Closure and Preferences
13 Pages Posted: 11 Oct 2015 Last revised: 11 May 2020
Date Written: March 11, 2020
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: Suggested Citation