IDEAS home Printed from https://ideas.repec.org/p/nig/wpaper/0098.html
   My bibliography  Save this paper

Strategy-proof fuzzy aggregation rules

Author

Listed:
  • Juan Perote Pena
  • Ashley Piggins

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

Abstract

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategyproof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategyproof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.

Suggested Citation

  • Juan Perote Pena & Ashley Piggins, 2005. "Strategy-proof fuzzy aggregation rules," Working Papers 0098, National University of Ireland Galway, Department of Economics, revised 2005.
    • Handle: RePEc:nig:wpaper:0098
    as

    Download full text from publisher

    File URL: http://www.economics.nuig.ie/resrch/paper.php?pid=105
    File Function: First version, 2005
    Download Restriction: no
    File URL: http://www.economics.nuig.ie/resrch/paper.php?pid=105
    File Function: Revised version, 2005
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Garcia-Lapresta, Jose Luis & Llamazares, Bonifacio, 2001. "Majority decisions based on difference of votes," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 463-481, June.
    2. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
    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. 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. Barbera, Salvador, 1983. "Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-417, June.
    6. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    7. Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
    8. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
    9. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401.
    10. Salvador Barberà, 2001. "An introduction to strategy-proof social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 619-653.
    11. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541, Elsevier.
    12. Blackorby, Charles, 1975. "Degrees of Cardinality and Aggregate Partial Orderings," Econometrica, Econometric Society, vol. 43(5-6), pages 845-852, Sept.-Nov.
    13. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
    14. 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.
    15. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    16. Leclerc, B., 1984. "Efficient and binary consensus functions on transitively valued relations," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 45-61, August.
    17. Tang, Fang-Fang, 1994. "Fuzzy Preferences and Social Choice," Bulletin of Economic Research, Wiley Blackwell, vol. 46(3), pages 263-269, July.
    18. 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.
    19. Barrett, C Richard & Pattanaik, Prasanta K, 1989. "Fuzzy Sets, Preference and Choice: Some Conceptual Issues," Bulletin of Economic Research, Wiley Blackwell, vol. 41(4), pages 229-253, October.
    20. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    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. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part one: general agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 747-786, April.
    2. 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.
    3. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    4. 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.
    5. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    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.

    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. 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.
    2. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    3. 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.
    4. 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.
    5. Alexander Reffgen, 2011. "Generalizing the Gibbard–Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 39-59, June.
    6. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 01-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    7. Miller, Michael K., 2009. "Social choice theory without Pareto: The pivotal voter approach," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 251-255, September.
    8. KayI, Çagatay & Ramaekers, Eve, 2010. "Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems," Games and Economic Behavior, Elsevier, vol. 68(1), pages 220-232, January.
    9. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    10. 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.
    11. Gordon, Sidartha, 2007. "Public decisions: Solidarity and the status quo," Games and Economic Behavior, Elsevier, vol. 61(2), pages 225-241, November.
    12. Juan Perote Peña, 2003. "Solidarity in Terms of Reciprocity," Economic Working Papers at Centro de Estudios Andaluces E2003/16, Centro de Estudios Andaluces.
    13. Donald E. Campbell & Jerry S. Kelly, 2007. "Organ Transplants, Hiring Committees, and Early Rounds of the Kappell Piano Competition," Working Papers 51, Department of Economics, College of William and Mary.
    14. Ju, Biung-Ghi, 2004. "Continuous selections from the Pareto correspondence and non-manipulability in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 573-592, August.
    15. James Schummer, 1999. "Almost-dominant Strategy Implementation," Discussion Papers 1278, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    17. Freixas, Josep & Parker, Cameron, 2015. "Manipulation in games with multiple levels of output," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 144-151.
    18. Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains in strategic voting," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 46-55.
    19. Fang-Fang Tang & Yongsheng Xu, 2021. "Corruption in Organizations: Some General Formulations and (In-)Corruptibility Results," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 38(1), pages 49-57, December.
    20. Ján Palguta, 2011. "Voting Experiments: Measuring Vulnerability of Voting Procedures to Manipulation," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 5(3), pages 324-345, November.

    More about this item

    Keywords

    Fuzzy aggregation rules; Strategy-proofness;

    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:0098. 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: 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. RePEc uses bibliographic data supplied by the respective publishers.