IDEAS home Printed from https://ideas.repec.org/p/nig/wpaper/0140.html
   My bibliography  Save this paper

Arrow's theorem and max-star transitivity

Author

Listed:
  • Conal Duddy
  • Juan Perote-Pena
  • Asjley Piggins

    (Department of Economics, National University of Ireland, Galway)

Abstract

In the literature on social choice and fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max-min transitivity condition is a member of this family, but there are infinitely many others. Restricting attention to fuzzy aggregation rules that satisfy counterparts of unanimity and independence of irrelevant alternatives, we characterise the set of max-star transitive relations that permit preference aggregation to be non-dictatorial. This set contains all and only those triangular norms that contain a zero divisor.

Suggested Citation

  • Conal Duddy & Juan Perote-Pena & Asjley Piggins, 2009. "Arrow's theorem and max-star transitivity," Working Papers 0140, National University of Ireland Galway, Department of Economics, revised 2009.
  • Handle: RePEc:nig:wpaper:0140
    as

    Download full text from publisher

    File URL: http://www.economics.nuig.ie/resrch/paper.php?pid=147
    File Function: First version, 2009
    Download Restriction: no

    File URL: http://www.economics.nuig.ie/resrch/paper.php?pid=147
    File Function: Revised version, 2009
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
    2. 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.
    3. Rajat Deb & Manabendra Dasgupta, 1996. "Transitivity and fuzzy preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 305-318.
    4. Maurice Salles, 2016. "Social choice," Chapters, in: Gilbert Faccarello & Heinz D. Kurz (ed.), Handbook on the History of Economic Analysis Volume III, chapter 36, pages 518-537, Edward Elgar Publishing.
    5. Asley Piggins & Maurice Salles, 2007. "Instances of Indeterminacy," Post-Print halshs-00337772, HAL.
    6. Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
    7. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
    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. Barrett, C.R. & Pattanaik, P.K. & Salles, M., 1990. "Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework," Institut des Mathématiques Economiques – Document de travail de l’I.M.E. (1974-1993) 9006, Institut des Mathématiques Economiques. LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS, Université de Bourgogne.
    10. Dutta, Bhaskar & Panda, Santosh C. & Pattanaik, Prasanta K., 1986. "Exact choice and fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 53-68, February.
    11. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
    12. Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2010. "Manipulating an aggregation rule under ordinally fuzzy preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 411-428, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maurice Salles, 2014. "‘Social choice and welfare’ at 30: its role in the development of social choice theory and welfare economics," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 1-16, January.
    2. Conal Duddy & Ashley Piggins, 2012. "The proximity condition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 353-369, July.
    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. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.

    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. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    2. 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.
    3. Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2010. "Manipulating an aggregation rule under ordinally fuzzy preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 411-428, March.
    4. Perote-Pena, Juan & Piggins, Ashley, 2007. "Strategy-proof fuzzy aggregation rules," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 564-580, June.
    5. Brian Hill, 2012. "Confidence in preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 273-302, July.
    6. 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.
    7. M. Sanver & Özer Selçuk, 2009. "Sophisticated preference aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 73-86, June.
    8. Geslin, Stephanie & Salles, Maurice & Ziad, Abderrahmane, 2003. "Fuzzy aggregation in economic environments: I. Quantitative fuzziness, public goods and monotonicity assumptions," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 155-166, April.
    9. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
    10. 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.
    11. 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.
    12. Dinko Dimitrov, 2001. "Fuzzy Preferences, Liberalism and Non-discrimination," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 2, pages 63-76.
    13. Subramanian, S., 2009. "The Arrow paradox with fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 265-271, September.
    14. Richard Baron & Mostapha Diss & Eric Rémila & Philippe Solal, 2015. "A geometric examination of majorities based on difference in support," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 123-153, June.
    15. Maurice Salles, 2014. "‘Social choice and welfare’ at 30: its role in the development of social choice theory and welfare economics," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 1-16, January.
    16. José Luis Garcí a-Lapresta & Bonifacio Llamazares, 2010. "Preference Intensities and Majority Decisions Based on Difference of Support Between Alternatives," Group Decision and Negotiation, Springer, vol. 19(6), pages 527-542, November.
    17. Campbell, Donald E. & Kelly, Jerry S., 1996. "Social choice trade-offs for an arbitrary measure: With application to uncertain or fuzzy agenda," Economics Letters, Elsevier, vol. 50(1), pages 99-104, January.
    18. Federico Fioravanti & Fernando Tohm'e, 2019. "Fuzzy Group Identification Problems," Papers 1912.05540, arXiv.org.
    19. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    20. Wesley H. Holliday & Mikayla Kelley, 2020. "A note on Murakami’s theorems and incomplete social choice without the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 243-253, August.

    More about this item

    Keywords

    Arrows theorem; triangular norm; fuzzy preference Algorithmic Trading; MACD;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    Statistics

    Access and download statistics

    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:nig:wpaper:0140. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/deucgie.html .

    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: Srinivas Raghavendra (email available below). General contact details of provider: https://edirc.repec.org/data/deucgie.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.