An extension of the Moulin No Show Paradox for voting correspondences

Jimeno, José L.; Pérez, Joaquín; García, Estefanía

doi:10.1007/s00355-008-0360-6

Cited by 26 publications

(31 citation statements)

References 12 publications

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“…Our thinking on this point has shifted over time, and we shall be arguing that the tie-breaking agenda approach yields an appropriate general methodology for adapting an arbitrary voting property to the irresolute context. Nonetheless, this approach was not the one employed by Pérez (2001) or by Jimeno et al (2009) when they extended Moulin's study of participation in the irresolute context. They used a variety of set extensions.…”

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confidence: 92%

Monotonicity properties and their adaptation to irresolute social choice rules

Sanver

Zwicker

2012

Soc Choice Welf

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What is a monotonicity property? How should such a property be recast, so as to apply to voting rules that allow ties in the outcome? Our original interest was in the second question, as applied to six related properties for voting rules: monotonicity, participation, one-way monotonicity, half-way monotonicity, Maskin monotonicity, and strategy-proofness. This question has been considered for some of these properties: by Peleg and Barberà for monotonicity, by Moulin and Pérez et al, for participation, and by many authors for strategy-proofness. Our approach, however, is comparative; we examine the behavior of all six properties, under three general methods for handling ties: applying a set extension principle (in particular, Gärdenfors' sure-thing principle), using a tie-breaking agenda to break ties, and rephrasing properties via the "t-a-t" approach, so that only two alternatives are considered at a time. In attempting to explain the patterns of similarities and differences we discovered, we found ourselves obliged to confront the issue of what it is, exactly, that identifies these properties as a class. We propose a distinction between two such classes: the "tame" monotonicity properties (which include participation, half-way monotonicity, and strategy proofness) and the strictly broader class of "normal" monotonicity properties (which include monotonicity and one-way monotonicity, but not Maskin monotonicity). We explain why the tie-breaking agenda, t-a-t, and Gärdenfors methods are equivalent for tame monotonicities, and how, for properties that are normal but not tame, set-extension methods can fail to be equivalent to the other two (and may fail to make sense at all).

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confidence: 92%

Monotonicity properties and their adaptation to irresolute social choice rules

Sanver

Zwicker

2012

Soc Choice Welf

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“…Let us now propose the following lemma, which is an extension of known lemmas established in Moulin (1988) and Jimeno et al (2009).…”

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confidence: 95%

“…Following Jimeno et al (2009) and García (2009) we define the concepts of participation to be used in this paper.…”

Section: Resultsmentioning

confidence: 99%

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No Show Paradox in Condorcet k-voting Procedures

2010

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In this paper we extend the negative known results about No Show Paradox in Condorcet voting functions and correspondences to the contexts of k-functions and k-correspondences, in which the outcome of the voting process is a unique k-committee (set of k candidates) or a family of k-committees. The main result of the paper states that for every Condorcet k-function and for every Condorcet k-correspondence, there are situations in which every optimistic or pessimistic voter with some specific preferences could manipulate the election by abstaining.

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“…For example, it is not known whether there exists a Pareto-optimal pairwise SCF that is strategyproof according to Gärdenfors' extension. Recently, the study of the manipulation of irresolute SCFs by other means than untruthfully representing one's preferences-e.g., by abstaining the election [26,21]-has been initiated. For the set extensions considered in this paper it is unknown which SCFs can be manipulated by abstention.…”

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confidence: 99%

Necessary and sufficient conditions for the strategyproofness of irresolute social choice functions

Brandt

Brill

2011

Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge

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While the Gibbard-Satterthwaite theorem states that every non-dictatorial and resolute, i.e., single-valued, social choice function is manipulable, it was recently shown that a number of appealing irresolute Condorcet extensions are strategyproof according to Kelly's preference extension. In this paper, we study whether these results carry over to stronger preference extensions due to Fishburn and Gärden-fors. For both preference extensions, we provide sufficient conditions for strategyproofness and identify social choice functions that satisfy these conditions, answering a question by Gärdenfors [15] in the affirmative. We also show that some more discriminatory social choice functions fail to satisfy necessary conditions for strategyproofness.

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An extension of the Moulin No Show Paradox for voting correspondences

Cited by 26 publications

References 12 publications

Monotonicity properties and their adaptation to irresolute social choice rules

Monotonicity properties and their adaptation to irresolute social choice rules

No Show Paradox in Condorcet k-voting Procedures

Necessary and sufficient conditions for the strategyproofness of irresolute social choice functions

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