Measurement of inequality with a finite number of pay states: the majorization set and its applications

Ramses H. Abul Naga* (Corresponding Author)

*Corresponding author for this work

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In this paper we examine the Lorenz ordering when the number of pay states is finite, as is most often the case in public sector employment. We characterize the majorization set: the set of pay scales such that some distribution u is more egalitarian than another distribution v, with u and v being two distributions of a given sum total. We show that while this set is infinite, it is generated as the convex hull of a finite number of points. We then discuss several applications of the result, including the problem of reducing inequality between groups, conditions under which different pay scales may reverse the ordering of two Lorenz curves, and the use of the majorization set in relation to optimal income taxation.
Original languageEnglish
Pages (from-to)99-123
Number of pages25
JournalEconomic Theory
Early online date2 Nov 2016
Publication statusPublished - Jan 2018

Bibliographical note

I am grateful to Vassily Gorbanov, Tarik Yalcin and Fabrizio Germano for extended discussions and suggestions, and to an associate editor and a reviewer for constructive comments. I also wish to thank Francesco Andreoli, Geoffrey Burton, Joe Swierzbinski, Alain Trannoy, Claudio Zoli and seminar participants at the Aix-Marseille School of Economics for discussions. I am responsible for any errors.


  • measurement of inequality
  • discrete data
  • majorization set
  • majorization matrix
  • convex sets and their separation


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