A Generalization of Sen’s Unification Theorem: Avoiding the Necessity of Pairs and Triplets

He, Junnan (2011): A Generalization of Sen’s Unification Theorem: Avoiding the Necessity of Pairs and Triplets.

Abstract

This paper is concerned with the axiomatic foundation of the revealed preference theory. Many well-known results in literature rest upon the ability to choose over budget sets that contains only 2 or 3 elements, the situations which are not observable in real life. In order to give a more realistic approach, this paper shows that many of the famous consistency requirements, such as those proposed by Arrow, Sen, Samuelson etc., are equivalent if the domain of choice functions satisfy some set theoretical properties. And these properties, unions and inclusions for example, are proposed in a way that gives observability.

• Item Type: MPRA Paper
• Language: English
• Keywords: Revealed Preference Theory; Rationality; Ordering; Preference; Choice function
• Subjects: D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory; D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles

References

Arrow, Kenneth J. (1959), “Rational Choice Functions and Orderings”, Economica, N.S., Vol. 26, pp. 121-127.

Bandyopadhyay, Taradas. (April, 1988), “Revealed Preference Theory, Ordering and the Axiom of Sequential Path Independence”, in The Review of Economic Studies, Vol. 55, No. 2, pp. 343-351.

Dudley, Richard M. (1989), Real Analysis and Probability, Cambridge Studies in Advanced Mathematics, Vol. 74, Cambridge University Press.

Hempel, Carl G. and Oppenheim, Paul. (April, 1948), “Studies in the Logic of Explanation”, Philosophy of Science, Vol. 15, No. 2, pp. 135-75.

Houthakker, Hendrik S. (1950), “Revealed Preference and the Utility Function”, Economica, Vol. 17, pp. 159-174.

Richter, Marcel K. (July, 1966), “Revealed Preference Theory”, Econometrica, Vol. 34, No. 3, pp. 635-645.

Samuelson, Paul A. (1938), “A Note on the Pure Theory of Consumer’s Behaviour”, Economica, N.S., Vol. 5, pp. 61-67.

Sen, Amartya K. (July, 1971), “Choice Functions and Revealed Preference”, The Review of Economic Studies, Vol. 38, No. 3, pp. 307-317.

Sen, Amartya K. (August, 1973), “Behaviour and the Concept of Preference”, Econometrica, New Series, Vol. 40, No. 159, pp. 241-259.

Sen, Amartya K. (July, 1973), “Maximization and the Act of Choice”, Econometrica, Vol. 65, No. 4, pp. 745-779.

Suzumura, Kotaro. (Feburary, 1976), “Rational Choice and Revealed Preference”, The Review of Economic Studies, Vol. 43, No. 1, pp.149-158.

Uzawa, Hirofumi. (1956), “A Note on Preference and Axiom of Choice”, Annals of Institute of Statistical Mathematics, Vol. 8, pp. 35-40.