A social‐psychological reconstruction of Amartya Sen’s measures of inequality and social welfare

Oded Stark,Wiktor Budzinski

doi:10.1111/kykl.12280

Abstract

AbstractThe Gini coefficient features prominently in Amartya Sen’s 1973 and 1997 seminal work on income inequality and social welfare. We construct the Gini coefficient from social‐psychological building blocks, reformulating it as a ratio between a measure of social stress and aggregate income. We determine when as a consequence of an income gain by an individual, an increase in the social stress measure dominates a concurrent increase in the aggregate income, such that the magnitude of the Gini coefficient increases. By integrating our approach to the construction of the Gini coefficient with Sen’s social welfare function, we are able to endow the function with a social‐psychological underpinning, showing that this function, too, is a composite of a measure of social stress and aggregate income. We reveal a dual role played by aggregate income as a booster of social welfare in Sen’s social welfare function. Quite surprisingly, we find that a marginal increase of income for any individual, regardless of the position of the individual in the hierarchy of incomes, improves welfare as measured by Sen’s social welfare function.

Highlights

In “On Economic Inequality” (1973 and 1997), Amartya Sen presented a formula of the Gini coefficient of inequality that has subsequently served as a standard representation of the coefficient
We integrate our approach to the construction of the Gini coefficient with Sen’s social welfare function. This application endows the function with a social-psychological underpinning; it uncovers a dual role played by the population’s aggregate income as a booster of social welfare, and it enables us to show that any marginal increase in income improves welfare as measured by Sen’s social welfare function, the effect of such an increase on the Gini coefficient notwithstanding - even if it amounts to increasing income inequality as measured by the coefficient
Because a marginal increase in any income increases both TI, TI and the income per capita term, the combined effect of these two changes, which operate in the same direction, results in a social welfare gain

Summary

Introduction

In “On Economic Inequality” (1973 and 1997), Amartya Sen presented a formula of the Gini coefficient of inequality that has subsequently served as a standard representation of the coefficient. This application endows the function with a social-psychological underpinning; it uncovers a dual role played by the population’s aggregate income as a booster of social welfare, and it enables us to show that any marginal increase in income improves welfare as measured by Sen’s social welfare function, the effect of such an increase on the Gini coefficient notwithstanding - even if it amounts to increasing income inequality as measured by the coefficient When the basis for making a judgment is the social welfare function formulated by Sen, the said intuition breaks down This observation has far-reaching consequences for a wide spectrum of policies, ranging from the promotion of economic growth that affects incomes unevenly to the design and rationale of tax schemes. The stress caused by low social status is often perceived as an intermediate factor linking the experience of relative deprivation with poor health outcomes (Wilkinson, 1997; Eibner and Evans, 2005; Cundiff et al, 2020). Delhey and Dragolov (2014) and others label this stress as “status anxiety.” In this paper we refer to the stress discussed in this paragraph as social-psychological stress or as stress caused by relative deprivation

Calibrating social stress

Modifying Sen’s presentation of the Gini coefficient

Revisiting Sen’s social welfare function

Findings

Discussion and conclusion