Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship
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.
Cite
@article{arxiv.1810.02004,
title = {Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship},
author = {M. Ali Khan and Metin Uyanık},
journal= {arXiv preprint arXiv:1810.02004},
year = {2019}
}
Comments
47 pages, 4 figures