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Social Choice and Welfare

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01-09-2015

On justifiable choice functions over opportunity sets

Author: Dan Qin

Published in: Social Choice and Welfare | Issue 2/2015

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Abstract

A choice function over opportunity sets is justifiable if there exists a choice function over alternatives such that an opportunity set (menu) is chosen from a collection of menus if and only if the former contains alternatives which reach the highest instrumentalist value, in terms of the choice function over alternatives, of all menus combined. This article explores necessary and sufficient conditions for justifiable choice function by general choice function, Chernoff consistent choice function, and path-independent choice function. This article also considers the condition under which the underlying choice function is binary, which leads to characterizations for binary-justifiability by acyclic, quasi-transitive, and transitive preferences.

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All choice consistent conditions are introduced in terms of \(c\), but also applies to \(c^{*}\).

The discussion of this paragraph is based on the observation of an anonymous referee.

This condition is slightly different from Ryan’s (2014) original condition in that the original one does not include \({\setminus } \{A\}\). It is observable that the original condition implies C. To preserve axiom independence, we modify the original condition to its current form. More importantly, our condition R has no essential effect on doubleton sets, whereas all other conditions work exclusively on doubleton sets, which makes the role of condition R clearer. Nevertheless, at the presence of C and WCM, which are assumed throughout this article, our condition R is equivalent to the original condition used by Ryan (2014).

The introduction of SE and Proposition 5 are both based on the observation of an anonymous referee.

BJC* is introduced by an anonymous referee.

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Title: On justifiable choice functions over opportunity sets
Author: Dan Qin
Publication date: 01-09-2015
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 2/2015
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-015-0890-7

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