Equity Axiom Research Articles

Cross-cultural equity evaluations: A questionnaire-experimental approach

The theoretical background of the empirical investigations to be reported in this paper are positionalist aggregation functions which are numerically representable. The broad Borda rule is proposed as an aggregation mechanism for the case of a complete profile of the so-called individual extended orderings. We modify this rule to reflect considerations of equity. Students from Germany, Israel, the Baltic States, Austria and Slovenia were confronted with questionnaires that describe ‘situations’, most of which reflect different aspects of needs. All situations start from the preference structure which underlies an equity axiom. We are focussing on the following three points: (a) What is the percentage of respondents satisfying the equity axiom? (b) How often do the students revise their initial decision when more and more people join the side of the more advantaged? (c) Are there major differences across countries and cultures?

Equity Axioms for Public Risks

From the perspective of a two-person society, we explain and analyze six axioms for equity among individuals who are exposed to the possibility of death from a public hazard. The axioms are concerned with how a given total risk (expected fatalities) is distributed over the four possible life/death consequences for the two people. Maximal subsets of mutually compatible equity axioms are identified first for a monotonic ordinal utility function and then for a more restrictive von Neumann-Morgenstern utility function.

Equality: On Sen's Weak Equity Axiom

Utilitarianism has a reputation, some say ill-deserved, as an egalitarian social theory. Deserved or not, the reputation has at least something to be said for it. If society aims at the greatest sum of individual utilities, and if the Law of Diminishing Marginal Utility holds, and if individual utility functions are more or less the same, then society ought to take from the well off and give to the poorly off until the utility that each receives from the last unit of every good is equal. A flaw in the reputation, however, is that both of the factual assumptions are false. The first one-the Law of Diminishing Marginal Utility-holds widely but not universally. The second assumption-that individual utility functions are more or less the same-is a gross oversimplification. It is not just that people's tastes differ. The point is rather that there are unfortunate people who, because of, say, a handicap, derive less satisfaction from various things than a normal person, and that there are also lucky people who derive more. I do not think that the failure of the first assumption, the Law of Diminishing Marginal Utility, creates serious difficulties for utilitarianism. But the failure of the second assumption, it seems to me, does.

Equity, Arrow's Conditions, and Rawls' Difference Principle

An Arrow social welfare function was designed not to incorporate any interpersonal comparisons. But some notions of equity rest on interpersonal comparisons. It is shown that a generalized social welfare function, incorporating interpersonal comparisons, can satisfy modifications of the Arrow conditions, and also a strong version of an equity axiom due to Sen. One such generalized social welfare function is the lexicographic form of Rawls' ARRow (1) INVESTIGATED the problem of how to amalgamate the personal welfare orderings of the members of a society into a social welfare ordering. His approach was deliberately designed to avoid making any kind of interpersonal comparison. He was then able to show that such an approach must fail as long as one insists on certain other apparently appropriate conditions. It would therefore seem that an obvious way around Arrow's impossibility theorem is to make interpersonal comparisons and to use them in the construc- tion of a social ordering. Moreover, some considerations of equity which many people would think relevant for making social choices are specifically excluded by Arrow's approach. This paper shows how, if interpersonal comparisons are made in a certain way, one can construct a social welfare ordering by a method which satisfies suitably modified forms of Arrow's 1963 conditions. Moreover-as is just as well, given that the interpersonal comparisons are deliberately based on a notion of equity- it is also possible to satisfy an extra condition, which is a kind of equity axiom. The lexicographic extension of Rawls' difference principle, or maximin rule, satisfies all these conditions. In addition, it is the only rule or principle which satisfies a condition which underlies Suppes' grading principle, together with these condi- tions. Section 2 presents preliminary definitions and notation, and shows how some considerations of equity are excluded by Arrow's approach to social choice. Section 3 shows how these considerations of equity may be represented by ordinal interpersonal comparisons of the kind discussed in Sen (6), how they are related to an equity axiom due to Sen (7), and how Sen's equity axiom may be generalized. Section 4 defines generalized social welfare functions (GSWF's) and shows how Arrow's conditions can be modified to apply to GSWF's. Section 5 'This is an expanded and subsequently revised version of a paper presented to the European