Closure and Preferences

13 Pages Posted: 11 Oct 2015 Last revised: 11 May 2020

See all articles by Christopher P. Chambers

Christopher P. Chambers

Georgetown University - Department of Economics

Alan D. Miller

Faculty of Law, Western University

M. Bumin Yenmez

Boston College

Date Written: March 11, 2020

Abstract

We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps' axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).

Keywords: preferences, closure operator, path independence, menu, Kreps

Suggested Citation

Chambers, Christopher P. and Miller, Alan D. and Yenmez, M. Bumin, Closure and Preferences (March 11, 2020). Journal of Mathematical Economics, Vol. 88, 161–166, Available at SSRN: https://ssrn.com/abstract=2671963 or http://dx.doi.org/10.2139/ssrn.2671963

Christopher P. Chambers

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States

Alan D. Miller

Faculty of Law, Western University ( email )

1151 Richmond Street
London, Ontario N6A3K7
Canada

HOME PAGE: http://alandmiller.com

M. Bumin Yenmez (Contact Author)

Boston College ( email )

140 Commonwealth Ave.
Maloney Hall 327
Chestnut Hill, MA 02467
United States

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