Anonymous and neutral majority rules

Bubboloni, Daniela; Gori, Michele

doi:10.1007/s00355-013-0787-2

Cited by 17 publications

(27 citation statements)

References 14 publications

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“…The next proposition, which generalizes Proposition 1 in Bubboloni and Gori (2014), shows that any subgroup U of G naturally acts on the set of preference profiles P. That result is rich of consequences as it allows to exploit many general facts from group theory.…”

Section: Symmetric Minimal Majority Rulesmentioning

confidence: 58%

“…Roughly speaking, the majority principle requires that if a large enough amount of people prefer an alternative to another one, then the former alternative must be socially preferred to the latter one. In the literature we can find several ways to interpret that principle, such as relative majority, absolute majority, qualified majority and so on; here we focus on the minimal majority principle introduced by Bubboloni and Gori (2014). Given an integer ν, called majority threshold, not exceeding the number of members in the committee but exceeding half of it and a preference profile, we say that a social preference is consistent with the ν-majority principle applied to the considered preference profile if the fact that an alternative is preferred to another one by at least ν individuals implies that the alternative is socially ranked over the other one.…”

Section: Introductionmentioning

confidence: 99%

“…That notion of symmetry provides a fruitful unified framework with a double advantage: arguments and proofs becomes simpler and more direct; the results reach a very satisfying level of generality (Theorems 7 and 11). Moreover, as in Bubboloni and Gori (2014), the algebraic machinery provides a method to potentially build all the rules described in Theorem A. In Section 7 we briefly discuss some examples that explain how the theoretical results can be explicitly applied in some simple cases.…”

Section: Introductionmentioning

confidence: 99%

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Symmetric majority rules

Bubboloni

Gori

2015

Mathematical Social Sciences

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In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle. In particular, supposing that individuals and alternatives are exogenously partitioned into subcommittees and subclasses, we provide necessary and sufficient conditions for the existence of reversal symmetric majority rules that are anonymous and neutral with respect to the considered partitions. We also determine a general method for constructing and counting those rules and we explicitly apply it to some simple cases.

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Section: Symmetric Minimal Majority Rulesmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetric majority rules

Bubboloni

Gori

2015

Mathematical Social Sciences

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“…and n to be 1, as shown by Dogan and Giritligil (2015), who reconsider the problem through a group theoretic approach. Interestingly, as Dogan and Giritligil (2015) as well as Bubboloni and Gori (2014) show, gcd(m!, n) = 1 turns out to be necessary and sufficient for the existence of anonymous and neutral social welfare functions (i.e., functions which assign to every preference profile a strict ranking of alternatives). 5 P N is such that a i P j a i+1 · · · a d P j a 1 · · · a i−2 P j a i−1 P j x 1 P j .…”

Section: Basic Notions and Notationmentioning

confidence: 87%

Anonymous, Neutral, and Resolute Social Choice Revisited

Ozkes¹,

Sanver²

2020

SSRN Journal

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We revisit the incompatibility of anonymity and neutrality in singleton-valued social choice. We first analyze the irresoluteness structure these two axioms together with Pareto efficiency impose on social choice rules and deliver a method to refine irresolute rules without violating anonymity, neutrality, and efficiency. Next, we propose a weakening of neutrality called consequential neutrality that requires resolute social choice rules to assign each alternative to the same number of profiles. We explore social choice problems in which consequential neutrality resolves impossibilities that stem from the fundamental tension between anonymity, neutrality, and resoluteness.

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“…The existence of anonymous, neutral and resolute spcs satisfying further properties is also studied by Bubboloni and Gori (2015), who focus on the majority principle, and Dogan and Giritligil (2015), who instead focus on monotonicity properties.…”

Section: Introductionmentioning

confidence: 99%

Breaking ties in collective decision-making

Bubboloni

Gori

2020

Decisions Econ Finan

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Many classic social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule. A tie-breaking rule is compulsory every time a single final decision is needed. Unfortunately, using a tie-breaking rule on some social preference (multiwinner social choice) correspondence can dramatically compromise its properties. In particular, very often, the arithmetic relation between the number of alternatives and the number of voters does not allow to maintain both anonymity and neutrality. In those cases, the only possibility is to look at suitable different forms of symmetry that are coherent with the decision context. We find out conditions which make a social preference (multiwinner social choice) correspondence admit a resolute refinement fulfilling some weak versions of the anonymity and neutrality principles. We also clear when it is possible to obtain, for those resolute refinements, the reversal symmetry (immunity to the reversal bias). The theory we develop turns out to be useful in many common applicative contexts and allows to explicitly construct those refinements. Keywords Social preference correspondence • Multiwinner social choice correspondence • Resoluteness • Anonymity • Neutrality • Tie-breaking rule JEL Classification D71 Daniela Bubboloni was supported by GNSAGA of INdAM.

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Anonymous and neutral majority rules

Cited by 17 publications

References 14 publications

Symmetric majority rules

Symmetric majority rules

Anonymous, Neutral, and Resolute Social Choice Revisited

Breaking ties in collective decision-making

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