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Rights Systems and Aggregation Functions on Property Spaces

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  • Marta Cardin

    (Department of Economics, Ca’Foscari University of Venice, Sestiere Cannaregio 873, 30121 Venezia, Italy)

Abstract

The notion of decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally, we study aggregation problems in which a subgroup of decision makers have the right to determine the properties of the aggregate. Then, we introduce property spaces and rights to properties and characterize aggregation operators that are consistent with rights to properties. Moreover, we define congruences in property spaces, and we propose a generalization of the Sugeno integral in our framework.

Suggested Citation

  • Marta Cardin, 2023. "Rights Systems and Aggregation Functions on Property Spaces," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3709-:d:1227598
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    References listed on IDEAS

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    1. Sidartha Gordon, 2015. "Unanimity in attribute-based preference domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 13-29, January.
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    3. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    4. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    5. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    6. Radomír Halaš & Jozef Pócs & Jana Pócsová, 2022. "Remarks on Sugeno Integrals on Bounded Lattices," Mathematics, MDPI, vol. 10(17), pages 1-9, August.
    7. Kretz, Claudio, 2021. "Consistent rights on property spaces," Journal of Economic Theory, Elsevier, vol. 197(C).
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