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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 a and ß, 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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Paper provided by University of Nottingham, School of Economics in its series Discussion Papers with number 08/04.

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Handle: RePEc:not:notecp:08/04

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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.;

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  1. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer, vol. 26(1), pages 167-175, 07. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, 02. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08. [Downloadable!] (restricted)
  6. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Blackwell Publishing, vol. 38(115), pages 307-17, July. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. Indraneel Dasgupta, . "Revealed Preference with Stochastic Demand Correspondence," Discussion Papers 07/06, University of Nottingham, School of Economics. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Pattanaik, Prasanta K & Peleg, Bezalel, 1986. "Distribution of Power under Stochastic Social Choice Rules," Econometrica, Econometric Society, vol. 54(4), pages 909-21, July. [Downloadable!] (restricted)
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