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Arrow's Proof and the Logic of Preference

Published online by Cambridge University Press:  14 March 2022

Frederic Schick
Frederic Schick*
Affiliation:
Rutgers University
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Abstract

This paper is a critique of Kenneth Arrow's thesis concerning the logical impossibility of a constitution. I argue that one of the premises of Arrow's proof, that of the transitivity of indifference, is untenable. Several concepts of preference are introduced and counter-instances are offered to the transitivity of indifference defined along the standard lines in terms of these concepts. Alternate analyses of indifference in terms of preference are considered, and it is shown that these do not serve Arrow's purposes either. Finally, it is argued that in the single special case in which indifference could plausibly be held to be transitive, Arrow's thesis is innocuous.

Type
Research Article
Information
Philosophy of Science , Volume 36 , Issue 2 , June 1969 , pp. 127 - 144
Copyright
Copyright © 1969 by The Philosophy of Science Association

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References

[1] Arrow, K. J., Social Choice and Individual Values, Wiley, New York, 1951 ; 2nd ed. 1963.Google Scholar
[2] Arrow, K. J., “Public and Private Values,” in [10].Google Scholar
[3] Arrow, K. J., “Values and Collective Decision Making,” in P. Laslett and W. G. Runciman (eds.), Philosophy, Politics and Society, third series, Blackwell, Oxford, 1967.Google Scholar
[4] Black, D., The Theory of Committees and Elections, Cambridge University Press, Cambridge, 1958.Google Scholar
[5] Blau, J. H., “The Existence of Social Welfare Functions,” Econometrica, 1957, p. 307.CrossRefGoogle Scholar
[6] Buchanan, J. M., “Social Choice, Democracy, and Free Markets,” Journal of Political Economy, 1954, p. 114.CrossRefGoogle Scholar
[7] Buchanan, J. M., and Tullock, G., The Calculus of Consent, University of Michigan Press, Ann Arbor, 1962.Google Scholar
[8] Chisholm, R. M., and Sosa, E., “On the Logic of ‘Intrinsically Better',” American Philosophical Quarterly, 1966, p. 244.Google Scholar
[9] Hildreth, C., “Alternate Conditions for Social Orderings,” Econometrica, 1953, p. 81.CrossRefGoogle Scholar
[10] Hook, S. (ed.), Human Values and Economic Policy, New York University Press, New York, 1967.Google Scholar
[11] Luce, R. D., “Semiorders and a Theory of Utility Discrimination,” Econometrica, 1956, p. 178.CrossRefGoogle Scholar
[12] Luce, R. D., and Raiffa, H., Games and Decisions, Wiley, New York, 1957.Google Scholar
[13] May, K. O., “Intransitivity, Utility and the Aggregation of Utility Patterns,” Econometrica, 1954, p. 1.CrossRefGoogle Scholar
[14] Murakami, Y., Logic and Social Choice, Routledge and Kegan Paul, London, 1968.Google Scholar
[15] Rothenberg, J., The Measurement of Social Value, Prentice-Hall, Englewood Cliffs, N.J., 1961.Google Scholar
[16] Wollheim, R., “A Paradox in the Theory of Democracy,” in P. Laslett and W. G. Runciman (eds.), Philosophy, Politics and Society, second series, Blackwell, Oxford, 1962.Google Scholar
[17] von Wright, G. H., The Logic of Preference, Edinburgh University Press, Edinburgh, 1963.Google Scholar