An axiomatic approach to the measurement of envy

We characterize a class of envy-as-inequity measures. There are three key axioms. Decomposability requires that overall envy is the sum of the envy within and between subgroups. The other two axioms deal with the two-individual setting and specify how the envy measure should react to simple changes in the individuals’ commodity bundles. The characterized class measures how much one individual envies another individual by the relative utility difference (using the envious’ utility function) between the bundle of the envied and the bundle of the envious, where the utility function that must be used to represent the ordinal preferences is the ‘ray’ utility function. The class measures overall envy by the sum of these (transformed) relative utility differences. We discuss our results in the light of previous contributions to envy measurement and multidimensional inequality measurement

Laissez-faire versus Pareto

AbstractConsider two principles for social evaluation. The first, “laissez-faire”, says that mean-preserving redistribution away from laissez-faire incomes should be regarded as a social worsening. This principle captures a key aspect of libertarian political philosophy. The second, weak Pareto, states that an increase in the disposable income of each individual should be regarded as a social improvement. We show that the combination of the two principles implies that total disposable income ought to be maximized. Strikingly, the relationship between disposable incomes and laissez-faire incomes must therefore be ignored, leaving little room for libertarian values

Equality and responsibility: ex ante and ex post redistribution mechanisms

We study redistribution in a setting where individual responsibility and circumstance characteristics determine pre-tax income. We distinguish between ex ante and ex post versions of the key principles of compensation and reward. Furthermore, we distinguish between absolute and relative versions of reward. On the basis of these axioms, we provide characterizations of five familiar and two new redistribution mechanisms