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Dictatorship versus manipulability

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  • Bednay, Dezső
  • Moskalenko, Anna
  • Tasnádi, Attila

Abstract

The Gibbard–Satterthwaite theorem roughly states that we have to accept dictatorship or manipulability in case of at least three alternatives. A large strand of the literature estimates the degree of manipulability of social choice functions (e.g. Aleskerov and Kurbanov (1999), Favardin et al. (2002), and Aleskerov et al. (2012)), most of them employing the Nitzan–Kelly index of manipulability. We take a different approach and introduce a non-dictatorship index based on our recent work Bednay et al. (2017), where we have analysed social choice functions based on their distances to the dictatorial rules. By employing computer simulations, we investigate the relationship between the manipulability and non-dictatorship indices of some prominent social choice functions, putting them into a common framework.

Suggested Citation

  • Bednay, Dezső & Moskalenko, Anna & Tasnádi, Attila, 2019. "Dictatorship versus manipulability," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 72-76.
    • Handle: RePEc:eee:matsoc:v:101:y:2019:i:c:p:72-76
    DOI: 10.1016/j.mathsocsci.2019.07.001
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    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. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Anonymous voting and minimal manipulability," Journal of Economic Theory, Elsevier, vol. 135(1), pages 533-544, July.
    3. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Minimally manipulable anonymous social choice functions," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 239-254, May.
    4. 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.
    5. Peter Fristrup & Hans Keiding, 1998. "Minimal manipulability and interjacency for two-person social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 455-467.
    6. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "Borda rule, Copeland method and strategic manipulation," Post-Print halshs-00069522, HAL.
    7. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    8. Hans Peters & Souvik Roy & Ton Storcken, 2012. "On the manipulability of approval voting and related scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 399-429, July.
    9. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    10. 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.
    11. 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.
    12. 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.
    13. Aleskerov, Fuad & Karabekyan, Daniel & Sanver, M. Remzi & Yakuba, Vyacheslav, 2012. "On the manipulability of voting rules: The case of 4 and 5 alternatives," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 67-73.
    14. Fuad Aleskerov & Daniel Karabekyan & Remzi Sanver & Vyacheslav Yakuba, 2009. "Evaluating the Degree of Manipulability of Certain Aggregation Procedures under Multiple Choices," Journal of the New Economic Association, New Economic Association, issue 1-2, pages 37-61.
    15. Nehring, Klaus & Puppe, Clemens, 2007. "Efficient and strategy-proof voting rules: A characterization," Games and Economic Behavior, Elsevier, vol. 59(1), pages 132-153, April.
    16. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    17. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Minimal manipulability: Unanimity and nondictatorship," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 675-691, August.
    18. Fuad Aleskerov & Daniel Karabekyan & M. Sanver & Vyacheslav Yakuba, 2011. "An individual manipulability of positional voting rules," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 431-446, December.
    19. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    JEL classification:

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

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