Contraction consistent stochastic choice correspondence |
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Authors: | Indraneel Dasgupta |
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Institution: | 1.Economics,Centre for Studies in Social Sciences,Kolkata,India |
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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 (SCC), 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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