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Contraction consistent stochastic choice correspondence

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  • Indraneel Dasgupta

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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 α and β, 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.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 37 (2011)
Issue (Month): 4 (October)
Pages: 643-658

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Handle: RePEc:spr:sochwe:v:37:y:2011:i:4:p:643-658

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Related research

Keywords: Stochastic choice correspondence; Contraction consistency; Regularity; Chernoff’s condition; Weak axiom of revealed preference; Weak axiom of stochastic revealed preference; Complete domain; Incomplete domain; D11; D71;

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  1. 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.
  2. Dasgupta, Indraneel, 2009. "Supply Theory sans Profit-Maximization," IZA Discussion Papers 4018, Institute for the Study of Labor (IZA).
  3. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, 02.
  4. 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.
  5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  6. 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 707-15, May.
  7. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  8. 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.
  9. 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.
  10. Indraneel Dasgupta & Prasanta Pattanaik, 2007. "‘Regular’ choice and the weak axiom of stochastic revealed preference," Economic Theory, Springer, vol. 31(1), pages 35-50, April.
  11. José Alcantud, 2006. "Notes and Comments: Stochastic demand correspondences and their aggregation properties," Decisions in Economics and Finance, Springer, vol. 29(1), pages 55-69, 05.
  12. Shasikanta Nandeibam, 2008. "A note on the structure of stochastic social choice functions," Social Choice and Welfare, Springer, vol. 30(3), pages 447-455, April.
  13. Pattanaik, Prasanta K & Peleg, Bezalel, 1986. "Distribution of Power under Stochastic Social Choice Rules," Econometrica, Econometric Society, vol. 54(4), pages 909-21, July.
  14. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08.
  15. Shasikanta Nandeibam, 2003. "Distribution of coalitional power in randomized multi-valued social choice," Social Choice and Welfare, Springer, vol. 20(1), pages 3-25.
  16. Taradas Bandyopadhyay & Indraneel Dasgupta & Prasanta Pattanaik, 2004. "A general revealed preference theorem for stochastic demand behavior," Economic Theory, Springer, vol. 23(3), pages 589-599, March.
  17. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer, vol. 26(1), pages 167-175, 07.
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Cited by:
  1. Jan Heufer, 2008. "Stochastic Revealed Preference and Rationalizability," Ruhr Economic Papers 0070, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.

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