A Maximal Domain of Preferences for Tops-only Rules in the Division Problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.Strategy-proofness, single-plateaued preferences

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences

A Maximal Domain for Stragegy-proof and No-vetoer Rules in the Multi-object Choice Model

April 2011, Revised February 201

Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules

It is shown that simple and coalitional strategy-proofness of an aggregation rule on any rich weakly unimodal domain of an idempotent interval space are equivalent properties if that space satisfies interval anti-exchange, a basic property also shared by a large class of convex geometries including -but not reducing to- trees and Euclidean convex spaces

Single-peakedness and strategy-proofness of generalized median voter schemes

We identify, in a continuous multidimensional framework, a maximal domain of preferences compatible with strategy-proofness for a given generalized median voter scheme. It turns out that these domains are a variation of single-peakedness. A similar but stronger result for the discrete case and single-peakedness has been already obtained by Barberà et al. (1999). However, both results are independent and their proofs involve different arguments.