Social Choice and Welfare

, Volume 6, Issue 3, pp 227–241 | Cite as

The computational difficulty of manipulating an election

  • J. J. BartholdiIII
  • C. A. Tovey
  • M. A. Trick


We show how computational complexity might protect the integrity of social choice. We exhibit a voting rule that efficiently computes winners but is computationally resistant to strategic manipulation. It is NP-complete for a manipulative voter to determine how to exploit knowledge of the preferences of others. In contrast, many standard voting schemes can be manipulated with only polynomial computational effort.


Computational Complexity Economic Theory Computational Effort Social Choice Vote Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bartholdi JJ III, Tovey CA, Trick MA (1989) Voting schemes for which it can be difficult to tell who won the election. Soc Choice Welfare 6: 157–165Google Scholar
  2. 2.
    Bartholdi JJ III, Tovey CA, Trick MA (1987) How hard is it to control an election? Econometrica (submitted)Google Scholar
  3. 3.
    Bollobas, B (1979) Graph theory. Graduate Texts 63. Springer, Berlin Heidelberg New YorkGoogle Scholar
  4. 4.
    Gardenfors P (1976) Manipulation of social choice functions. J Econ Theory 13:217–228Google Scholar
  5. 5.
    Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. WH Freeman, San FranciscoGoogle Scholar
  6. 6.
    Gibbard A (1973) Manipulation of voting schemes. Econometrica 41:587–601Google Scholar
  7. 7.
    Gottinger HW (1987) Choice and complexity. Math Soc Sci 14:1–17Google Scholar
  8. 8.
    Kazic B, Keene RD, Lim KA (eds) (1986) The official laws of chess. Maxmillan, New YorkGoogle Scholar
  9. 9.
    Lewis A (1985) On the effectively computable realizations of choice functions. Math Soc Sci 10: 43–80Google Scholar
  10. 10.
    Morrison M (ed) (1978) Official rules of chess, 2nd Edn. David McKay, New YorkGoogle Scholar
  11. 11.
    Niemi RG, Riker WH (1976) The choice of voting systems. Sci Am 234:21–27Google Scholar
  12. 12.
    Nurmi H (1983) Voting procedures: a summary analysis. Br J Polit Sci 13:181–208Google Scholar
  13. 13.
    Nurmi H (1986) Problems of finding optimal voting and representation systems. E J Oper Res 24:91–98Google Scholar
  14. 14.
    Satterthwaite MA (1975) Strategy-proofness and Arrow's conditions. J Econ Theory 10:187–217Google Scholar
  15. 15.
    Stearns R (1959) The voting problem. Am Math Mon 66:761–763Google Scholar
  16. 16.
    Tovey CA (1984) A simplified NP-complete satisfiability problem. Disc Appl Math 8:85–89Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • J. J. BartholdiIII
    • 1
  • C. A. Tovey
    • 1
  • M. A. Trick
    • 1
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations