduction; 2. Notation; 3. From individual preferences to social preferences; 4. Dictators and oligarchies; 5. Hypothesis on individual preferences; 6. Arrow's theorem; 7. Proof of the theorem; 8. Remarks about weak orders; References.

Covers topics such as: models of economic exchange and production, uncertainty, optimality, public goods, social improvement criteria, life and death choices, majority voting, Arrow's theorem, and theories of implementation and mechanism design. This book aims to make value judgments about economic and political mechanisms

1.A Dictator Must Always Exist -- 2.Arrow's Theorem is a Powerful Tool for Understanding Many Social Phenomena -- 3.Catherine the Great and Genghis Khan: Power has no Gender -- 4.Some Open Problems for a General Mathematical Theory of Social Structures -- 5.Phenomenology of Leadership -- 6.Phenomenology of Dictatorship

This book discusses collective decision making from the perspective of social choice and game theory. The chapters are written by well-known scholars in the field. The topics range from Arrow's Theorem to the Condorcet and Ostrogorski Paradoxes, from vote distributions in the European Council to influence processes and information sharing in collective decision making networks; from cardinal utility to restricted domains for social welfare functions; from rights and game forms to responsibility in committee decision making; and from dueling to bargaining. The book reflects the richness and diversity of the field of collective decision making and shows the usefulness and adequacy of social choice and game theory for the study of it. It starts with typical social choice themes like Arrow's Theorem and ends with typical game theoretical topics, like bargaining and interval games. In between there is a mixture of views on collective decision making in which both social choice and game theoretic aspects are brought in. The book is dedicated to Harrie de Swart, who organized the well-known Social Choice Colloquia at the University of Tilburg in the Netherlands.

Voting -- Two candidates -- Social choice functions -- Criteria for social choice -- Which methods are good? -- Arrow's theorem -- Variations on the theme -- Apportionment -- Hamilton's method -- Divisor methods -- Criteria and impossibility -- The method of Balinski and Young -- Deciding among divisor methods -- History of apportionment int he United States -- Conflict -- Strategies and outcomes -- Chance and expectation -- Solving zero-sum games -- Conflict and cooperation -- Nash equilibria -- The prisoner's dilemma -- The electoral college -- Weighted voting -- Whose advantage?

Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Figures and Tables -- Preface and Acknowledgements -- Introduction: The Social Choice Approach to Institutional Planning Theory -- Part I: Democracy, Rationality, and Planning: Applying Arrow's Theorem -- 1 Paradox of Dialogical Decision-making -- 2 Evaluation and Arguments: Balancing the Procedural Values of Priority Setting Techniques -- 3 Institutions of Communicative-calculative Synthesis: Structured Group Processes -- 4 Decision Cycles in Two Transport Planning Cases -- Part II: Public Interest and Protected Spheres: Applying Sen's Theorem -- 5 Democratic Planning and the Liberal Paradox -- 6 Loyalty Dilemmas in Advocacy Planning -- 7 Privacy as a Planning Problem: Transport-related Examples -- 8 Equality and Planning with Protected Spheres -- Part III: Manipulation in Planning: Applying Gibbard and Satterthwaite's Theorem -- 9 Power Concentration or Manipulation in the Planning Process -- 10 Planning Style and Agency Properties -- 11 Agency Profiles Applied to Positive Planning Theory -- 12 Economics of Dialogue: Hard Trade-offs in Communicative Planning -- Epilogue: Challenge and Response -- Bibliography -- Glossary of Social Choice Terms -- Index.

