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Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship

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  • M. Ali Khan
  • Metin Uyan{i}k

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 only stem from it. The six theorems are novel to both the economic and the mathematical literature: they generalize pioneering results of Eilenberg (1941), Sonnenschein (1965), Schmeidler (1971) and Sen (1969), and are relevant to several applied contexts, as well as to ongoing theoretical work.

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  • M. Ali Khan & Metin Uyan{i}k, 2018. "Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship," Papers 1810.02004, arXiv.org, revised Oct 2018.
  • Handle: RePEc:arx:papers:1810.02004
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    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D00 - Microeconomics - - General - - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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