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Third-degree stochastic dominance and inequality measurement

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Abstract

We investigate the third-degree stochastic dominance order, which is receiving increasing attention in the field of inequality measurement. Observing that this partial order fails to satisfy the von Neumann–Morgenstern independence property in the space of random variables, we introduce the concepts of strong and local third-degree stochastic dominance, which do not suffer from this deficiency. We motivate these two new binary relations and characterize them in the spirit of the Lorenz characterization of the second-degree stochastic order, comparing our findings with the closest results in inequality literature.

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Authors and Affiliations

  1. Toulouse School of Economics, GREMAQ-IDEI-IUF, Manufacture des Tabacs, Aile Jean-Jacques Laffont 21, allée de Brienne, 31000, Toulouse, France

    Michel Le Breton

  2. Department of Economics, University of Verona, Via dell’Università 4, 37129, Verona, Italy

    Eugenio Peluso

Authors
  1. Michel Le Breton
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  2. Eugenio Peluso
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Correspondence to Eugenio Peluso.

Additional information

A preliminary version of this paper was presented at the second Canazei Winter School on Inequality and Collective Welfare Theory (IT2). We would like to thank all participants for their comments and suggestions. We are especially grateful to Rolf Aaberge, Peter Lambert, Maria G. Monti, Ernesto Savaglio, John Weymark, Claudio Zoli and two anonymous referees who provided very detailed and insightful comments.

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Le Breton, M., Peluso, E. Third-degree stochastic dominance and inequality measurement. J Econ Inequal 7, 249–268 (2009). https://doi.org/10.1007/s10888-008-9077-0

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  • DOI: https://doi.org/10.1007/s10888-008-9077-0

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