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Contraction consistent stochastic choice correspondence


  • Indraneel Dasgupta



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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Suggested Citation

  • Indraneel Dasgupta, 2011. "Contraction consistent stochastic choice correspondence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 643-658, October.
  • Handle: RePEc:spr:sochwe:v:37:y:2011:i:4:p:643-658
    DOI: 10.1007/s00355-011-0572-z

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    References listed on IDEAS

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    Cited by:

    1. Jan Heufer, 2011. "Stochastic revealed preference and rationalizability," Theory and Decision, Springer, vol. 71(4), pages 575-592, October.

    More about this item


    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;

    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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