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Contraction Consistent Stochastic Choice Correspondence

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  • Dasgupta, Indraneel

    (Indian Statistical Institute)

Abstract

We model a general choice environment via probabilistic choice correspondences, with (possibly) incomplete domain and infinite universal set of alternatives. We offer a consistency restriction regarding choice when the feasible set contracts. This condition, 'contraction consistency', subsumes earlier notions such as Chernoff's Condition, Sen's ? and ?, and regularity. We identify a restriction on the domain of the stochastic choice correspondence, under which contraction consistency is equivalent to the weak axiom of revealed preference in its most general form. When the universal set of alternatives is finite, this restriction is also necessary for such equivalence. Analogous domain restrictions are also identified for the special case where choice is deterministic but possibly multi-valued. Results due to Sen (Rev Econ Stud 38: 307-317, 1971) and Dasgupta and Pattanaik (Econ Theory 31: 35-50, 2007) fall out as corollaries. Thus, conditions are established, under which our notion of consistency, articulated only in reference to contractions of the feasible set, suffices as the axiomatic foundation for a general revealed preference theory of choice behaviour.

Suggested Citation

  • Dasgupta, Indraneel, 2009. "Contraction Consistent Stochastic Choice Correspondence," IZA Discussion Papers 4596, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp4596
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    References listed on IDEAS

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    1. Shasikanta Nandeibam, 2008. "A note on the structure of stochastic social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 447-455, April.
    2. Dasgupta Indraneel, 2009. "Supply Theory sans Profit Maximization," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-16, July.
    3. Indraneel Dasgupta & Prasanta Pattanaik, 2007. "‘Regular’ choice and the weak axiom of stochastic revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 35-50, April.
    4. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    5. José Alcantud, 2006. "Notes and Comments: Stochastic demand correspondences and their aggregation properties," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 29(1), pages 55-69, May.
    6. Taradas Bandyopadhyay & Indraneel Dasgupta & Prasanta Pattanaik, 2004. "A general revealed preference theorem for stochastic demand behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 589-599, March.
    7. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    8. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    9. Nandeibam, Shasikanta, 1996. "Coalitional Power Structure in Stochastic Social Choice Functions with an Unrestricted Preference Domain," Journal of Economic Theory, Elsevier, vol. 68(1), pages 212-233, January.
    10. Shasikanta Nandeibam, 2003. "Distribution of coalitional power in randomized multi-valued social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(1), pages 3-25.
    11. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    12. Bandyopadhyay, Taradas & Bandyopadhyay, Bandyopadhyay & Pattanaik, Prasanta K., 2002. "Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference," Journal of Economic Theory, Elsevier, vol. 107(2), pages 483-489, December.
    13. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    14. Dasgupta Indraneel & Pattanaik P. K, 2010. "Revealed Preference with Stochastic Demand Correspondence," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, August.
    15. Bandyopadhyay, Taradas & Dasgupta, Indraneel & Pattanaik, Prasanta K., 1999. "Stochastic Revealed Preference and the Theory of Demand," Journal of Economic Theory, Elsevier, vol. 84(1), pages 95-110, January.
    16. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, February.
    17. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 167-175, July.
    18. Pattanaik, Prasanta K & Peleg, Bezalel, 1986. "Distribution of Power under Stochastic Social Choice Rules," Econometrica, Econometric Society, vol. 54(4), pages 909-921, July.
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    Cited by:

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    2. Davide Martinetti & Susana Montes & Susana Díaz & Bernard Baets, 2018. "On a correspondence between probabilistic and fuzzy choice functions," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 247-264, September.

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    More about this item

    Keywords

    weak axiom of stochastic revealed preference; regularity; complete domain; stochastic choice correspondence; weak axiom of revealed preference; Chernoff’s condition; contraction consistency; incomplete domain;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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