Preface -- Acknowledgements -- List of Figures -- List of Tables -- Fuzzy Social Choice -- 1.1 The Purpose and Plan of the Book -- 1.2 General Concepts -- 1.2.1 Sets -- 1.2.2 Subsets -- 1.2.3 Relations -- 1.2.4 Fuzzy Intersection and Union -- 1.2.5 Residuum -- References -- Classical Social Choice Theorems -- 2.1 Arrows Theorem -- 2.2 Discussion -- 2.3 Gibbard-Sattherthwaite Theorem -- 2.4 The Median Voter Theorem -- 2.5 The Maximal Set -- References -- Rationality of Fuzzy Preferences -- 3.1 The Structure of Fuzzy Preference Relations -- 3.2 Consistency of Fuzzy Preferences and the Fuzzy Maximal Set -- 3.3 Empirical Application I: Deriving an FWPR from a Fuzzy Preference Function -- References -- Arrow and the Aggregation of Fuzzy Preferences -- 4.1 Fuzzifying Arrow's Conditions -- 4.1.1 Transitivity -- 4.1.2 Weak Paretianism -- 4.1.3 Independence of Irrelevant Alternatives -- 4.1.4 Dictatorship -- 4.2 Making and Breaking Arrow's Theorem -- 4.3 Empirical Application II: The Spatial Model and Fuzzy Aggregation -- References -- Characteristics of Strategy-Proof Fuzzy Social Choice -- 5.1 Fuzzy Choice and Manipulation -- 5.2 Fuzzy Social Choice: Definitions and Concepts -- 5.2.1 Fuzzifying ASB II -- 5.2.2 Relaxing the Conditions of Abdelaziz et. al. -- 5.3 Findings -- 5.4 Implications for the Spatial Model -- 5.5 Conclusions -- References -- Fuzzy Black's Median Voter Theorem -- 6.1 The Structure of Fuzzy Rules and Strict Preference -- 6.2 Basic Definitions and Concepts -- 6.3 New and Old Fuzzy Voting Rules -- 6.4 Single-Peaked Preferences and the Maximal Set -- 6.5 Extending Black's Median Voter Theorem -- 6.6 An Application -- 6.7 Conclusions and Spatial Models -- References -- Representing Thick Indifference in Spatial Models -- 7.1 Stability and Thick Indifference in Individual Preferences

Introduction -- Summary of the chapters -- A comparison of social choice and deliberative theories of democracy -- Introduction -- Discourse and democracy -- Social choice theory -- Criticisms of deliberative democracy -- Criticisms of social choice theory -- Conclusion -- Circumventing arrow's theorem -- Introduction -- What hope for democracy? -- Can deliberative democracy and social choice theory be made compatible? -- Abandoning democratic purity -- Limiting participation -- Conclusion -- An empirical test of social choice and deliberative theories of democracy -- Introduction -- A broad description of the institution -- Case studies: administration and governance of the West, and the location of the Capital -- Case study 1. The Northwest Ordinance of 1784 -- Settlement and distribution of Western lands 1785 -- The Northwest Ordinance 1787 -- Case study 2: The location of the capital -- Conclusion -- Hobbesian sovereignty and the specter of tyranny -- Introduction -- Hobbesian sovereignty -- Hobbes? s intentions.

Cover -- Half Title -- Dedication -- Title Page -- Copyright Page -- Table of Contents -- Acknowledgements -- 1 Education and the state -- Introduction -- West's 'market model' -- 2 Equality of opportunity -- Introduction -- West on equality of opportunity -- Williams on equality of opportunity -- Rawls on equality of opportunity -- Why Dworkin cares about equality -- For 'equality of opportunity' read 'an adequate education for all' -- 3 Education for democracy -- Introduction -- West on education for democracy -- Education for participation in democracy -- State versus nonstate education for democracy: contingent arguments -- State versus nonstate education for democracy: noncontingent arguments -- Justifications for democracy and fitness tests for participation -- 'Education for democracy': markets and the state -- 4 Education for autonomy -- Introduction -- White on a compulsory curriculum for autonomy -- Raz on the state promotion of autonomy: negative arguments -- Raz on the state promotion of autonomy -- Challenging Raz's 'contingent objection' -- The epistemic argument and the curriculum -- Against state promotion of education for autonomy -- 5 Democratic control of education -- Introduction -- Democratic control of the curriculum: an argument from political equality -- Improving democracy by improving voting systems -- Riker and Nathan on the limitations of democracy -- Questioning the conditions of Arrow's theorem -- Logrolling and democratic control of education -- Democracy versus markets -- Fleshing out West's 'minimum adequate education for all' -- 6 Education as a public good -- Introduction -- Grace on education as a public good -- Education and the 'public goods dilemma' -- West's market model and externalities -- West's market model and the 'public goods dilemma' -- 7 Education and the state revisited -- Bibliography