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Non-existence of continuous choice functions

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  • Nishimura, Hiroki
  • Ok, Efe A.

Abstract

Let X be a compact, or path-connected, metric space whose topological dimension is at least 2. We show that there does not exist a continuous choice function (i.e., single-valued choice correspondence) defined on the collection of all finite feasible sets in X. Not to be void of content, therefore, a revealed preference theory in the context of most infinite consumption spaces must either relinquish the fundamental continuity property or allow for multi-valued choice correspondences.

Suggested Citation

  • Nishimura, Hiroki & Ok, Efe A., 2014. "Non-existence of continuous choice functions," Journal of Economic Theory, Elsevier, vol. 153(C), pages 376-391.
    • Handle: RePEc:eee:jetheo:v:153:y:2014:i:c:p:376-391
    DOI: 10.1016/j.jet.2014.07.006
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    Cited by:

    1. Narayanaswamy Balakrishnan & Efe A. Ok & Pietro Ortoleva, 2021. "Inferential Choice Theory," Working Papers 2021-60, Princeton University. Economics Department..
    2. Piermont, Evan, 2022. "Disentangling strict and weak choice in random expected utility models," Journal of Economic Theory, Elsevier, vol. 202(C).

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    More about this item

    Keywords

    Choice functions; Rationality; Continuity;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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