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On the Measurement of Dissimilarity and Related Orders

Author

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  • Francesco Andreoli

    () (Université de Cergy-Pontoise, THEMA; ESSEC Business School, Cergy-Pontoise; University of Verona)

  • Claudio Zoli

    () (University of Verona)

Abstract

We consider populations partitioned into groups, whose members are distributed across a finite number of classes such as, for instance, types of occupation, residential locations, social status of fathers, levels of education, health or income. Our aim is to assess the dissimilarity between the patterns of distributions of the different groups. These evaluations are relevant for the analysis of multi-group segregation, socioeconomic mobility, equalization of opportunity and discrimination. We conceptualize the notion of dissimilarity making use of reasonable transformations of the groups' distributions, based on sequences of transfers and exchanges of population masses across classes and/or groups. Our analysis clarifies the substantial differences underlying the concept of dissimilarity when applied to ordered or to permutable classes. In both settings, we illustrate the logical connections of dissimilarity evaluations with matrix majorization preorders, and provide equivalent implementable criteria to test unambiguous reductions in dissimilarity. Furthermore, we show that inequality evaluations can be interpreted as special cases of dissimilarity assessments and discuss relations with concepts of segregation and discrimination.

Suggested Citation

  • Francesco Andreoli & Claudio Zoli, 2012. "On the Measurement of Dissimilarity and Related Orders," Working Papers 274, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2012-274
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    References listed on IDEAS

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    Cited by:

    1. Casilda Vega & Oscar Volij, 2014. "Segregation, informativeness and Lorenz dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 547-564, October.
    2. Peter Nijkamp & Jacques Poot, 2015. "Cultural Diversity - A Matter of Measurement," CReAM Discussion Paper Series 1502, Centre for Research and Analysis of Migration (CReAM), Department of Economics, University College London.
    3. Allanson, Paul, 2014. "Income stratification and the measurement of interdistributional inequality between multiple groups," SIRE Discussion Papers 2015-34, Scottish Institute for Research in Economics (SIRE).
    4. Allanson, Paul, 2014. "Income stratification and the measurement of interdistributional inequality between multiple groups," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-34, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Monojit Chatterji & Sushil Mohan & Sayantan Ghosh Dastidar, 2015. "Determinants of public education expenditure: evidence from Indian states," International Journal of Education Economics and Development, Inderscience Enterprises Ltd, vol. 6(1), pages 1-19.

    More about this item

    Keywords

    dissimilarity; matrix majorization; Zonotopes; multi-group segregation; discrimination.;

    JEL classification:

    • J71 - Labor and Demographic Economics - - Labor Discrimination - - - Hiring and Firing
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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