Abstract
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.
Highlights
An allocation is envy-free if no individual prefers another individual’s commodity bundle to his own
The characterized class measures how much one individual envies another individual by the relative utility difference 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
We discuss our results in the light of previous contributions to envy measurement and multidimensional inequality measurement
Summary
An allocation is envy-free if no individual prefers another individual’s commodity bundle to his own. Throughout, we discuss the connections with envy measures proposed by Feldman and Kirman (1974), Chaudhuri (1986), Diamantaras and Thomson (1989), Tadenuma and Thomson (1995) and Fleurbaey (2008). We formulate two axioms, betweenness and proportionality, that deal with envy comparisons in the simple two-individual setting. The axioms betweenness and r -proportionality imply that Ei j is an increasing function of the ratio ui (x j )/ui (xi ), where xi and x j are the bundles of individuals i and j and ui is a ‘ray’ utility representation of i’s ordinal preferences.
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