On Acceptant and Substitutable Choice Rules

34 Pages Posted: 20 Jul 2017 Last revised: 23 Sep 2018

See all articles by Battal Dogan

Battal Dogan

Department of Economics, University of Bristol

Serhat Dogan

Bilkent University - Department of Economics

Kemal Yildiz

Bilkent University - Department of Economics

Date Written: September 10, 2018

Abstract

Each acceptant and substitutable choice rule is known to have a maximizer-collecting representation: there exists a list of priority orderings such that from each choice set that includes more elements than the capacity, the choice is the union of the priority orderings' maximizers (Aizerman and Malishevski, 1981). We introduce the notion of a prime atom and constructively prove that the number of prime atoms of a choice rule determines its smallest size maximizer-collecting representation. We show that responsive choice rules require the maximal number of priority orderings in their maximizer-collecting representations among all acceptant and substitutable choice rules. We characterize maximizer-collecting choice rules in which the number of priorities equals the capacity. We also show that if the capacity is greater than three and the number of elements exceeds the capacity by at least two, then no acceptant and substitutable choice rule has a maximizer-collecting representation of the size equal to the capacity.

Keywords: Choice rules, acceptance, substitutability, path independence, prime atom

JEL Classification: D01, D03, C78, D47, D78

Suggested Citation

Dogan, Battal and Dogan, Serhat and Yildiz, Kemal, On Acceptant and Substitutable Choice Rules (September 10, 2018). Available at SSRN: https://ssrn.com/abstract=3004112 or http://dx.doi.org/10.2139/ssrn.3004112

Battal Dogan

Department of Economics, University of Bristol ( email )

United Kingdom

Serhat Dogan

Bilkent University - Department of Economics ( email )

06533 Ankara
Turkey

Kemal Yildiz (Contact Author)

Bilkent University - Department of Economics ( email )

Bilkent University, Dept. of Economics
BILKENT
Ankara, 06800
Turkey

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