IDEAS home Printed from https://ideas.repec.org/p/gat/wpaper/1302.html
   My bibliography  Save this paper

Strategic manipulability of self-selective social choice rules

Author

Listed:
  • Mostapha Diss

    (Université de Lyon, Lyon, F-69007, France ; CNRS, GATE Lyon St Etienne,F-69130 Ecully, France, Université Jean Monnet, Saint-Etienne, F-42000, France)

Abstract

We provide exact relations giving the probability of individual and coalitional manipulation of three specific social choice functions (Borda rule, Copeland rule, Plurality rule) in three-alternative elections when the notion of self-selectivity is imposed. The results suggest that the Borda rule is more vulnerable to coalitional manipulation than the Copeland rule and the Plurality rule. However, Plurality rule seems to be more vulnerable to individual manipulability when the number of voters is greater than a certain threshold value. In addition, the probability of individual and coalitional manipulation tends to vanish significantly when the notion of selfs-electivity is imposed.

Suggested Citation

  • Mostapha Diss, 2013. "Strategic manipulability of self-selective social choice rules," Working Papers 1302, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
  • Handle: RePEc:gat:wpaper:1302
    as

    Download full text from publisher

    File URL: ftp://ftp.gate.cnrs.fr/RePEc/2013/1302.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stefan Maus & Hans Peters & Ton Storcken, 2007. "Minimal manipulability: anonymity and unanimity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 247-269, September.
    2. Diss, Mostapha & Louichi, Ahmed & Merlin, Vincent & Smaoui, Hatem, 2012. "An example of probability computations under the IAC assumption: The stability of scoring rules," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 57-66.
    3. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    4. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, vol. 69(2), pages 289-316, August.
    5. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    6. Salvador Barber?Author-Name: Carmen Bevi?Author-Email: Carmen.Bevia@uab.es, "undated". "Stable Condorcet Rules," UFAE and IAE Working Papers 539.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    7. Salvador Barbera & Matthew O. Jackson, 2004. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," The Quarterly Journal of Economics, Oxford University Press, vol. 119(3), pages 1011-1048.
    8. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
    9. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    10. Lepelley, Dominique & Valognes, Fabrice, 2003. "Voting Rules, Manipulability and Social Homogeneity," Public Choice, Springer, vol. 116(1-2), pages 165-184, July.
    11. David A. Smith, 1999. "Manipulability measures of common social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 639-661.
    12. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "Borda rule, Copeland method and strategic manipulation," Post-Print halshs-00069522, HAL.
    13. Semih Koray & Bulent Unel, 2003. "Characterization of self-selective social choice functions on the tops-only domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 495-507, June.
    14. Gehrlein, William V & Lepelley, Dominique, 2003. "On Some Limitations of the Median Voting Rule," Public Choice, Springer, vol. 117(1-2), pages 177-190, October.
    15. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    16. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "original papers : Borda rule, Copeland method and strategic manipulation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 213-228.
    17. Pierre Favardin & Dominique Lepelley, 2006. "Some Further Results on the Manipulability of Social Choice Rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 485-509, June.
    18. Nicolas Houy, 2004. "A note on the impossibility of a set of constitutions stable at different levels," Cahiers de la Maison des Sciences Economiques v04039, Université Panthéon-Sorbonne (Paris 1).
    19. Lepelley, Dominique & Mbih, Boniface, 1987. "The proportion of coalitionally unstable situations under the plurality rule," Economics Letters, Elsevier, vol. 24(4), pages 311-315.
    20. Barbera, Salvador & Bevia, Carmen, 2002. "Self-Selection Consistent Functions," Journal of Economic Theory, Elsevier, vol. 105(2), pages 263-277, August.
    21. 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. Aleksandras KRYLOVAS & Natalja KOSAREVA & Edmundas Kazimieras ZAVADSKAS, 2016. "Statistical Analysis of KEMIRA Type Weights Balancing Methods," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 19-39, September.
    2. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers hal-01757761, HAL.
    3. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.

    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. Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    2. Diss, Mostapha & Louichi, Ahmed & Merlin, Vincent & Smaoui, Hatem, 2012. "An example of probability computations under the IAC assumption: The stability of scoring rules," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 57-66.
    3. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    4. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    5. Bednay, Dezső & Moskalenko, Anna & Tasnádi, Attila, 2019. "Dictatorship versus manipulability," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 72-76.
    6. SLINKO, Arkadii & KORAY, Semih, 2006. "Self-Selective Social Choice Functions," Cahiers de recherche 2006-21, Universite de Montreal, Departement de sciences economiques.
    7. Krzysztof Kontek & Honorata Sosnowska, 2020. "Specific Tastes or Cliques of Jurors? How to Reduce the Level of Manipulation in Group Decisions?," Group Decision and Negotiation, Springer, vol. 29(6), pages 1057-1084, December.
    8. Gehrlein, William V. & Moyouwou, Issofa & Lepelley, Dominique, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 352-365.
    9. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    10. James Green-Armytage & T. Nicolaus Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    11. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, vol. 69(2), pages 289-316, August.
    12. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.
    13. Green-Armytage, James, 2011. "Strategic voting and nomination," MPRA Paper 32200, University Library of Munich, Germany.
    14. Yuliya Veselova, 2016. "The difference between manipulability indices in the IC and IANC models," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 609-638, March.
    15. Yuliya A. Veselova, 2020. "Does Incomplete Information Reduce Manipulability?," Group Decision and Negotiation, Springer, vol. 29(3), pages 523-548, June.
    16. Azrieli, Yaron & Kim, Semin, 2016. "On the self-(in)stability of weighted majority rules," Games and Economic Behavior, Elsevier, vol. 100(C), pages 376-389.
    17. Daeyoung Jeong & Semin Kim, 2017. "Interim Self-Stable Decision Rules," Working papers 2017rwp-108, Yonsei University, Yonsei Economics Research Institute.
    18. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
    19. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    20. Pritchard, Geoffrey & Wilson, Mark C., 2009. "Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 35-57, July.

    More about this item

    Keywords

    Voting rules; Self-selectivity; Stability; Manipulability; Probability;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:gat:wpaper:1302. 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/gateefr.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: Nelly Wirth (email available below). General contact details of provider: https://edirc.repec.org/data/gateefr.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.