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An extension theorem for rational choice functions

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  • Stephen A. Clark

Abstract

A choice function is strictly rational whenever it can be rationalized by a preference relation in a manner such that alternatives in a choice set are strictly preferred to alternatives in the corresponding rejection set. We demonstrate an Extension Theorem which asserts that a preference relation strictly rationalizes the choice function if and only if the choice function satisfies the Weak Axiom of Revealed Preference and the preference relation is an extension of the revealed weak preference relation. Then we consider various applications to rational choice theory.

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  • Stephen A. Clark, 1988. "An extension theorem for rational choice functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(3), pages 485-492.
    • Handle: RePEc:oup:restud:v:55:y:1988:i:3:p:485-492.
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    File URL: http://hdl.handle.net/10.2307/2297397
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    Cited by:

    1. Christopher Tyson, 2013. "Behavioral implications of shortlisting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 941-963, October.
    2. Clark, Stephen A., 1995. "Indecisive choice theory," Mathematical Social Sciences, Elsevier, vol. 30(2), pages 155-170, October.
    3. Athanasios Andrikopoulos, 2019. "A Generalization of Arrow’s Lemma on Extending a Binary Relation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-6, April.
    4. Christopher Tyson, 2013. "Behavioral implications of shortlisting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 941-963, October.
    5. Athanasios Andrikopoulos, 2019. "On the extension of binary relations in economic and game theories," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 277-285, June.
    6. Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany.
    7. Paola Manzini & Marco Mariotti, 2009. "Consumer choice and revealed bounded rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 379-392, December.
    8. Athanasios Andrikopoulos, 2017. "Generalizations of Szpilrajn's Theorem in economic and game theories," Papers 1708.04711, arXiv.org.
    9. José Alcantud & Gianni Bosi & Carlos Palmero & Magalì Zuanon, 2006. "Mathematical utility theory and the representability of demand by continuous homogeneous functions," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 5(3), pages 195-205, December.
    10. J. C. R. Alcantud & G. Bosi & C. Rodríguez-Palmero & M. Zuanon, 2003. "The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour," Microeconomics 0308002, University Library of Munich, Germany.

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