Hans van der Stel

Strategy-Proof Probabilistic Rules for Expected Utility Maximizers

We consider social choice rules which select a lottery over outcomes for each progile of individual preferences. Agents are assumed to have preferences over lotteries satisfying the axioms of expected utility. We exhibit a large class of rules satisfying strategy- proofness.

Generalized median solutions, strategy-proofness and strictly convex norms

Generalized location problems withn agents are considered, who each report a point inm-dimensional Euclidean space. A solution assigns a compromise point to thesen points, and the individual utilities for this compromise point are equal to the negatives of the distances to the individual positions. These distances are measured by a given strictly convex norm, common to all agents. Form=2, it is shown that if a Pareto optimal, strategy-proof and anonymous solution exists, thenn must be odd, and the solution is obtained by taking the median coordinatewise, where the coordinates refer to a basis that is orthogonal with respect to the given norm. Furthermore, in that case (m=2) such a solution always exists. Form > 2, existence of a solution depends on the norm.

Range convexity, continuity, and strategy-proofness of voting schemes

A voting scheme assigns to each profile of alternatives reported byn individuals a compromise alternative. A voting scheme is strategy-proof if no individual is better off by lying, i.e., not reporting a best alternative. In this paper the main results concern the case where the set of alternatives is the Euclidean plane and the preferences are Euclidean. It is shown that for strategy-proof voting schemes continuity is equivalent to convexity of the range of the voting scheme. Using a result by Kim and Roush (1984), this leads to characterizations of surjective or unanimous, anonymous, strategy-proof voting schemes.Furthermore, the paper contains an extensive discussion of related results in the area.

Strategy-Proofness for General Domains of Alternatives and Restricted Domains of Preferences

This abstract is a summary of the main recent results obtained by the three authors concerning strategy-proofness in social choice problems with general (and typically, continuous) domains of alternatives and restricted domains of preferences. Contrary to the classical papers by Arrow (1963), Gibbard (1973), and Satterthwaite (1975), in many cases possibility results are found, typically involving median-like solutions and extensions thereof.