John A. Weymark

Generalized gini inequality indices

Abstract When incomes are ranked in descending order the social-evaluation function corresponding to the Gini relative inequality index can be written as a linear function withthe weights being the odd numbers in increasing order. We generalize this function by allowing the weights to be an arbitrary non-decreasing sequence of numbers. This results in a class of generalized Gini relative inequality indices and a class of generalized Gini absolute inequality indices. An axiomatic characterization of the latter class is also provided.

Utility in Social Choice

In Arrovian [Arrow (1951, 1963)] social choice theory, the objective is to construct a social welfare function—a mapping which assigns a social preference ordering to each admissible profile of individual preferences—satisfying several a priori appealing conditions. Arrow showed that the only social welfare functions satisfying his axioms are dictatorial in the sense that there exists an individual whose strict preference over any two social alternatives is always replicated in the social ordering, no matter what the preferences of the remaining members of society happen to be. This negative result has initiated a series of contributions which attempt to avoid Arrow’s impossibility theorem by weakening one or more of his original axioms. The results in this literature are, on the whole, rather negative as well.

Ethical índices of Income Mobility

Ethical indices of income mobility measure the change in welfare resulting from mobility. The concept of mobility we explore consists of a welfare comparison between the actual time path of the income distribution with a hypothetical time path obtained by supposing that starting from the actual first-period distribution, the remaining income receipts exhibit complete immobility.

A reconciliation of recent results in optimal taxation theory

Abstract The recent papers by Guesnerie and Diewert on tax reforms are interpreted as contributions to the characterization of second-best optima. This paper demonstrates that when it is possible to achieve any feasible direction of change in supplies by a differential change in producer prices, there are unique producer support prices. Under these circumstances, the apparent differences between Guesnerie and Diewert are reconciled. Optimality conditions with nonunique support prices are also considered.

Arrow's theorem with social quasi-orderings

The collective rationality requirement in Arrows theorem is weakened to demanding a social quasi-ordering (a reflexive and transitive but not necessarily complete binary relation). This weakening leads to the existence of a group such that (a) whenever all members of the group strictly prefer one alternative to another then so does society and (b) whenever two members of the group have opposite strict preferences over a pair of alternatives then the pair is socially not ranked. This theorem is then used to provide an axiomatization of the strong Pareto rule. These results are compared and contrasted to Gibbards oligarchy theorem and Sens axiomatization of the Pareto extension rule.

Arrovian Social Choice Theory on Economic Domains

This article surveys the literature that investigates the consistency of Arrows social choice axioms when his unrestricted domain assumptions are replaced by domain conditions that incorporate the restrictions on agendas and preferences encountered in economic environments. Both social welfare functions and social choice correspondences are considered.

Efficient strategy-proof exchange and minimum consumption guarantees

For exchange economies with classical economic preferences, it is shown that any strategy-proof social choice function that selects Pareto optimal outcomes cannot guarantee everyone a consumption bundle bounded away from the origin. This result demonstrates that there is a fundamental conflict between efficiency and distributional goals in exchange economies if the social choice rule is required to be strategy-proof.

Financing education using optimal redistributive taxation

In this article, the joint use of an income tax and public provision of education as instruments to achieve the governments distributional objectives are considered. Individuals differ in innate labour productivity and in aptitude to acquire skills through education. Actual labour productivity depends on both innate skill and the amount of education received. Using a generalized version of the Mirrlees tax problem that incorporates these features, qualitative properties of an optimal tax schedule are investigated.

Generalized Gini Indices of Equality of Opportunity

This article considers the ranking of profiles of opportunity sets on the basis of their equality. A version of the Pigou–Dalton transfer principle that is appropriate for the measurement of opportunity inequality is introduced and used to axiomatize the class of generalized Gini equality of opportunity orderings. A characterization of the class of generalized Gini social preference orderings for opportunity profiles is also provided.

Bunching properties of optimal nonlinear income taxes

Bunching is said to occur if individuals with different characteristics receive the same commodity bundle. This article analyzes bunching in a finite population optimal nonlinear income tax problem. Several easily-computed sufficient conditions for the optimality of particular bunching patterns as well as a simple necessary and sufficient condition for the optimal allocation to exhibit no bunching are presented. In addition, a characterization of the optimal allocation is provided. Is is shown that the bunching pattern obtained by S. Lollivier and J.-C. Rochet is a consequence of a convexity condition which is automatically satisfied in their continuum model but which is not generally satisfied in a finite model.