The computational difficulty of manipulating an election

Abstract

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.

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References

  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: 157–165

    Google Scholar 

  2. 2.

    Bartholdi JJ III, Tovey CA, Trick MA (1987) How hard is it to control an election? Econometrica (submitted)

  3. 3.

    Bollobas, B (1979) Graph theory. Graduate Texts 63. Springer, Berlin Heidelberg New York

    Google Scholar 

  4. 4.

    Gardenfors P (1976) Manipulation of social choice functions. J Econ Theory 13:217–228

    Google Scholar 

  5. 5.

    Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. WH Freeman, San Francisco

    Google Scholar 

  6. 6.

    Gibbard A (1973) Manipulation of voting schemes. Econometrica 41:587–601

    Google Scholar 

  7. 7.

    Gottinger HW (1987) Choice and complexity. Math Soc Sci 14:1–17

    Google Scholar 

  8. 8.

    Kazic B, Keene RD, Lim KA (eds) (1986) The official laws of chess. Maxmillan, New York

    Google Scholar 

  9. 9.

    Lewis A (1985) On the effectively computable realizations of choice functions. Math Soc Sci 10: 43–80

    Google Scholar 

  10. 10.

    Morrison M (ed) (1978) Official rules of chess, 2nd Edn. David McKay, New York

    Google Scholar 

  11. 11.

    Niemi RG, Riker WH (1976) The choice of voting systems. Sci Am 234:21–27

    Google Scholar 

  12. 12.

    Nurmi H (1983) Voting procedures: a summary analysis. Br J Polit Sci 13:181–208

    Google Scholar 

  13. 13.

    Nurmi H (1986) Problems of finding optimal voting and representation systems. E J Oper Res 24:91–98

    Google Scholar 

  14. 14.

    Satterthwaite MA (1975) Strategy-proofness and Arrow's conditions. J Econ Theory 10:187–217

    Google Scholar 

  15. 15.

    Stearns R (1959) The voting problem. Am Math Mon 66:761–763

    Google Scholar 

  16. 16.

    Tovey CA (1984) A simplified NP-complete satisfiability problem. Disc Appl Math 8:85–89

    Google Scholar 

Download references

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The authors appreciate many helpful comments and suggestions by the editor and three anonymous referees. We also thank Michel Balinski, Salvador Barbera, Jean-Pierre Barthelemy, and Peyton Young for stimulating discussions.

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Bartholdi, J.J., Tovey, C.A. & Trick, M.A. The computational difficulty of manipulating an election. Soc Choice Welfare 6, 227–241 (1989). https://doi.org/10.1007/BF00295861

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Keywords

  • Computational Complexity
  • Economic Theory
  • Computational Effort
  • Social Choice
  • Vote Rule