IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v55y2014icp11-14.html
   My bibliography  Save this article

The proof of the Gibbard–Satterthwaite theorem revisited

Author

Listed:
  • Svensson, Lars-Gunnar
  • Reffgen, Alexander

Abstract

This paper provides three short proofs of the classical Gibbard–Satterthwaite theorem. The theorem is first proved in the case with only two voters. The general case follows then from an induction argument over the number of voters. The proof of the theorem is further simplified when the voting rule is neutral. The simple arguments in the proofs may be especially useful in classroom situations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:55:y:2014:i:c:p:11-14
    DOI: 10.1016/j.jmateco.2014.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406814001177
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2014.09.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    5. 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. Drichoutis, Andreas C. & Lusk, Jayson L. & Pappa, Valentina, 2016. "Elicitation formats and the WTA/WTP gap: A study of climate neutral foods," Food Policy, Elsevier, vol. 61(C), pages 141-155.
    2. Uuganbaatar Ninjbat, 2018. "Impossibility theorems with countably many individuals," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 9(3), pages 333-350, August.
    3. Drichoutis, Andreas C. & Vassilopoulos, Achilleas & Lusk, Jayson L. & Nayga, Rodolfo M. Jr., 2015. "Reference dependence, consequentiality and social desirability in value elicitation: A study of fair labor labeling," 143rd Joint EAAE/AAEA Seminar, March 25-27, 2015, Naples, Italy 202705, European Association of Agricultural Economists.
    4. Drichoutis, Andreas C. & Vassilopoulos, Achilleas & Lusk, Jayson & Nayga, Rodolfo M., 2015. "Fair farming: Preferences for fair labor certification using four elicitation methods," MPRA Paper 62546, University Library of Munich, Germany.
    5. Gori, Michele, 2021. "Manipulation of social choice functions under incomplete information," Games and Economic Behavior, Elsevier, vol. 129(C), pages 350-369.
    6. Giotis, Thomas & Drichoutis, Andreas C., 2020. "Consumer acceptance and willingness-to-pay for insect-based foods: The role of proximity of insects in the food chain," MPRA Paper 104840, University Library of Munich, Germany.

    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. Miller, Michael K., 2009. "Social choice theory without Pareto: The pivotal voter approach," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 251-255, September.
    2. 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.
    3. 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.
    4. Cato, Susumu, 2009. "Another induction proof of the Gibbard-Satterthwaite theorem," Economics Letters, Elsevier, vol. 105(3), pages 239-241, December.
    5. 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.
    6. 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).
    7. 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.
    8. Cato, Susumu, 2011. "Maskin monotonicity and infinite individuals," Economics Letters, Elsevier, vol. 110(1), pages 56-59, January.
    9. repec:cte:werepe:we081207 is not listed on IDEAS
    10. Anup Pramanik & Arunava Sen, 2016. "Pairwise partition graphs and strategy-proof social choice in the exogenous indifference class model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 1-24, June.
    11. Pierre Bernhard & Marc Deschamps, 2018. "Arrow’s (im)possibility theorem," Post-Print hal-01941037, HAL.
    12. Ninjbat, Uuganbaatar, 2012. "Another direct proof for the Gibbard–Satterthwaite Theorem," Economics Letters, Elsevier, vol. 116(3), pages 418-421.
    13. Uuganbaatar Ninjbat, 2012. "Symmetry vs. complexity in proving the Muller-Satterthwaite theorem," Economics Bulletin, AccessEcon, vol. 32(2), pages 1434-1441.
    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. 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.
    17. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    18. Dindar, Hayrullah & Lainé, Jean, 2017. "Manipulation of single-winner large elections by vote pairing," Economics Letters, Elsevier, vol. 161(C), pages 105-107.
    19. Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.
    20. Frantisek Turnovec, 2016. "Manipulability of Voting Procedures, Strategic Voting ad Strategic Nomination," EcoMod2016 9223, EcoMod.
    21. Michel Breton & Vera Zaporozhets, 2009. "On the equivalence of coalitional and individual strategy-proofness properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 287-309, August.

    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:eee:mateco:v:55:y:2014:i:c:p:11-14. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.