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A model of social welfare improving transfers

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  • Brice Magdalou

    (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

We establish an equivalence theorem between (i) dominance of one society by another, according to a finite sequence of social welfare improving transfers and (ii) dominance according to a class of social welfare functions, in the following framework: individual outcomes are multidimensional but finitely divisible in each dimension, a distribution simply counts the number of individuals having each possible outcome, and the considered set of transfers has the structure of a discrete cone. This framework encompasses most of the social welfare improving transfers investigated in the literature such as, for instance, Pigou-Dalton progressive transfers. As by-products, our model sheds new light on some surprising results in the literature on social deprivation, and provides new arguments on the key role of the expected utility model in decision-making under risk.

Suggested Citation

  • Brice Magdalou, 2018. "A model of social welfare improving transfers," CEE-M Working Papers hal-01975452, CEE-M, Universtiy of Montpellier, CNRS, INRA, Montpellier SupAgro.
    • Handle: RePEc:hal:wpceem:hal-01975452
    Note: View the original document on HAL open archive server: https://hal.science/hal-01975452
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    References listed on IDEAS

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    1. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2019. "Inequality measurement with an ordinal and continuous variable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 453-475, March.
    2. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2019. "Inequality measurement with an ordinal and continuous variable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 453-475, March.
    3. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    5. Mathieu Faure & Nicolas Gravel, 2017. "Equality among Unequals," Working Papers halshs-01430195, HAL.
    6. Alain Chateauneuf & Patrick Moyes, 2002. "Non-welfarist approaches to inequality measurement," Post-Print hal-00156676, HAL.
    7. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    8. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2021. "Ranking distributions of an ordinal variable," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 33-80, February.
    9. Brice Magdalou & Patrick Moyes, 2009. "Deprivation, welfare and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 253-273, February.
    10. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2014. "Ranking Distributions of an Ordinal Attribute," AMSE Working Papers 1450, Aix-Marseille School of Economics, France.
    11. Amiel, Yoram & Cowell, Frank A., 1992. "Measurement of income inequality : Experimental test by questionnaire," Journal of Public Economics, Elsevier, vol. 47(1), pages 3-26, February.
    12. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    13. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    16. Müller, Alfred & Scarsini, Marco, 2012. "Fear of loss, inframodularity, and transfers," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1490-1500.
    17. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    18. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
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    Cited by:

    1. John A. Weymark, 2020. "Commentary on “From unidimensional to multidimensional inequality: a review”," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 55-59, April.
    2. Aouani, Zaier & Chateauneuf, Alain, 2020. "Multidimensional inequality and inframodular order," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 74-79.
    3. Ramses H. Abul Naga, 2022. "The minimal Hilbert basis of the Hammond order cone," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 191-215, October.
    4. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2021. "Ranking distributions of an ordinal variable," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 33-80, February.
    5. Bertoli-Barsotti, Lucio & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2024. "Gini-stable Lorenz curves and their relation to the generalised Pareto distribution," Journal of Informetrics, Elsevier, vol. 18(2).

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    More about this item

    Keywords

    welfare-improving transfers; stochastic dominance.; inequality; social welfare;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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