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Lexical Measures of Social Inequality: From Pigou‐Dalton to Hammond
Author(s) -
OuYang Kui
Publication year - 2019
Publication title -
review of income and wealth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.024
H-Index - 57
eISSN - 1475-4991
pISSN - 0034-6586
DOI - 10.1111/roiw.12402
Subject(s) - mathematical economics , axiom , inequality , anonymity , economics , measure (data warehouse) , generalization , log sum inequality , independence (probability theory) , mathematics , axiomatic system , pareto principle , pigou effect , econometrics , welfare economics , law , statistics , computer science , political science , mathematical analysis , geometry , database , macroeconomics
A measure of social inequality is essentially a rational ordering over a space of social distributions. However, different measures, including the most popular ones, may provide very different rankings over the same set of typical distributions. We thus propose an axiomatic approach to inequality measurement mainly based on the Hammond principle, a natural generalization of the Pigou‐Dalton principle, attempting to clarify the true nature of social inequality: the rich get richer and the poor get poorer. Under the standard assumptions of anonymity and scale independence, we show that a social inequality ordering is the leximinimax measure if and only if it satisfies the first Hammond principle, and it is the leximaximin measure if and only if it satisfies the second Hammond principle.