# Sprumont's characterization of the uniform rule when all single-peaked preferences are admissible

@article{Weymark1999SprumontsCO, title={Sprumont's characterization of the uniform rule when all single-peaked preferences are admissible}, author={John A. Weymark}, journal={Review of Economic Design}, year={1999}, volume={4}, pages={389-393} }

Abstract. Sprumont (1991) has established that the only allocation rule for the division problem that is strategy-proof, efficient, and anonymous is the uniform rule when the domain is the set of all possible profiles of continuous single-peaked preferences. Sprumont's characterization of the uniform rule is shown to hold on any larger domain of single-peaked preferences.

## 12 Citations

### Maximal Domain of Preferences in the Division Problem

- EconomicsGames Econ. Behav.
- 2001

This work identifies the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry.

### Fully allocating a commodity among agents with single-peaked preferences

- Economics
- 2014

We survey the literature devoted to the study of the problem of allocating an infinitely divisible commodity among agents whose preferences are single-peaked. We formulate a number of normative and…

### Investigación Operativa The uniform rule in the division problem

- Economics
- 2011

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with singlepeaked preferences on the set of their potential shares. A…

### Maximal Domain for Strategy-proof Rules in Allotment Economies

- EconomicsSoc. Choice Welf.
- 2006

There is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable: it is the single-plateaued domain.

### The uniform rule in the division problem

- Economics
- 2011

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with singlepeaked preferences on the set of their potential shares. A…

### The division problem with voluntary participation

- EconomicsSoc. Choice Welf.
- 2012

A subclass of efficient and consistent rules is studied and extensions of the uniform rule that deal explicitly with agents’ voluntary participation are characterized.

### Strategy-proof social choice

- Economics
- 2010

This paper surveys the literature on strategy-proofness from a historical perspective. While I discuss the connections with other works on incentives in mechanism design, the main emphasis is on…

### Mechanism Theory

- Economics
- 2014

Some of the basic results and insights of the literature on mechanism design are presented. In that literature game theoretic reasoning is used to model social institutions as varied as voting…

### When Too Little is as Good as Nothing at All: Rationing a Disposable Good Among Satiable People with Acceptance Thresholds

- EconomicsGames Econ. Behav.
- 2012

This work characterize all of the the Pareto-efficient rules that satisfy these two properties and proposes another fairness axiom called awardee-envy-freeness, which is incompatible with strategy-proofness.

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- Economics
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We consider the problem of allocating some amount of a commodity among a group of agents with single-peaked preferences. We show that the uniform rule is the only rule satisfying equal treatment of…

### Maximal Domain of Preferences in the Division Problem

- EconomicsGames Econ. Behav.
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This work identifies the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry.

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We consider the problem of alloting shares of a task or good among agents with single peaked preferences over their own shares. Previous characterizations have examined rules, such as the uniform…

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Please send paper request to MAILTO:efgo@city.edu.hk In a recent paper, Sprumont (1991) showed that the uniform rule (Benassy, 1982) on the single-peaked domain (Black, 1948) is the only rule that…