This is a preview of subscription content, log in via an institution to check access.
References
Alfred Tarski, “Truth and Proof,”Scientific American, June, 1969.
K.O. May, “Intransitivity, Utility, and the Aggregation of Preference Patterns,”Econometrica, XXII, 1954.
Thomas Schwartz, “On the Possibility of Rational Policy Evaluation,”Theory and Decision, 1, 1970.
Ibid.
A.K. Sen,Collective Choice and Social Welfare, Holden Day, 1970, pp. 10, 15, 16, 81.
J. von Neumann and O. Morgenstern,The Theory of Games and Economic Behavior, Princeton, 1947, pp. 39–40.
R. Duncan Luce, “Semiorders and a Theory of Utility Discrimination,”Econometrica, Vol. 24, 1956, pp. 178–191. Luce characterizes a class of relations called semiorders from which he proves an interesting representation theorem. A version of his definition and theorem is as follows: Definition: ≥is a semiorder on A iff ≥is a binary relation on A and for every x,y,z and w in A, 1) Either x≥y or y≥x; 2) If not y≥x, and y≥z and z≥y and not w≥z then not w≥x; 3) If neither y≥x nor z≥y, and y≥w and w≥y, then not both (x≥w and w≥x) and (z≥w and w≥z). Theorem 1: If u is a function from A into the reals and ε is a positive real and ≥is a relation on A and for every s,y in A, x≥y iff, u(x)>u (y)+ε or |u(x)−u(y)|≤ε, then ≥is a semiorder on A. Theorem 2: If ≥is a semiorder on A and A is finite, then for some function u from A into the reals and some positive real ε, for every x, y in A, x≥y iff, u(x)>u(y)+ε or |u(x)−u(y)|≤ε.
It should be noted that Assumption 1 is much weaker than the plausable assumption that the domain of C include all functions from I into semi-orders on S. This semiorder assumption would in turn, however, be much weaker than (implied by but does not imply) Fishburn's assumption, which the author has become aware of, that the domain of C includes all functions from I into strict partial orders on S. See: P.C. Fishburn,The Theory of Social Choice, Princeton University Press, 1973, pp. 83–84.
Dennis Packard, “Rational Ranking Functions for Cyclical Comparatives,” Dissertation, Stanford, 1974.
Thomas Schwartz, “Rationality and the Myth of the Maximum,”Nous, May, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Packard, D.J. Social choice theory and citizens' intransitive weak preference—A paradox. Public Choice 22, 107–111 (1975). https://doi.org/10.1007/BF01719055
Issue Date:
DOI: https://doi.org/10.1007/BF01719055