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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.

Examined are the implications for social welfare functions of restricting the domain of individual preferences to type-one preferences, which assume that each person has a most preferred alternative in a euclidean space, & that alternatives are ranked according to their euclidean distance from this point. The result is that if one imposes K. J. Arrow's (Social Choice and Individual Values, 2nd edition, New Haven: Yale U Press, 1963) conditions of collective rationality, IIA, & the Pareto principle on the social welfare function, then it must be dictatorial. This result may not seem surprising, but it stands in marked contrast to the problem considered by A. Gibbard ("Manipulation of Voting Schemes: A General Result," Econometrica, 1973, 41, 587-601) & M. A. Satterthwaite ("Strategy-Proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions," Journal of Economic Theory, 1975, 10, 187-217) of finding a social-choice function. With unrestricted domain, under the Gibbard-Satterthwaite hypotheses, choices must be dictatorial. With type-one preferences, this result has been previously shown to not be true. This finding identifies a significant difference between the Arrow & Gibbard-Satterthwaite problems. 7 Figures, 18 References. Modified HA.

A comparatively short proof of the following theorems is given: If a social choice function, which in any voting situation selects only one alternative as the winning alternative, has at least three posible outcomes & is not dictatorial, then it is subject to strategic manipulation by single individuals. This theorem has been proved independently by A. Gibbard ("Manipulation of Voting Schemes: A General Result," Econometrica, 1973, 41, 587-601) & M. Satterthwaite ("Strategy-proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions," Journal of Economic Theory, 1975, 10, 187-217). The new proof of the theorem is based on a version of Arrow's impossibility theorem shown by B. Hansson ("Voting and Group Decision Functions," Synthese, 1969, 20, 526-537). AA.

The impossibility theorem developed by Kenneth Arrow has implications for both rationality and morality in political thought. Transitivity in a collective ordering can be assured only with a decisive set, but this outcome is acknowledged as morally undesirable. The alternatives exhibited by the theorem thus seem to require a choice between rationality and morality. But exit routes can be cut out of this dilemma with the idea of a conditional ordering, one where warranting factors attach to a ranking of alternatives. Conditional orderings form two senses of collective rationality. One is represented by compound directives, which avoid the rational problems of the theorem by warranting local orderings. The second is moral fusion, which requires a reasoned dominance in collective outcomes. These two forms of conditional rationality put into relief the restricted scope of the composition rules and individualism of Arrow's theorem, and suggest alternative relationships of individual and social whole.

Kenneth Arrow's treatment of social choice ("A Difficulty in the Concept of Social Welfare," Journal of Political Economy, 1950, 58, 328-346) led to the formulation of his 'Impossibility Theorem', according to which it would be impossible for a society to ethically consider the preferences of all its members in formulating policies. By making certain changes in Arrow's assumptions, the contradictions he encountered can be avoided. Arguments are presented which arrive at a "social choice procedure that will translate judgments of preference priority into a social ordering." A determination of preference priority leads to a theorem very similar to John Rawls' difference principle (A THEORY OF JUSTICE, Cambridge, Mass: 1971) which recognizes the moral priority of those in the worst social position. Appendix. J. N. Mayer.

