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The Generalized Gini Welfare Function in the Framework of Symmetric Choquet Integration

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Multicriteria and Multiagent Decision Making with Applications to Economics and Social Sciences

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 305))

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Abstract

In the context of Social Welfare and Choquet integration, we briefly review, on the one hand, the classical Gini inequality index for populations of n ≥ 2 individuals, including the associated Lorenz area formula, and on the other hand, the k-additivity framework for Choquet integration introduced by Grabisch, particularly in the additive and 2-additive symmetric cases. We then show that any 2-additive symmetric Choquet integral can be written as the difference between the arithmetic mean and a multiple of the classical Gini inequality index, with a given interval constraint on the multiplicity parameter. In the special case of positive parameter values this result corresponds to the well-known Ben Porath and Gilboa’s formula for Weymark’s generalized Gini welfare functions, with linearly decreasing (inequality averse) weight distributions.

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Authors and Affiliations

  1. Department of Economics and Management, University of Trento, Via Inama, 5, 38122, Trento, Italy

    Silvia Bortot & Ricardo Alberto Marques Pereira

Authors
  1. Silvia Bortot
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  2. Ricardo Alberto Marques Pereira
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Correspondence to Silvia Bortot .

Editor information

Editors and Affiliations

  1. , Department of Architecture, Second University of Napoli, Via San Lorenzo s/n, Aversa, 81031, Italy

    Aldo G. S. Ventre

  2. “G. d’Annunzio", Department of Letters, Arts and, University of Chieti-Pescara, Via dei Vestini 31, Chieti, 66100, Italy

    Antonio Maturo

  3. Faculty of Military Technology, Department of Mathematics and Physics, University of Defence, Kounicova 65, Brno, 66210, Czech Republic

    Šárka Hošková-Mayerová

  4. , Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, Warsaw, 01-447, Poland

    Janusz Kacprzyk

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Bortot, S., Marques Pereira, R.A. (2013). The Generalized Gini Welfare Function in the Framework of Symmetric Choquet Integration. In: Ventre, A., Maturo, A., Hošková-Mayerová, Š., Kacprzyk, J. (eds) Multicriteria and Multiagent Decision Making with Applications to Economics and Social Sciences. Studies in Fuzziness and Soft Computing, vol 305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35635-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-35635-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35634-6

  • Online ISBN: 978-3-642-35635-3

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