Edizione: Softcover reprint of the original 1st ed. 1985
The mathematical theory of voting has intellectual roots extending back two centuries to the writings of Borda and Condorcet. Yet it has only been in the last forty years that general theorems have begun to emerge. With the publication of this volume, Norman Schofield brings the results together in a ,common framework. SOCIAL CHOICE AND DEMOCRACY, however, is not merely a synthetic exercise, for Schofield's own work over the last decade has constituted a major initiative in deepening and' broadening our general understanding of voting arrangements. At last the results of his research, bits and pieces of which have been reported in a number of journals of international standing and in various collections, are coherently and systematically presented as an entirety. For students of democracy -- chiefly philosophers and political scientists, but increasingly economists as well -- the insights of this volume are profound. From it I infer the following.
1: Introduction.- 1.1. Rational Choice.- 1.2. The Theory of Social Choice.- 1.3. Restrictions on the Set of Alternatives.- 1.4. Structural Stability of the Core.- 2: Social Choice.- 2.1. Preference Relations.- 2.2. Social Preference Functions.- 2.3. Arrowian Impossibility Theorems.- 2.4. Power and Rationality.- 2.5. Choice and Functions.- 3: Voting Rules.- 3.1. Simple Binary Preference Functions.- 3.2. Acyclic Voting Rules on Restricted Sets of Alternatives.- 3.3. Manipulation of Choice Functions on Finite Sets of Alternatives.- 3.4. Restrictions on the Preferences of Society.- 4: The Core.- 4.1. Existence of a Choice.- 4.2. Existence of a Core in Low Dimensions.- 4.3. Convex Preferences.- 4.4. Non-Convex Preference.- 4.5. The Necessity of the Dimension Constraint.- 5: Local Cycles.- 5.1. Voting Cycles in Dimension v(?)—1.- 5.2. Implementation of Choice Functions in Dimension v(?) — 1.- 5.3. Cycles and the Stability Dimension.- 5.4. The Stability Dimension v*( ?).- 6: Structural Stability.- 6.1. Plott Symmetry Conditions.- 6.2. Structural Stability of the Optima Set.- 6.3. Structural Instability of the Optima Set.- 6.4. Stability of the Core and of Cycles.- 7: Classification of Voting Rules.- 7.1. The Stability and Instability Dimensions.- 7.2. Voting Rules in Low Dimensions.- 7.3. Majority Rule with an Infinite Electorate.- 8: Democratic Theory.- 8.1. Liberalism and Populism.- 8.2. Populist Democracy and Institutionalism.- 8.3. Liberal Theory and Electoral Politics.- 8.4. Preferences and Beliefs.- Glossary of Concepts.- Index of Authors.- Index of Terms and Definitions.
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