IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01941037.html
   My bibliography  Save this paper

Arrow’s (im)possibility theorem

Author

Listed:
  • Pierre Bernhard

    (BIOCORE - Biological control of artificial ecosystems - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - INRA - Institut National de la Recherche Agronomique - LOV - Laboratoire d'océanographie de Villefranche - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - IMEV - Institut de la Mer de Villefranche - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

  • Marc Deschamps

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

Abstract

Arrow's (im)possibility theorem is one of the most famous and important contri- butions in economics. It concerns the difficulty to aggregate a set of individual preferences, given as rankings of a set of available alternatives, into a unique social preferences ranking via a social welfare function, or into a unique social choice. Arrow proves that in a specific framework, it is impossible to find a social welfare function which simultaneously satisfies four conditions: universal domain, weak Pareto principle, independence of irrelevant alternatives, and no dictator. Our no- tice presents this theorem, one of its proofs, and, we hope, invites the reader to discover social choice theory

Suggested Citation

  • Pierre Bernhard & Marc Deschamps, 2018. "Arrow’s (im)possibility theorem," Post-Print hal-01941037, HAL.
    • Handle: RePEc:hal:journl:hal-01941037
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-01941037v1
    as

    Download full text from publisher

    File URL: https://inria.hal.science/hal-01941037v1/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
    2. Patrick Suppes, 2005. "The pre-history of Kenneth Arrow's social choice and individual values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 319-326, December.
    3. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    4. 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.
    5. repec:bla:econom:v:44:y:1977:i:173:p:81-88 is not listed on IDEAS
    6. Kenneth J. Arrow, 1987. "Arrow on Arrow: an Interview," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 23, pages 637-657, Palgrave Macmillan.
    7. Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16.
    8. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    9. 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.
    10. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    11. 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)

    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. Ning Yu, 2015. "A quest for fundamental theorems of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 533-548, March.
    2. Uuganbaatar Ninjbat, 2015. "Impossibility theorems are modified and unified," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 849-866, December.
    3. Elizabeth Maggie Penn, 2015. "Arrow’s Theorem and its descendants," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 14, pages 237-262, Edward Elgar Publishing.
    4. Salvador Barberà, 2003. "A Theorem on Preference Aggregation," UFAE and IAE Working Papers 601.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    5. Ning Neil Yu, 2013. "A one-shot proof of Arrow’s theorem and the Gibbard–Satterthwaite theorem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 145-149, November.
    6. Cato, Susumu, 2011. "Maskin monotonicity and infinite individuals," Economics Letters, Elsevier, vol. 110(1), pages 56-59, January.
    7. Islam, Jamal & Mohajan, Haradhan & Moolio, Pahlaj, 2010. "Methods of voting system and manipulation of voting," MPRA Paper 50854, University Library of Munich, Germany, revised 06 May 2010.
    8. Miller, Michael K., 2009. "Social choice theory without Pareto: The pivotal voter approach," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 251-255, September.
    9. Priscilla Man & Shino Takayama, 2013. "A unifying impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 249-271, October.
    10. Davide Grossi, 2021. "Lecture Notes on Voting Theory," Papers 2105.00216, arXiv.org.
    11. Cato, Susumu, 2009. "Another induction proof of the Gibbard-Satterthwaite theorem," Economics Letters, Elsevier, vol. 105(3), pages 239-241, December.
    12. Uuganbaatar Ninjbat, 2012. "Symmetry vs. complexity in proving the Muller-Satterthwaite theorem," Economics Bulletin, AccessEcon, vol. 32(2), pages 1434-1441.
    13. Gaudeul, Alexia, 2009. "A (micro) course in microeconomic theory for MSc students," MPRA Paper 15388, University Library of Munich, Germany.
    14. Samejima, Yusuke, 2005. "Strategic candidacy, monotonicity, and strategy-proofness," Economics Letters, Elsevier, vol. 88(2), pages 190-195, August.
    15. Artemov, Georgy, 2014. "An impossibility result for virtual implementation with status quo," Economics Letters, Elsevier, vol. 122(3), pages 380-385.
    16. Kotaro Suzumura, 2002. "Introduction to social choice and welfare," Temi di discussione (Economic working papers) 442, Bank of Italy, Economic Research and International Relations Area.
    17. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    18. Svensson, Lars-Gunnar & Reffgen, Alexander, 2014. "The proof of the Gibbard–Satterthwaite theorem revisited," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 11-14.
    19. Dindar, Hayrullah & Lainé, Jean, 2017. "Manipulation of single-winner large elections by vote pairing," Economics Letters, Elsevier, vol. 161(C), pages 105-107.
    20. Donaldson, Jason & Piacentino, Giorgia & Malenko, Nadya, 2017. "Deadlock on the Board," CEPR Discussion Papers 12503, C.E.P.R. Discussion Papers.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:journl:hal-01941037. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.