Closure and Preferences

12 Pages Posted: 11 Oct 2015  

Christopher P. Chambers

Georgetown University - Department of Economics

Alan D. Miller

University of Haifa - Faculty of Law; University of Haifa - Department of Economics

M. Bumin Yenmez

Boston College

Date Written: October 9, 2015

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). Finally, we carry the concept to the theory of path-independent choice functions.

Keywords: preferences, closure operator, path independence

Suggested Citation

Chambers, Christopher P. and Miller, Alan D. and Yenmez, M. Bumin, Closure and Preferences (October 9, 2015). 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

University of Haifa - Faculty of Law ( email )

Mount Carmel
Haifa, 31905
Israel
+972-52-503-9259 (Phone)

HOME PAGE: http://econ.haifa.ac.il/~admiller

University of Haifa - Department of Economics ( email )

Haifa 31905
Israel
+972-52-503-9259 (Phone)

HOME PAGE: http://econ.haifa.ac.il/~admiller

M. Bumin Yenmez (Contact Author)

Boston College ( email )

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

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