We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of alternatives: by comparison of worstalternatives, best alternatives, or by comparison based on stochastic dominance. We perform a similar exercise for...

Collective decisions are modeled by preference correspondences (rules). In particular, we focus ona new condition: "update monotonicity" for preference rules. Although many so-called impossibilitytheorems for the choice rules are based on -or related to- monotonicity conditions, this...

We consider voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences. Assuming continuity, y-strategy-proofness - meaning that coalitions of size smaller or equal to a small number y cannot manipulate - and unanimity, we show that such rules are...

Impossibility theorems for preference correspondences based on a new monotonicity concept arediscussed. Here monotonicity means that if preferences update in such a way that they get closerto an outcome then at the new situation this outcome remains chosen. Strong monotonicity requiresfurther...

In a model with finitely many agents who have single-dipped Euclidean preferences on a polytope inthe Euclidean plane, a rule assigns to each profile of reported dips a point of the polytope. Asingle-best point is a point which is the unique point at maximal distance from some other pointof the...

We study sets of preferences that are convex with respect to the betweeness relation induced by the Kemeny distance for preferences. It appears that these sets consist of all preferences containing a certain partial ordering and the other way around all preferences containing a given partial...

Domains of individual preferences for which the well-known impossibility theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. To comprehend the limitations these results imply for social choice rules, we search for the largest domains that are possible. Here, we...

Under a k-approval scoring rule each agent attaches a score of one to his k most preferred alternatives and zero to the other alternatives. The rule assigns the set of alternatives with maximal score. Agents may extend preferences to sets in several ways: they may compare the worst alternatives,...

In a model with finitely many agents who have single-dipped Euclidean preferences on a disc in theEuclidean plane, a rule assigns to each profile of reported dips a point of the disc. It is provedthat any strategy-proof and Pareto optimal rule is a dictatorial. This framework models...

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and initial endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying strategy-proofness, Pareto...