What do normative indices of multidimensional inequality really measure?

Abstract

We argue that normative indices of multidimensional inequality do not only measure a distribution's extent of inequity (i.e., the gaps between the better-off and the worse-off), but also its extent of inefficiency (i.e., the non-realized mutually beneficial exchanges of goods). We provide a decomposition that allows quantifying these two parts of inequality. Exact formulas of the inequity and inefficiency components are provided for a generic class of social welfare functions. The inequity component turns out to be a two-stage measure, which applies a unidimensional inequality measure to the vector of well-being levels. We critically discuss two prominent transfer principles, viz., uniform majorization and correlation increasing majorization, in the light of the decomposition. A decomposition of inequality in human development illustrates the analysis.

Who's afraid of aggregating money metrics?

“…In this approach, inequality is defined as the social welfare gain that could be obtained by optimally redistributing the societal bundle. 19 In a setting with homogeneous preferences, we have argued elsewhere that it is important to decompose this social welfare gain into an equity gain and an efficiency gain, with only the equity gain capturing true inequality (Bosmans et al 2015). We leave the extension to heterogeneous preferences for future work.…”

Prioritarian Poverty Comparisons with Cardinal and Ordinal Attributes

“…Therefore, these principles, which are prominent but controversial in the body of literature (see Bosmans et al . () for a discussion), receive a new ethical underpinning using priority.…”

A Fairness Justification of Utilitarianism

“…Least concave numerical representations of preferences were studied in Debreu (1976) and Kannai (1977). These were later applied to measure risk (Kihlstrom and Mirman (1981)), inequality (Atkinson and Bourguignon (1982), Bosmans, Decancq, and Ooghe (2015)), and poverty (Atkinson (2003)). 17 To preserve interpersonal comparability of the opportunity-equivalent well-being functions, we derive the least joint concave representations of preferences: the transformation ensuring least concavity of the representations is jointly imposed on all individuals.…”

“…This transformation ensures that each individual's numerical representations of preferences is concave and, consequently, that society does not endorse regressive transfers. On the measurement of social welfare by the sum of money metrics, see also the characterization by Bosmans, Decancq, and Ooghe (2016). 9 As Arrow (1963, p. 109) wrote, the ordinal informational basis is a grounding feature and key contribution of Bergson's approach: "It is the great merit of Bergson's 1938 paper to have carried the same [ordinalist] principle into the analysis of social welfare.…”