François Maniquet

Compensation and responsibility

Many distributive issues involve situations in which initial characteristics make individuals unequal. In view of prevailing moral sentiments, some of these characteristics call for compensating transfers, and some do not. We study the literature on this problem of compensation. This literature follows the distinction between the ethical principle of compensation and that of responsibility. According to the former, a good resource allocation system should neutralize the differential influence over agents’ outcomes of the characteristics that elicit compensation. According to the latter, a good resource allocation system should remain neutral with respect to inequality arising from the influence of characteristics that do not elicit compensation. The principle of responsibility can be interpreted as a libertarian principle of natural reward, or as a principle of utilitarian reward. Depending on whether the emphasis is put on the principle of compensation or of responsibility, and depending on how the latter is interpreted, there exist four main families of solutions to compensation problems. We review the axiomatic analyses of these four families of solutions in the different models in which they have been studied. We also review the applications that have been made of these solutions to problems of income taxation, education investment, social mobility and health insurance systems.Abstract Many distributive issues involve situations in which initial characteristics make individuals unequal. In view of prevailing moral sentiments, some of these characteristics call for compensating transfers, and some do not. We study the literature on this problem of compensation. This literature follows the distinction between the ethical principle of compensation and that of responsibility. According to the former, a good resource allocation system should neutralize the differential influence over agents’ outcomes of the characteristics that elicit compensation. According to the latter, a good resource allocation system should remain neutral with respect to inequality arising from the influence of characteristics that do not elicit compensation. The principle of responsibility can be interpreted as a libertarian principle of natural reward, or as a principle of utilitarian reward. Depending on whether the emphasis is put on the principle of compensation or of responsibility, and depending on how the latter is interpreted, there exist four main families of solutions to compensation problems. We review the axiomatic analyses of these four families of solutions in the different models in which they have been studied. We also review the applications that have been made of these solutions to problems of income taxation, education investment, social mobility and health insurance systems.

An equal right solution to the compensation-responsibility dilemma

In a simple model where skills may differ among agents, we propose to giv e them an equal right to the resources, interpreted as including both the technological possibilities and the skill profile. An equal right guarantees to each agent a minimal welfare level which depends only on her preferences. The conflicting objectives of unequal skill compensation and preferences responsability are then partially achieved.

Help the Low Skilled or Let the Hardworking Thrive? A Study of Fairness in Optimal Income Taxation

In a model where agents have unequal wages and heterogeneous preferences, we study the optimal redistribution via an income tax, when the social objective is based on a combination of efficiency and fairness principles, and when incentive issues are taken into account. We show how some fairness principles entail specific features for the optimal taxes, such as progressivity or tax exemption for incomes below the minimum wage.

Utilitarianism versus fairness in welfare economics

Utilitarianism has been opposed to theories of fairness (especially Rawls’s theory) in many respects. We want to focus here on a particular division that has been seldom discussed, although it is reflected in the structure of welfare economics. Welfare economics is indeed currently separated into two very different branches. One branch deals with social welfare functions and devotes a substantial energy to the study of utilitarianism. The other studies fair allocation in economic models and, formally, its main focus is on allocation rules. The difference is the following. A social welfare function associates each member in a class of possible contexts with a ranking of all possible alternatives, whereas an allocation rule only associates each member in the class with a selection of “best” alternatives. As it has long since been noted in the theory of social choice, an allocation rule is a kind of ranking, albeit simple (any two selected allocations as well as any two nonselected allocations being deemed socially indifferent), and a ranking immediately leads to an allocation rule (which selects the best alternative in every context). Actually, there is a second important difference between these two branches. The arguments of the social welfare functions studied by the former are interpersonally comparable utilities (usually comparable in levels, differences, or ratios), whereas the whole body of literature representing the latter is purely ordinal, making use of no other welfare information than the preferences of the agents over simple alternatives.1

