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Social Choice and Welfare

Erschienen in:

22.06.2016 | Original Paper

On the uniqueness of the yolk

verfasst von: Mathieu Martin, Zéphirin Nganmeni, Craig A. Tovey

Erschienen in: Social Choice and Welfare | Ausgabe 3/2016

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Abstract

The yolk, an important concept of spatial majority voting theory, is assumed to be unique when the number of individuals is odd. We prove that this claim is true in \( {\mathbb {R}} ^{2}\) but false in \( {\mathbb {R}} ^{3}\), and discuss the differing implications of non-uniqueness from the normative and predictive perspectives.

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For a simple and very clear presentation, see Miller (2015).

If n is odd then, \(S\subseteq N\) is a minimal blocking coalition if and only if S is a minimal winning coalition.

For a discussion on the limiting median lines, see Stone and Tovey (1992). In this example, there is no Tovey “anomaly”.

See Owen (1990) for a presentation of these concepts and their links to solutions of side-payment games.

Indeed, they were careful to describe the yolk as “a minimal sphere which intersects with every median hyperplane” (page 59, emphasis added), whereas they define a different ball as “the smallest closed ball containing all ideal points” (page 58, emphasis added). It is easy to see that the latter is unique.

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Titel: On the uniqueness of the yolk
verfasst von: Mathieu Martin
Zéphirin Nganmeni
Craig A. Tovey
Publikationsdatum: 22.06.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2016
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-016-0979-7

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