IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i3p436-d333580.html
   My bibliography  Save this article

Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

Author

Listed:
  • Armajac Raventós-Pujol

    (Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain)

  • María J. Campión

    (Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain)

  • Esteban Induráin

    (Institute for Advanced Materials and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain)

Abstract

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

Suggested Citation

  • Armajac Raventós-Pujol & María J. Campión & Esteban Induráin, 2020. "Decomposition and Arrow-Like Aggregation of Fuzzy Preferences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:436-:d:333580
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/3/436/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/3/436/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2011. "Arrow’s theorem and max-star transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(1), pages 25-34, January.
    2. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    3. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
    4. Gregory Richardson, 1998. "The structure of fuzzy preferences: Social choice implications," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 359-369.
    5. Louis Fono & Nicolas Andjiga, 2007. "Utility function of fuzzy preferences on a countable set under max-*-transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 667-683, June.
    6. Conal Duddy & Ashley Piggins, 2018. "On some oligarchy results when social preference is fuzzy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 717-735, December.
    7. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
    8. Kelly, Jerry S., 1978. "Arrow Impossibility Theorems," Elsevier Monographs, Elsevier, edition 1, number 9780124033504 edited by Shell, Karl.
    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. Louis Fono & Maurice Salles, 2011. "Continuity of utility functions representing fuzzy preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 669-682, October.
    2. Hannu Nurmi, 2001. "Resolving Group Choice Paradoxes Using Probabilistic and Fuzzy Concepts," Group Decision and Negotiation, Springer, vol. 10(2), pages 177-199, March.
    3. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    4. Conal Duddy & Ashley Piggins, 2018. "On some oligarchy results when social preference is fuzzy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 717-735, December.
    5. Davide Grossi, 2021. "Lecture Notes on Voting Theory," Papers 2105.00216, arXiv.org.
    6. Federico Fioravanti, 2024. "Fuzzy Classification Aggregation," Papers 2402.17620, arXiv.org, revised Mar 2024.
    7. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 267-284, July.
    8. Perote-Pena, Juan & Piggins, Ashley, 2007. "Strategy-proof fuzzy aggregation rules," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 564-580, June.
    9. Rajsbaum, Sergio & Raventós-Pujol, Armajac, 2022. "A Combinatorial Topology Approach to Arrow's Impossibility Theorem," MPRA Paper 112004, University Library of Munich, Germany.
    10. Richard Barrett & Maurice Salles, 2006. "Social Choice With Fuzzy Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200615, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    11. Dinko Dimitrov, 2001. "Fuzzy Preferences, Liberalism and Non-discrimination," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 2, pages 63-76.
    12. Peter Casey & Mark Wierman & Michael Gibilisco & John Mordeson & Terry Clark, 2012. "Assessing policy stability in Iraq: a fuzzy approach to modeling preferences," Public Choice, Springer, vol. 151(3), pages 409-423, June.
    13. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    14. S. Subramanian, 2010. "Liberty, equality, and impossibility: some general results in the space of 'soft' preferences," Journal of Economic Policy Reform, Taylor & Francis Journals, vol. 13(4), pages 325-341.
    15. Subramanian, S., 2009. "The Arrow paradox with fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 265-271, September.
    16. Federico Fioravanti, 2024. "Fuzzy Classification Aggregation," Working Papers 312, Red Nacional de Investigadores en Economía (RedNIE).
    17. Csaba, László, 2014. "Átmenettan és közgazdaságtan. Módszertani tanulságok egy részterület műveléséből [Transitology" and economics. Methodological lessons to be drawn from work in a partial territory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 53-67.
    18. Crispin H. V. Cooper, 2020. "Quantitative Models of Well-Being to Inform Policy: Problems and Opportunities," Sustainability, MDPI, vol. 12(8), pages 1-13, April.
    19. Kotaro Suzumura, 2020. "Reflections on Arrow’s research program of social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 219-235, March.
    20. Leo Katz & Alvaro Sandroni, 2020. "Limits on power and rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 507-521, March.

    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:8:y:2020:i:3:p:436-:d:333580. 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.