
Characterizing the Top Cycle via Strategyproofness
Gibbard and Satterthwaite have shown that the only singlevalued social ...
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Computing and Testing Pareto Optimal Committees
Selecting a set of alternatives based on the preferences of agents is an...
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Arrovian Aggregation of Convex Preferences and Pairwise Utilitarianism
We consider social welfare functions that satisfy Arrow's classic axioms...
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Escaping Arrow's Theorem: The AdvantageStandard Model
There is an extensive literature in social choice theory studying the co...
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Balancedness of Social Choice Correspondences
A social choice correspondence satisfies balancedness if, for every pair...
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Learning Choice Functions via ParetoEmbeddings
We consider the problem of learning to choose from a given set of object...
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FalseNameProof Facility Location on Discrete Structures
We consider the problem of locating a single facility on a vertex in a g...
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On the Indecisiveness of KellyStrategyproof Social Choice Functions
Social choice functions (SCFs) map the preferences of a group of agents over some set of alternatives to a nonempty subset of alternatives. The GibbardSatterthwaite theorem has shown that only extremely unattractive singlevalued SCFs are strategyproof when there are more than two alternatives. For setvalued SCFs, or socalled social choice correspondences, the situation is less clear. There are miscellaneous  mostly negative  results using a variety of strategyproofness notions and additional requirements. The simple and intuitive notion of Kellystrategyproofness has turned out to be particularly compelling because it is weak enough to still allow for positive results. For example, the Pareto rule is strategyproof even when preferences are weak, and a number of attractive SCFs (such as the top cycle, the uncovered set, and the essential set) are strategyproof for strict preferences. In this paper, we show that, for weak preferences, only indecisive SCFs can satisfy strategyproofness. In particular, (i) every strategyproof rankbased SCF violates Paretooptimality, (ii) every strategyproof supportbased SCF (which generalize Fishburn's C2 SCFs) that satisfies Paretooptimality returns at least one most preferred alternative of every voter, and (iii) every strategyproof nonimposing SCF returns a Condorcet loser in at least one profile.
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