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2019 | OriginalPaper | Buchkapitel

3. The (In)Vulnerability of 20 Voting Procedures to Lack of Monotonicity in a Restricted Domain

verfasst von : Dan S. Felsenthal, Hannu Nurmi

Erschienen in: Voting Procedures Under a Restricted Domain

Verlag: Springer International Publishing

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Abstract

This chapter focuses on the possibility that some well-known voting procedures lead to specific types of monotonicity paradoxes in preference profiles that are characterized by the presence and election of a Condorcet winner. Moulin’s (Journal of Economic Theory 45:53–64, 1988) theorem establishes the incompatibility of Condorcet-consistency and invulnerability to the No-Show paradox in voting procedures when there are more than three alternatives to be chosen from. We ask whether this conclusion would also hold in the proper subset of profiles distinguished by the property that a Condorcet winner exists and is elected in the initial profile. Our focus is on 20 voting procedures designed to elect a single candidate. These procedures include both Condorcet-consistent and non-consistent rules. The former are, however, only briefly touched upon because their invulnerability to most types of monotonicity violations in the restricted domain is obvious.

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Vorheriges Kapitel 20 Voting Procedures Designed to Elect a Single Candidate

Nächstes Kapitel The (In)Vulnerability of 20 Voting Procedures to the Inconsistency Paradox (aka Reinforcement Paradox) in a Restricted Domain

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The (In)Vulnerability of the various voting procedures to the Inconsistency (aka Reinforcement) paradox will be analyzed in Chap. 4.

The (In)Vulnerability of the various voting procedures to the No-Show paradox will be analyzed in Chap. 5.

When the notation a > b is used with respect to a single voter or with respect to a group of voters it means that the voter(s) rank(s) candidate a ahead of candidate b. When it is used with respect to the entire electorate it means that a majority of the voters rank a ahead of b.

This example refutes the statement made by Felsenthal and Tideman (2013, p. 71, fn 10) according to which Nanson’s and Dodgson’s methods are invulnerable to downward monotonicity failure in variable electorates.

Although Young’s procedure too is shown in Table 3.1 to be invulnerable to all four types of monotonicity failure under the domain constraint imposed, it is vulnerable to upward monotonicity failure in variable electorate when the initial social preference ordering contains a majority cycle. For an example see Felsenthal and Nurmi (2017, Sect. 5.9.2, pp. 81–82).

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Titel: The (In)Vulnerability of 20 Voting Procedures to Lack of Monotonicity in a Restricted Domain
verfasst von: Dan S. Felsenthal
Hannu Nurmi
Verlag: Springer International Publishing
Buch: Voting Procedures Under a Restricted Domain
Print ISBN: 978-3-030-12626-1

Electronic ISBN: 978-3-030-12627-8

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-12627-8_3