On Capacity-Filling and Substitutable Choice Rules

31 Pages Posted: 20 Jul 2017 Last revised: 23 Feb 2020

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 capacity-filling 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 alternatives than the capacity, the choice is the union of the priority orderings’ maximizers (Aizerman and Malishevski, 1981). We introduce the notion of a critical set and constructively prove that the number of critical sets for 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 smallest size maximizer-collecting representations among all capacity-filling and substitutable choice rules. We also analyze maximizer-collecting choice rules in which the number of priority orderings equals the capacity. We show that if the capacity is greater than three and the number of alternatives exceeds the capacity by at least two, then no capacity-filling 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 Capacity-Filling 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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