Suchergebnisse

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.

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.

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.

If the class of admissible preference orderings is restricted in a manner appropriate for economic & political models, then K. J. Arrow's (Social Choice and Individual Values, New York: Wiley, 1963) impossibility theorem for social welfare function continues to be valid. Specifically, if the space of alternatives is R****, n(greater than or equal to) 3, where each dimension represents a different public good, & if each person's preferences are restricted to be convex, continuous, & strictly monotonic, then no social welfare function exists that satisfies unanimity, independence of irrelevant alternatives, & nondictatorship. 1 Figure. HA.

Recently, C. R. Plott & A. K. Sen have introduced axioms on choice functions which are necessary & sufficient for a rational choice function (alternatives are chosen as if there were maximal alternatives of a binary relation) to have a quasitransitive rationalization. The relationship of Plott's & Sen's axioms & other axioms on choice functions to quasitransitivity are shown. There are many axioms that characterize quasitransitive rationality for rational choice functions. Plott's axiom of path independence ("Path Independence, Rationality, and Social Choice," Econometrica, 1973, 41, 1075-1091) is characterized by Sen's "alpha" axiom ("Choice Functions and Revealed Preference," Review of Economic Studies, 1971, 38, 307-318) & an axiom introduced here. The results are applied to the question of social choice. If ethical conditions like K. J. Arrow's (see SA 0508/B6797) are placed on the social choice function in a binary form, then the impossibility theorem still obtains even if the choice function is not rational, but does satisfy Plott's condition of quasitransitivity. But if the ethical conditions are not binary in form, then ethical social choice is possible. Modified AA.