On the manipulability of voting rules: The case of 4 and 5 alternatives

Aleskerov, Fuad; Karabekyan, Daniel; Sanver, M. Remzi; Yakuba, Vyacheslav

doi:10.1016/j.mathsocsci.2011.10.001

Cited by 30 publications

(14 citation statements)

References 15 publications

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“…More recently, set-extension methods have been applied to measure degree of manipulation (see Aleskerov et al (2011Aleskerov et al ( , 2012). 9 Speaking loosely, suppose that t initially was close to winning, with s doing much worse, and then some change to the profile helps t, and helps s by even more.…”

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confidence: 99%

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: 99%

Monotonicity properties and their adaptation to irresolute social choice rules

Sanver

Zwicker

2012

Soc Choice Welf

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“…Minimal The description of the procedures, except for the k-stable set rule, is given in [5]. Different versions of the k-stable set were introduced in [3]. In [1], extended preferences were introduced, in which many alternatives are ordered based on the singlevalued preferences of the agents.…”

Section: In This Matrix Inmentioning

confidence: 99%

“…Now we list the considered rules and discuss the choice of the sample profile. We follow the definitions and notations of [3,5]. The alternative x belongs to the k-stable set for k = 1, 2, 3, if one of following two conditions hold: a) the alternative x is undominated by alternatives outside the k-stable set via majority relation l, or b) if 9y 6 2 kSS : ylx then 9z 1 ; .…”

Section: The Aggregation Proceduresmentioning

confidence: 99%

Manipulability of Majoritarian Procedures in Two-Dimensional Downsian Model

Karabekyan

Yakuba

2020

Lecture Notes in Business Information Processing

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For the two-dimensional Downsian model the degree of manipulability of 16 known aggregation procedures, based on the majority relation, is evaluated using the Nitzan-Kelly index. Extended preferences for multi-valued choices are used to evaluate the fact of manipulation. Individual manipulability of agents is considered, when manipulating agent moves its ideal point over the plane. The range of possible manipulating positions of the agents is restricted to some rectangle on the two-dimensional coordinate space, within the feasible area of positions of alternatives and agents. The preferences of agents are assumed to be linear orders, constructed by the proximity of the alternatives to the agents, ordered according to Euclidean distance. The computer calculations, using Monte-Carlo simulations has been performed for 3, 4, and 5 alternatives and for even number of agents from 4 to 20. 100 thousands profiles were generated for each number of alternativesnumber of agents case. The results of the simulations show that there are groups of procedures with relatively low degree of manipulability for all of the considered multiple-choice extensions.

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“…One prominent example is the multivariate Pólya-Eggenberger urn model (see, e.g., Johnson and Kotz (1977)), which has been used for instance in Berg (1985); Gehrlein and Lepelley (2010); Lepelley and Valognes (2003) in order to analyze the relationship between group homogeneity and the probability of the voting paradox or the manipulability of different aggregation functions. The Pólya-Eggenberger model contains two other well-established models as special cases: impartial culture and impartial anonymous culture, which are also often presumed in studies of the voting paradox and the manipulability of aggregation procedures (see, e.g., Aleskerov et al (2012); Diss et al (2012); Pritchard and Slinko (2006)). Other model-based approaches, in which the orders in the profile are assumed to be randomly drawn with replacement, measure the homogeneity of the generating process by the probabilities p i (i = 1, .…”

Section: Preference Homogeneity In Related Workmentioning

confidence: 99%

A probabilistic evaluation framework for preference aggregation reflecting group homogeneity

Jansen¹,

Schollmeyer²,

Augustin³

2018

Mathematical Social Sciences

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Groups differ in the homogeneity of their members' preferences. Reflecting this, we propose a probabilistic criterion for evaluating and comparing the adequateness of preference aggregation procedures that takes into account information on the considered group's homogeneity structure. Further, we discuss two approaches for approximating our criterion if information is only imperfectly given and show how to estimate these approximations from data. As a preparation, we elaborate some general minimal requirements for measuring homogeneity and discuss a specific proposal for a homogeneity measure. Finally, we investigate our framework by comparing aggregation rules in a simulation study.

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On the manipulability of voting rules: The case of 4 and 5 alternatives

Cited by 30 publications

References 15 publications

Monotonicity properties and their adaptation to irresolute social choice rules

Monotonicity properties and their adaptation to irresolute social choice rules

Manipulability of Majoritarian Procedures in Two-Dimensional Downsian Model

A probabilistic evaluation framework for preference aggregation reflecting group homogeneity

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