Implementability and Horizontal Equity Imply No-Envy

THE REQUIREMENT OF NO-ENVY is at the heart of recent equity theory. An allocation is free from envy if no agent strictly prefers the bundle of goods which is assigned to another agent to the one she/he gets. An allocation rule satisfies No-Envy if it only selects envy-free allocations. In this paper, we examine the relationship between No-Envy and implementability in a general model. Our main result is that in monotonically closed domains the No-Envy property is satisfied by any allocation rule which is both horizontally equitable and Nash Implementable. The requirement of horizontal equity, called Equal Treatment of Equals, simply states that two agents having the same preferences should be treated equally, i.e., should be assigned the same welfare level. The monotonic closedness condition on the domain of admissible preferences is satisfied in many private and/or public good environments, as discussed below. Quasi-linear domains, however, are examples of nonmonotonically closed domains. Our result confirms the widespread intuition that the No-Envy requirement is justified not only from an equity point of view but also from an implementation standpoint (see Hammond (1979) and Champsaur and Laroque (1981)). Moreover, it throws some light on several previous results where specific allocation rules defined over monotonically closed domains are characterized by Nash Implementability among other axioms. As a consequence of our analysis, No-Envy can be weakened into Equal Treatment of Equals in these characterizations (see, e.g., Thomson (1990) and Nagahisa and Suh (1995)). Similar arguments apply to decentralization problems where informational efficiency is the primary concern. For instance, Calsamiglia and Kirman (1993) characterized the Equal Income Walrasian rule on the basis of informational efficiency, Pareto Optimality, and No-Envy. Again, No-Envy can be replaced by Equal Treatment of Equals in this result.2 On the other hand, our result also explains why Nash Implementable allocation rules violating No-Envy over monotonically closed domains all fail to satisfy Equal Treatment of Equals. Examples include the Lindahl solution, the ratio equilibrium solution (Kaneko (1977)) and the balanced linear cost share solution (Mas-Colell and Silvestre (1989)); see Corchon (1989) and Wilkie (1990). At the end of the paper, we show that if we restrict ourselves to allocation functions (that is, allocation rules selecting one and only one allocation per economy), then a similar result holds for Strategy-Proofness, provided the Satterthwaite-Sonnenschein (1981) property of Non-Bossiness is also imposed. That is, in monotonically closed

Approval quorums dominate participation quorums

We study direct democracy with population uncertainty. Voters’ participation is often among the desiderata by the election designer. We show that with a participation quorum, i.e. a threshold on the fraction of participating voters below which the status quo is kept, the status quo may be kept in situations where the planner would prefer the reform, or the reform is passed when the planner prefers the status quo. On the other hand, using an approval quorum, i.e. a threshold on the number of voters expressing a ballot in favor of the reform below which the status quo is kept, we show that those drawbacks of participation quorums are avoided. Moreover, an electoral system with approval quorum performs better than one with participation quorum even when the planner wishes to implement the corresponding participation quorum social choice function.

On the equivalence between welfarism and equality of opportunity

Abstract.A welfarist way of allocating resources consists in 1) equipping individuals with comparable indices of their well-being and 2) applying a unique aggregation rule to individual well-being levels. An equality of opportunity way of allocating resources consists in 1) making the distinction between personal characteristics which are under and beyond individuals’ control, and 2) decreasing inequalities due to differences in characteristics beyond individuals’ control. We show that under the proviso that indifferent individuals should not influence social judgements, welfarist and equal opportunity judgements on resource allocation are equivalent.

Approval voting and Arrow’s impossibility theorem

Approval voting has attracted considerable attention in voting theory, but it has rarely been investigated in an Arrovian framework of collective preference (”social welfare”) functions and never been connected with Arrow’s impossibility theorem. The article explores these two directions. Assuming that voters have dichotomous preferences, it first characterizes approval voting in terms of its collective preference properties and then shows that these properties become incompatible if the collective preference is also taken to be dichotomous. As approval voting and majority voting happen to share the same collective preference function on the dichotomous domain, the positive result also bears on majority voting, and is seen to extend May’s and Inada’s early findings on this rule. The negative result is a novel and perhaps surprising version of Arrow’s impossibility theorem, because the axiomatic inconsistency here stems from the collective preference range, not the individual preference domain.

Fairness and well-being measurement

We assume that economic justice requires resources to be allocated fairly, and we construct individual well-being measures that embody fairness principles in interpersonal comparisons. These measures are required to respect agents’ preferences. Across preferences well-being comparisons are required to depend on comparisons of the bundles of resources consumed by agents. We axiomatically justify two main families of well-being measures reminiscent to the ray utility and money-metric utility functions.

On resource monotonicity in the fair division problem

In the context of the classical fair division problem, we show that Efficiency and Resource Monotonicity are incompatible with the following ‘‘Conditional Equal Split’’ condition: If equal split of the collective endowment is efficient, it should be among the recommended allocations.