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.     

Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences

Collective decision problems are considered with a finite number of agents who have single-peaked preferences on the real line. A probabilistic decision scheme assigns a probability distribution over the real line to every profile of reported preferences. The main result of the paper is a characterization of the class of unanimous and strategy-proof probabilistic schemes with the aid of fixed probability distributions that play a role similar to that of the phantom voters in H. Moulin (Public Choice35 (1980), 437-455). Thereby, the work of Moulin (1980) is extended to the probabilistic framework. Journal of Economic Literature Classification Numbers: D71, D81.     

On the location of public bads: strategy-proofness under two-dimensional single-dipped preferences

In a model with finitely many agents who have single-dipped Euclidean preferences on a polytope in the Euclidean plane, a rule assigns to each profile of reported dips a point of the polytope. A point $x$ of the polytope is called single-best if there is a point $y$ of the polytope such that $x$ is the unique point of the polytope at maximal distance from $y$ . It is proved that if the polytope does not have either exactly two single-best points or exactly four single-best points which form the vertices of a rectangle, then any Pareto optimal and strategy-proof rule is dictatorial. If the polytope has exactly two single-best points, then there are non-dictatorial strategy-proof and Pareto optimal rules, which can be described by committee voting (simple games) between the two single-best points. This also holds if there are exactly four single-best points which form the vertices of a rectangle, but in that case, we limit ourselves to describing an example of such a rule. The framework under consideration models situations where public bads such as garbage dumping grounds or nuclear plants have to be located within a confined region.     

Reallocation of an infinitely divisible good

Summary. We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties. Received: August 29, 1995; revised version June 26, 1996     

Minimal manipulability: Unanimity and nondictatorship

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 found for unanimous social choice functions. In the case of three alternatives the lower bound is found for surjective social choice functions. In both cases all social choice functions reaching the lower bound are characterized for more than two agents. In the case of two agents the characterized social choice functions form a subset of the set of all social choice functions reaching the minimum.     

Arrow's Possibility Theorem for one-dimensional single-peaked preferences

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow's requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2^N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave.     

An axiomatic re-characterization of the Kemeny rule

Review of Economic Design - The Kemeny rule is one of the well studied decision rules. In this paper we show that the Kemeny rule is the only rule which is unbiased, monotone, strongly...