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The equity core and the Lorenz-maximal allocations in the equal division core

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Abstract

In this note, we give a geometrical decomposition of the equity core as a finite union of polyhedrons. As a consequence, we characterize the non-emptiness of the equity core (Selten in Decision theory and social ethics: issues in social choice, Reidel, Dordrecht, 289–301,  1978) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta and Ray in Games Econ Behav 3:403–422, 1991).

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Notes

  1. The finiteness of the Lorenz-maximal allocations in the equal division core was previously showed by Llerena et al. (2008) in a working paper. Recently, Iehlé (2014) found the same result using a lattice approach.

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Acknowledgments

This is a revision of a working paper previously titled “A simple procedure for computing strong constrained egalitarian allocations” (2008) and it is part of Vilella’s PhD. Dissertation. We are grateful to Carles Rafels for his very helpful comments. We also thank two anonymous referees for detailed comments and suggestions, and to the Generalitat de Catalunya under project 2014SGR631 and Ministerio de Ciencia e Innovación under project ECO2011-22765 for its support.

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Authors and Affiliations

  1. Departament de Gestió d’Empreses, Universiat Rovira i Virgili-CREIP, Av. Universitat 1, 43204, Reus, Spain

    Francesc Llerena & Cori Vilella

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  1. Francesc Llerena
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  2. Cori Vilella
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Correspondence to Cori Vilella.

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Llerena, F., Vilella, C. The equity core and the Lorenz-maximal allocations in the equal division core. Math Meth Oper Res 81, 235–244 (2015). https://doi.org/10.1007/s00186-015-0494-0

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