On the equivalence between progressive taxation and inequality reduction

We establish the precise connections between progressive taxation and inequality reduction, in a setting where the level of tax revenue to be raised is endogenously fixed and tax schemes are balanced. We show that, in contrast with the traditional literature on taxation, the equivalence between inequality reduction and the combination of progressivity and income order preservation does not always hold in this setting. However, we show that, among rules satisfying consistency and, either revenue continuity, or revenue monotonicity, the equivalence remains intact.progressivity, inequality reduction, income order preservation, consistency, taxation

Nonsymmetric variants of the prekernel and the prenucleolus

A solution on a class of TU games that satisfies the axioms of the pre-nucleolus or -kernel except the equal treatment property and is single valued for two-person games, is a nonsymmetric pre-nucleolus (NSPN) or -kernel (NSPK). In this paper we investigate the NSPKs and NSPNs and their relations to the positive prekernel and to the positive core. It turns out that any NSPK is a subsolution of the positive prekernel. Moreover, it is shown that an arbitrary NSPK, when applied to a TU game, intersects the set of preimputations whose dissatisfactions coincide with the dissatisfactions of an arbitrary element of any other NSPK applied to this game. This result also provides a new proof of sufficiency of the characterizing condition for NSPKs due to the first author in his PhD thesis published in 1994 as a discussion paper. Any NSPN belongs to "its" NSPK. Several classes of NSPNs are presented, all of them are subsolutions of the positive core. It is shown that any NSPN is a subsolution of the positive core provided that it satisfies the equal treatment property on an infinite universe of potential players. Moreover, we prove that, for any game that has a nonempty anticore, any NSPN selects its prenucleolus as its unique element.TU game; Solution concept; Kernel; Nucleolus; Core; Equal treatment

Progressive and merging-proof taxation

We investigate the implications and logical relations between progressivity (a principle of distributive justice) and merging-proofness (a strategic principle) in taxation. By means of two characterization results, we show that these two principles are intimately related, despite their different nature. In particular, we show that, in the presence of continuity and consistency (a widely accepted framework for taxation) progressivity implies merging-proofness and that the converse implication holds if we add an additional strategic principle extending the scope of merging-proofness to a multilateral setting. By considering operators on the space of taxation rules, we also show that progressivity is slightly more robust than merging-proofness.taxation, progressivity, merging-proofness, consistency, operators.

Progressive and merging-proof taxation

We investigate the implications and logical relations between progressivity (a principle of distributive justice) and merging-proofness (a strategic principle) in taxation. By means of two characterization results, we show that these two principles are intimately related, despite their different nature. In particular, we show that, in the presence of continuity and consistency (a widely accepted framework for taxation) progressivity implies merging-proofness and that the converse implication holds if we add an additional strategic principle extending the scope of merging-proofness to a multilateral setting. By considering operators on the space of taxation rules, we also show that progressivity is slightly more robust than merging-proofness.taxation, progressivity, merging-proofness, consistency, operators

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.

Asymmetric parametric division rules

We describe and characterize the family of asymmetric parametric division rules for the adjudication of conflicting claims. We use two approaches to characterize this family. The first approach follows the existing literature in defining a claims problem. As part of the characterization in this setting, we present two novel axioms which restrict how a division rule indirectly allocates between different versions of the same claimant. The second approach departs from the existing literature by expanding the definition of a claims problem to allow claimants to have multiple claims. The characterization in this setting uses the same set of axioms, though modified for this expanded domain, used by Young (1987) to characterize the family of symmetric parametric division rules. We show that these two approaches are essentially equivalent

EGALITARIAN RULES IN CLAIMS PROBLEMS WITH INDIVISIBLE GOODS

In this work we deal with rationing problems. In particular with claims problems with indivisible goods, that is, problems in which a certain amount of indivisible units (of an homogeneous good), has to be distributed among a group of agents, when this amount is not enough to satisfy agents' demands. We define discrete rules to solve those problems that involve notions of fairness similar to those supporting the constrained-equal awards and the constrained-equal losses rules in the continuous case. Axiomatic characterizations of those solutions are provided.indivisible goods, claims problems, equal awards solution, equal losses solution.

Uniform, Equal Division, and Other Envy-free Rules between the Two

This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the subclass of strategy-proof rules and show that the subclass also forms a complete lattice. In both cases, the upper bound is the uniform rule, the lower bound is the equal division rule, and any other rule is between the two.

GENERALIZED EXTERNALITY GAMES

Externality games are studied in Grafe et al. (1998). We define a generalization of this class of games and show, using the methodology in Izquierdo and Rafels (1996 and 2001), some properties of the new class of generalized externality games. They include, among others, the algebraic structure of the game, convexity, and their implication for the study of cooperative solutions. Also the proportional rule is characterized for this class of games.