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Topological connectedness and behavioral assumptions on preferences: a two-way relationship

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  • M. Ali Khan

    (Johns Hopkins University)

  • Metin Uyanık

    (University of Queensland)

Abstract

This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or indecisive, in the presence of a continuity hypothesis that is, in principle, non-testable. It identifies topological connectedness of the (choice) set over which the continuous binary relation is defined as being crucial to this question. Referring to the two-way relationship as the Eilenberg–Sonnenschein (ES) research program, it presents four synthetic, and complete, characterizations of connectedness and its natural extensions and two consequences that stem from it. The six theorems make connections that have eluded decision theory and thereby generalize the pioneering work of Eilenberg, Sonnenschein, Schmeidler and Sen. We draw the relevance to several applied contexts, as well as to ongoing theoretical work.

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  • M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    • Handle: RePEc:spr:joecth:v:71:y:2021:i:2:d:10.1007_s00199-019-01206-7
    DOI: 10.1007/s00199-019-01206-7
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    More about this item

    Keywords

    k-Connected; k-Non-triviality; Complete; Transitive; Fragile; Flimsy;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D00 - Microeconomics - - General - - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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