Contraction Consistent Stochastic Choice Correspondence
AbstractWe 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 InfoPaper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 4596.
Length: 20 pages
Date of creation: Nov 2009
Date of revision:
Publication status: published in: Social Choice and Welfare, 2011, 37 (4), 643-658
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Other versions of this item:
- Indraneel Dasgupta, 2011. "Contraction consistent stochastic choice correspondence," Social Choice and Welfare, Springer, vol. 37(4), pages 643-658, October.
- Indraneel Dasgupta, . "Contraction consistent stochastic choice correspondence," Discussion Papers 08/04, University of Nottingham, School of Economics.
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-12-11 (All new papers)
- NEP-DCM-2009-12-11 (Discrete Choice Models)
- NEP-UPT-2009-12-11 (Utility Models & Prospect Theory)
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