A Note on the Separability Principle in Economies with Single-Peaked

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and continuity (with respect to the social endowment). We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of continuity. Furthermore, we prove that Pareto optimality, equal division lower bound, and separability imply no-envy. Using this result, we strengthen one of Chun's (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, equal division lower bound, separability, and either continuity or duplication-invariance.fair division with single-peaked preferences, separability, duplication-invariance, uniform rule.

A note on the separability principle in economies with single-peaked

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and continuity (with respect to the social endowment). We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of continuity. Furthermore, we prove that Pareto optimality, equal division lower bound, and separability imply no-envy. Using this result, we strengthen one of Chun's (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, equal división lower bound, separability, and either continuity or duplication-invariance

Efficiency and converse reduction-consistency in collective choice

We consider the problem of selecting a subset of a feasible set over which each agent has a strict preference. We propose an invariance property, converse reduction-consistency, which is the converse of reduction-consistency introduced by Yeh (2006), and study its implications. Our results are two characterizations of the Pareto rule: (1) it is the only rule satisfying efficiency and converse reduction-consistency and (2) it is the only rule satisfying one-agent efficiency, converse reduction-consistency, and reduction-consistency.consistency converse consistency efficiency Pareto rule social choice correspondences.

Revealed Political Power

This paper adopts a \revealed preference" approach to the question of what can be inferred about bias in a political system. We model an economy and its political system from the point of view of an \outside observer." The observer sees a nite sequence of policy data, but does not observe either the citizens' preference prole or underlying distribution of political power that produced the policies. The observer makes inferences about distribution of political power as if political power were derived from a wealth-weighted voting system with weights that can vary with the state of the economy. The weights determine the nature and magnitude of the wealth bias. Positive weights on relative income in any period indicate an \elitist" bias in the political system whereas negative weights indicate a \populist" one. As a benchmark, any policy data is shown to be rationalized by any system of wealthweighted voting. However, by augmenting the observer's observations with polling data, nontrivial inference is possible. We show that joint restrictions resulting from the policy and polling data together imply upper and lower bounds on the set of rationalizing biases. These bounds can be explicitly calculated and can be used to discern instances of elitist bias; in other times they show populist bias. Additional restrictions on the preference domain can rule out the unbiased benchmark case of equal representation.wealth-bias, elitist bias, populist bias, weighted majority winner, rationalizing weights, "Anything Goes Theorem"