IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i17p3709-d1227598.html
   My bibliography  Save this article

Rights Systems and Aggregation Functions on Property Spaces

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/17/3709/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/17/3709/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Domenico Cantone & Alfio Giarlotta & Stephen Watson, 2019. "Congruence relations on a choice space," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 247-294, February.
    2. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    3. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    4. Radomír Halaš & Jozef Pócs & Jana Pócsová, 2022. "Remarks on Sugeno Integrals on Bounded Lattices," Mathematics, MDPI, vol. 10(17), pages 1-9, August.
    5. Kretz, Claudio, 2021. "Consistent rights on property spaces," Journal of Economic Theory, Elsevier, vol. 197(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dietrich, Franz, 2012. "Judgment aggregation and the discursive dilemma," MPRA Paper 36772, University Library of Munich, Germany.
    2. Luca Anzilli & Silvio Giove, 2020. "Multi-criteria and medical diagnosis for application to health insurance systems: a general approach through non-additive measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 559-582, December.
    3. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    4. Domenico Cantone & Alfio Giarlotta & Stephen Watson, 2021. "Choice resolutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 713-753, May.
    5. Ya-Qiang Xu & Le-Sheng Jin & Zhen-Song Chen & Ronald R. Yager & Jana Špirková & Martin Kalina & Surajit Borkotokey, 2022. "Weight Vector Generation in Multi-Criteria Decision-Making with Basic Uncertain Information," Mathematics, MDPI, vol. 10(4), pages 1-11, February.
    6. repec:spo:wpmain:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS
    7. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    8. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    9. Peter Reichert & Klemens Niederberger & Peter Rey & Urs Helg & Susanne Haertel-Borer, 2019. "The need for unconventional value aggregation techniques: experiences from eliciting stakeholder preferences in environmental management," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 197-219, November.
    10. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
    11. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    12. 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.
    13. Giarlotta, Alfio & Petralia, Angelo & Watson, Stephen, 2022. "Bounded rationality is rare," Journal of Economic Theory, Elsevier, vol. 204(C).
    14. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    15. Vicenç Torra, 2022. "Andness Directedness for t-Norms and t-Conorms," Mathematics, MDPI, vol. 10(9), pages 1-10, May.
    16. Chunqiao Tan & Xiaohong Chen, 2016. "Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 311-352, March.
    17. José Luis García-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira & Ana Marta Urrutia, 2010. "A class of poverty measures induced by the dual decomposition of aggregation functions," Working Papers 160, ECINEQ, Society for the Study of Economic Inequality.
    18. Bonifacio Llamazares, 2019. "An Analysis of Winsorized Weighted Means," Group Decision and Negotiation, Springer, vol. 28(5), pages 907-933, October.
    19. Sidartha Gordon, 2014. "Unanimity in Attribute-Based Preference Domains," SciencePo Working papers Main hal-01061994, HAL.
    20. Karlson Pfannschmidt & Pritha Gupta & Bjorn Haddenhorst & Eyke Hullermeier, 2019. "Learning Context-Dependent Choice Functions," Papers 1901.10860, arXiv.org, revised Oct 2021.
    21. Fabrizio Durante & Juan Fernández-Sánchez & Wolfgang Trutschnig & Manuel Úbeda-Flores, 2020. "On the Size of Subclasses of Quasi-Copulas and Their Dedekind–MacNeille Completion," Mathematics, MDPI, vol. 8(12), pages 1-11, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3709-:d:1227598. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.