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‘Regular’ choice and the weak axiom of stochastic revealed preference

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Abstract

We explore the relation between two ‘rationality conditions’ for stochastic choice behavior: regularity and the weak axiom of stochastic revealed preference (WASRP). We show that WASRP implies regularity, but the converse is not true. We identify a restriction on the domain of the stochastic choice function, which suffices for regularity to imply WASRP. When the universal set of alternatives is finite, this restriction is also necessary for regularity to imply WASRP. Furthermore, we identify necessary and sufficient domain restrictions for regularity to imply WASRP, when the universal set of alternatives is finite and stochastic choice functions are all degenerate. Results in the traditional, deterministic, framework regarding the relation between Chernoff’s condition and the weak axiom of revealed preference follow as special cases. Thus, general conditions are established, under which regularity can substitute for WASRP as the axiomatic foundation for a theory of choice behavior.

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Authors and Affiliations

  1. School of Economics, University of Nottingham, Nottingham, NG7 2RD, UK

    Indraneel Dasgupta

  2. Department of Economics, University of California, Riverside, CA, 92521, USA

    Prasanta K. Pattanaik

Authors
  1. Indraneel Dasgupta
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  2. Prasanta K. Pattanaik
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Correspondence to Prasanta K. Pattanaik.

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Dasgupta, I., Pattanaik, P.K. ‘Regular’ choice and the weak axiom of stochastic revealed preference. Economic Theory 31, 35–50 (2007). https://doi.org/10.1007/s00199-005-0074-2

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  • DOI: https://doi.org/10.1007/s00199-005-0074-2

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