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...

An impossibility theorem for preference aggretating rules is discussed. In this theorem no transitivity condition or acyclicity condition is imposed on the preferences: neither on the individual level nor on the aggregated level. Under the conditions that aggregation is non-dictatorial,...

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,...

This paper is concerned with the number of profiles at which a nondictatorial social choice function is manipulable. For three or more alternatives the lower bound is derived when the social choice function is nondictatorial and unanimous. In the case of three alternatives the lower bound is...

By virtue of the Kemeny distance strategy-proofness of preference rules is defined. It is shown that a preference rule, which assigns a complete relation to every profile of complete relations is non-imposed and strategy-proof if and only if it is pairwise voting in committees. So,...

Gibbard''s (1973) and Satterthwaite''s (1975) result implies that anonymous surjective social choice functions on more than two alternatives are manipulable. Placing some mild constraints on the number of agents compared to the number of alternatives, we show what the minimal number of...

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...

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...

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.

A game form constitutionally implements a social choice correspondence if it implements it in Nash equilibrium and, moreover, the associated effectivity functions coincide. This paper presents necessary and sufficient conditions for a unanimous social choice correspondence to be constitutionally...