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Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour

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Author Info

  • Pritchard, Geoffrey
  • Wilson, Mark C.

Abstract

We consider the problem of manipulation of elections using positional voting rules under impartial culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters who must be recruited to form a manipulating coalition. It is shown that the manipulation problem may be well approximated by a very simple linear program in two variables. This permits a comparative analysis of the asymptotic (large-population) manipulability of the various rules. It is seen that the manipulation resistance of positional rules with 5 or 6 (or more) candidates is quite different from the more commonly analyzed three- and four-candidate cases.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 1 (July)
Pages: 35-57

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:35-57

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Web page: http://www.elsevier.com/locate/inca/505565

Related research

Keywords: Manipulation Impartial culture Borda Anti-plurality Scoring rule Social choice;

References

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  1. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
  2. Maus,Stefan & Peters,Hans & Storcken,Ton, 2004. "Minimal manipulability: Unanimity and Nondictatorship," Research Memorandum 005, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Biung-Ghi Ju, 2005. "A characterization of plurality-like rules based on non-manipulability, restricted efficiency, and anonymity," International Journal of Game Theory, Springer, vol. 33(3), pages 335-354, 09.
  4. Kleijnen, J.P.C. & Groenendaal, W.J.H. van, 1992. "Simulation: A statistical perspective," Open Access publications from Tilburg University urn:nbn:nl:ui:12-388278, Tilburg University.
  5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  6. Geoffrey Pritchard & Mark Wilson, 2007. "Exact results on manipulability of positional voting rules," Social Choice and Welfare, Springer, vol. 29(3), pages 487-513, October.
  7. Lepelley, Dominique & Mbih, Boniface, 1987. "The proportion of coalitionally unstable situations under the plurality rule," Economics Letters, Elsevier, vol. 24(4), pages 311-315.
  8. 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.
  9. Saari, Donald G, 1990. " Susceptibility to Manipulation," Public Choice, Springer, vol. 64(1), pages 21-41, January.
  10. David A. Smith, 1999. "Manipulability measures of common social choice functions," Social Choice and Welfare, Springer, vol. 16(4), pages 639-661.
  11. Geoffrey Pritchard & Arkadii Slinko, 2006. "On the Average Minimum Size of a Manipulating Coalition," Social Choice and Welfare, Springer, vol. 27(2), pages 263-277, October.
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Cited by:
  1. Hans Peters & Souvik Roy & Ton Storcken, 2012. "On the manipulability of approval voting and related scoring rules," Social Choice and Welfare, Springer, vol. 39(2), pages 399-429, July.

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