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Social Choice and Welfare

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05-03-2021 | Original Paper

Dominance in spatial voting with imprecise ideals

Authors: Mathieu Martin, Zéphirin Nganmeni, Craig A. Tovey

Published in: Social Choice and Welfare | Issue 1/2021

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Abstract

We introduce a dominance relationship in spatial voting with Euclidean preferences, by treating voter ideal points as balls of radius \(\delta\). Values \(\delta >0\) model imprecision or ambiguity as to voter preferences from the perspective of a social planner. The winning coalitions may be any consistent monotonic collection of voter subsets. We characterize the minimum value of \(\delta\) for which the \(\delta\)-core, the set of undominated points, is nonempty. In the case of simple majority voting, the core is the yolk center and \(\delta\) is the yolk radius.

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Place \(n-1\) ideal points at the vertices of a regular \((n-1)\)-polygon, and place the nth ideal point at the polygon center. Then for any small perturbation of the points, the nth point remains undominated.

Stricly speaking, the yolk is not a solution concept since it was built as a tool to enclose the uncovered set. However, following Owen (Owen 1990), we interpret the yolk as a near-core concept.

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Title: Dominance in spatial voting with imprecise ideals
Authors: Mathieu Martin
Zéphirin Nganmeni
Craig A. Tovey
Publication date: 05-03-2021
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 1/2021
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-021-01316-z

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