The Concerns of Welfare Economics -- The Concerns of Social Choice Theory -- Practical Concerns of Welfare Economics and Social Choice Theory -- 1 Preferences and Utility -- Fundamental Assumptions -- Best Alternatives and Utility Functions -- The Formal Model of Preferences -- to Social Preferences -- Exercises -- Selected References -- 2 Barter Exchange -- Allocations -- The Edgeworth Box Diagram -- Pareto Optimal Allocations and the Core -- Algebraic Examples -- Final Notes on the Core: The Number of Coalitions -- Exercises -- Selected References -- 3 Market Exchange and Optimality -- The Two-Person, Two-Goods Model -- Competitive Equilibrium in an Exchange Economy: Formal Preliminaries -- The First Fundamental Theorem of Welfare Economics -- The Second Fundamental Theorem of Welfare Economics -- An Algebraic Example -- Exercises -- Selected References -- 4 Production and Optimality -- Optimal Production Plans -- Competitive Equilibrium Production Plans -- The First Fundamental Theorem of Welfare Economics, Production Version -- The Second Fundamental Theorem of Welfare Economics, Production Version -- Extending the Production Model, and Combining Production and Exchange -- An Algebraic Example in a Simple Production Model -- Exercises -- Selected References -- 5 Externalities -- Externalities in an Exchange Economy: An Example -- Pigouvian Taxes and Subsidies: The Exchange Example Continued -- Pigouvian Taxes and Subsidies: A Production Example -- Exercises -- Selected References -- 6 Public Goods -- The Public Goods Model -- The Samuelson Public Good Optimality Condition -- Private Financing of the Public Good and the Free Rider Problem -- The Wicksell-Lindahl Tax Scheme -- Fixed Tax Shares and Majority Voting -- The Demand-Revealing Tax Scheme -- The Groves-Ledyard Tax Scheme -- Selected References -- 7 Compensation Criteria -- Notational Preliminaries -- The Pareto Criterion -- The Kaldor Criterion -- The Scitovsky Criterion -- The Samuelson Criterion -- Exercises -- Selected References -- 8 Fairness and the Rawls Criterion -- Fairness -- The Rawls Criterion -- Exercises -- Selected References -- 9 Majority Voting -- The Majority Voting Criterion -- Majority Voting and Single-Peakedness -- Majority Voting and Single-Peakedness: The Multidimensional Case -- Exercises -- Selected References -- 10 Arrow's Impossibility Theorem -- The Model -- Requirements on the Collective Choice Rule -- Applying the Requirements -- Arrow's Impossibility Theorem -- Relaxing the Universality Requirement -- Reaction to Arrow's Impossibility Theorem -- Exercises -- Selected References -- 11 Strategic Behavior -- Examples of Strategic Behavior -- The Gibbard-Satterthwaite Impossibility Theorem -- Significance of the Gibbard-Satterthwaite Theorem -- Exercises -- Selected References -- 12 Epilog -- Author Index.

Arrow's paradox, important to the foundation of social choice theory & individual choice theory, was solved by reducing Arrow's rationality assumptions to acyclicity. Another paradox is presented which requires the abandonment of acyclicity as well. The construction of the paradox allows for certain intransitivities of individual indifference resulting from less than n significant one. The following are assumed: (1) the Citizens' intransitive weak preference, (2) the Strong Pareto Principle, & (3) Ternary acyclicity. The acceptance of the reasonableness of assumptions 1 & 2, forces the rejection of assumption 3; all of which is a fundamental change in the theory of social choice. S. Lupton.

Condorcet's paradox of voting and Arrow's impossibility theorem are by now well known. Inspired by Arrow's treatment of social choice, others have presented alternative proofs of his theorem and different impossibility results. Professor Fishburn has recently treated us to some interesting new voting paradoxes. It is important to have the area of inconsistency among the various treatments explored and clearly mapped out. It is equally important to come to terms with the known inconsistencies in order to construct a solid social choice edifice on safe ground. Coming to terms with the inconsistencies must surely mean deciding between alternative normative conditions when all of them cannot be satisfied simultaneously. This paper attempts to do just that by adding some computational criteria to the standard list of normative criteria and then singling out a subset as being more important (to the author at least) than the rest. Since the 'important' criteria are mutually consistent they can be used to derive some properties of democratic decision processes. Simple majority rule, applied in sequential elimination, is distinguished as the best collective decision method. It fails to satisfy the Pareto, or unanimity, criterion – one often regarded as a sine qua non of social choice – but when this condition is added to the author's list an impossibility result obtains. An argument is proposed to counter the suggestion that Pareto optimality be added to the list and some other condition removed.