Social Choice and Welfare

, Volume 41, Issue 4, pp 763–787 | Cite as

On the generalization and decomposition of the Bonferroni index

  • Elena Bárcena-Martin
  • Jacques SilberEmail author
Original Paper


A simple algorithm is proposed which defines the Bonferroni as the product of a row vector of individual population shares, a linear mathematical operator called the Bonferroni matrix and a column vector of income shares. This algorithm greatly simplifies the decomposition of the Bonferroni index by income sources or classes and population subgroups. The proposed algorithm links also the Bonferroni index to the concepts of relative deprivation and social welfare and leads to a generalization where the traditional Bonferroni and Gini indices are special cases. The paper ends with an empirical illustration based on EU-SILC data for the year 2008.


Total Income Gini Index Lorenz Curve Income Source Relative Deprivation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Facultad de Ciencias Económicas y Empresariales Universidad de MálagaMalagaSpain
  2. 2.Department of EconomicsBar-Ilan UniversityRamat-GanIsrael
  3. 3.CEPS/INSTEADEsch-sur-AlzetteLuxembourg

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