Walter Bossert

Redistribution mechanisms based on individual characteristics

Abstract This paper analyses the question of how to redistribute individual incomes if those incomes are determined by the agents characteristics . It is assumed that some of these characteristics are to be considered ‘relevant’, whereas others should be ‘irrelevant’. A redistribution mechanism assigns a post-tax income distribution to each characteristics profile. The objective is to eliminate the influence of irrelevant characteristics while preserving the contributions of relevant characteristics to the individual pre-tax incomes. An axiomatic approach is used to provide characterizations of a specific redistribution mechanism. Furthermore, it is shown that the income function (the function linking pre-tax incomes to characteristics) must have a separability property if some plausible conditions are imposed on a redistribution mechanism.

Redistribution and compensation (

In a model where individual incomes depend on the agents characteristics, we provide characterizations of several redistribution mechanisms. These mechanisms are designed to eliminate the effects of characteristics that are to be considered “irrelevant”, while preserving the influence of “relevant” characteristics on individual incomes. The mechanisms discussed here are egalitarian-equivalent and conditionally egalitarian mechanisms, as well as averaging versions of these rules.

Utilitarianism and the theory of justice

This chapter provides a survey of utilitarian theories of justice. We review and discuss axiomatizations of utilitarian and generalized-utilitarian social-evaluation functionals in a welfarist framework. Section 2 introduces, along with some basic definitions, social-evaluation functionals. Furthermore, we discuss several information-invariance assumptions. In Section 3, we introduce the welfarism axioms unrestricted domain, binary independence of irrelevant alternatives and Pareto indifference, and use them to characterize welfarist social evaluation. These axioms imply that there exists a single ordering of utility vectors that can be used to rank all alternatives for any profile of individual utility functions. We call such an ordering a social-evaluation ordering, and we introduce several examples of classes of such orderings. In addition, we formulate some further basic axioms. Section 4 provides characterizations of generalized-utilitarian social-evaluation orderings, both in a static and in an intertemporal framework. Section 5 deals with the special case of utilitarianism. We review some known axiomatizations and, in addition, prove a new characterization result that uses an axiom we call incremental equity. In Section 6, we analyze generalizations of utilitarian principles to variable-population environments. We extend the welfarism theorem to a variable-population framework and provide a characterization of critical-level generalized utilitarianism. Section 7 provides an extension to situations in which the alternatives resulting from choices among feasible actions are not known with certainty. In this setting, we discuss characterization as well as impossibility results. Section 8 concludes.

Ordering infinite utility streams

We reconsider the problem of ordering infinite utility streams. As has been established in earlier contributions, if no representability condition is imposed, there exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams. We examine the possibility of adding suitably formulated versions of classical equity conditions. First, we provide a characterization of all ordering extensions of the generalized Lorenz criterion as the only strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. Second, we offer a characterization of an infinite-horizon extension of leximin obtained by adding an equity-preference axiom to strong Pareto and finite anonymity.

Strategy-proofness of social welfare functions: The use of the Kemeny distance between preference orderings

The Kemeny distance for preference orderings is used to determine individual rankings of social preferences. Based on this distance function, the strategy-proofness of social welfare functions is examined. Our main result is an impossibility theorem stating that no social welfare function can be strategy-proof, if some additional properties are required.

Preference extension rules for ranking sets of alternatives with a fixed cardinality

This paper analyzes the problem of deriving a ranking of fixed-cardinality subsets of a universal set from a given ranking of the elements of this universal set. Only subsets with a given number of elements are being ranked, which is where the approach in this paper differs from the literature on extension rules that establish preference relations on the power set of the universal set. Common examples for areas where such preferences on subsets with a fixed cardinality are needed are elections of committees of a given size, many-to-one matchings, and decision problems under ignorance. The main result of the paper is a characterization of a class oflexicographic rank-ordered rules by means of two axioms, namely, aresponsiveness condition used in the matching literature and a well-knownneutrality requirement which ensures that the names of the alternatives are irrelevant for the ranking of the sets.

Rational choice and two-person bargaining solutions

Abstract This paper provides an alternative proof of a recent result by Peters and Wakker concerning the rationalizability of a two-person bargaining solution by an ordering on the gains of the agents over the disagreement outcome. A set of sufficient conditions for rationalizability in the two-person case is given by Pareto optimality, continuity, and independence of irrelevant alternatives. Whereas the original proof is self-contained, the proof given here provides a link between this result and the existing literature on rational choice. In addition, some auxiliary results that are of some interest are derived. As a by-product of the proof, it is shown that a rationalizing ordering can be endowed with some regularity properties.

Quasi-orderings and population ethics

Population ethics contains several principles that avoid the repugnant conclusion. These rules rank all possible alternatives, leaving no room for moral ambiguity. Building on a suggestion of Parfit, this paper characterizes principles that provide incomplete but ethically attractive rankings of alternatives with different population sizes. All of them rank same-number alternatives with generalized utilitarianism.

An alternative solution to bargaining problems with claims

Abstract An axiomatic characterization of a new egalitarian-type solution for bargaining problems with claims is provided. This claim-egalitarian solution selects the weakly Pareto optimal point in the feasible set such that the losses of all agents from their respective claims are equal. If there are more than two agents, the claim-egalitarian solution violates the individual rationality condition. The same problem occurs (even in the two-person case) if a larger class of problems is considered. To avoid this shortcoming, an individually rational extension of this solution is introduced and characterized.

Leximin population ethics

This paper concerns the ethical issues that arise when policy decisions have to be taken that affect population size and characteristics. Such policies include social security systems, intertemporal resource allocation decisions, and policies designed to influence fertility rates. The authors provide characterizations of Leximin principles for social evaluation in an intertemporal framework, so that they can be used to compare social alternatives with different population sizes. The main axioms used in our characterizations are Hammond Equity together with Independence of the Utilities of the Dead (a plausible intertemporal consistency requirement) for the Critical-Level Leximin principles, and Positional Leximin Consistency (an axiom that allows non-constant critical levels) for the Positional-Extension Leximin principle. The performance of these principles is compared in the pure population problem and we argue that the Critical-Level Leximin principles are ethically more attractive than Positional-Extension Leximin.