Anonymous voting and minimal manipulability

We compare the manipulability of different choice rules by considering the number of manipulable profiles. We establish the minimal number of such profiles for tops-only, anonymous, and surjective choice rules, and show that this number is attained by unanimity rules with status quo.public economics ;

The Pareto Frontier for Random Mechanisms

We study the trade-offs between strategyproofness and other desiderata, such as efficiency or fairness, that often arise in the design of random ordinal mechanisms. We use approximate strategyproofness to define manipulability, a measure to quantify the incentive properties of non-strategyproof mechanisms, and we introduce the deficit, a measure to quantify the performance of mechanisms with respect to another desideratum. When this desideratum is incompatible with strategyproofness, mechanisms that trade off manipulability and deficit optimally form the Pareto frontier. Our main contribution is a structural characterization of this Pareto frontier, and we present algorithms that exploit this structure to compute it. To illustrate its shape, we apply our results for two different desiderata, namely Plurality and Veto scoring, in settings with 3 alternatives and up to 18 agents.Comment: Working Pape

Minimal Manipulability: Anonymity and Unanimity

This paper is concerned with the minimal number of profiles at which a unanimous and anonymous social choice function is manipulable. The lower bound is derived when there are three alternatives to choose from. Examples of social choice functions attaining the lower bound are given. We conjecture that these examples are in fact all minimally manipulable social choice functions. Since some of these examples are even Pareto optimal, we have also derived the lower bound for Pareto optimal and anonymous social choice functions. Some of the minimally manipulable Pareto optimal and anonymous social choice functions can be interpreted as status quo voting.mathematical economics;

Strategy-proof judgment aggregation.

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.

Threshold Strategy-Proofness: On Manipulability in Large Voting Problems

In voting problems where agents have well behaved (Lipschitz continuous) utility functions on a multidimensional space of alternatives, a voting rule is threshold strategy-proof if any agent can only obtain a limited utility gain by not voting for a most preferred alternative,given that the number of agents is large enough. For anonymous voting rules it is shown that this condition is not only implied by but in fact equivalent to the influence of any single agent reducing to zero as the number of agents grows. If there are at least five agents, the mean rule (taking the average vote) is shown to be the unique anonymous and unanimous voting rule that meets a lower bound with respect to the number of agents needed to obtain threshold strategy-proofness.Economics ;

Comparing Voting by Committees According to their Manipulability

Arribillaga acknowledges financial support received from the Universidad Nacional de San Luis, through Grant 319502, and from the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through Grant PIP 112-200801-00655. Massó acknowledges financial support received from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563) and Grant ECO2014-53051-P, and from the Generalitat de Catalunya, through Grant SGR2014-515. The paper was partly written while Massó was visiting the Department of Economics at Stanford University. He wishes to acknowledge the hospitality of its members as well as financial support received from the Spanish Ministerio de Educación, Cultura y Deporte, through Project PR2015-00408.We consider the class of voting by committees to be used by a society to collectively choose a subset from a given set of objects. We offer a simple criterion to compare two voting by committees without dummy agents according to their manipulability. This criterion is based on the set-inclusion relationships between the two corresponding pairs of sets of objects, those at which each agent is decisive and those at which each agent is vetoer. We show that the binary relation "to be as manipulable as" endows the set of equivalence classes of anonymous voting by committees (i.e., voting by quotas) with a complete upper semilattice structure, whose supremum is the equivalence class containing all voting by quotas with the property that the quota of each object is strictly larger than one and strictly lower than the number of agents. Finally, we extend the comparability criterion to the full class of all voting by committees