Rationalization of indecisive choice behavior by majoritarian ballots

TL;DR

This paper introduces a model explaining indecisive choice behavior through majoritarian ballots, linking it to the Chernoff axiom, and analyzes the minimum number of ballots needed for justification.

Contribution

It formalizes majoritarianism in choice behavior, connects it to Chernoff axiom, and determines the asymptotic minimum size of liberal justification.

Findings

Majoritarianism is equivalent to Chernoff axiom.

Two paradigms of majoritarianism are analyzed: simple majority and single ballot.

Asymptotic minimum size of liberal justification is derived.

Abstract

We describe a model that explains possibly indecisive choice behavior, that is, quasi-choices (choice correspondences that may be empty on some menus). The justification is here provided by a proportion of ballots, which are quasi-choices rationalizable by an arbitrary binary relation. We call a quasi-choice $s$-majoritarian if all options selected from a menu are endorsed by a share of ballots larger than $s$. We prove that all forms of majoritarianism are equivalent to a well-known behavioral property, namely Chernoff axiom. Then we focus on two paradigms of majoritarianism, whereby either a simple majority of ballots justifies a quasi-choice, or the endorsement by a single ballot suffices - a liberal justification. These benchmark explanations typically require a different minimum number of ballots. We determine the asymptotic minimum size of a liberal justification.