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Single transferable vote resists strategic voting

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Abstract

We give evidence that Single Tranferable Vote (STV) is computationally resistant to manipulation: It is NP-complete to determine whether there exists a (possibly insincere) preference that will elect a favored candiate, even in an election for a single seat. Thus strategic voting under STV is qualitatively more difficult than under other commonly-used voting schemes. Furthermore, this resistance to manipulation is inherent to STV and does not depend on hopeful extraneous assumptions like the presumed difficulty of learning the preferences of the other voters. We also prove that it is NP-complete to recognize when an STV election violates monotonicity. This suggests that non-monotonicity in STV elections might be perceived as less threatening since it is in effect “hidden” and hard to exploit for strategic advantage.

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References

  1. Anonymous (1989) Proportional Representation: Ballot Counting, Tally Sheets, and Background Information, prepared for the municipal election, Cambridge, Massachusetts, November 1989, FLM Cambridge, Research Division. Available from the Election Commission of the City of Cambridge, 362 Green Street, Cambridge, Massachusetts 02139

  2. Austen-Smith D, Banks J (1990) Monotonicity in electoral systems. Manuscript, Department of Economics, University of Rochester, Rochester, NY. Polit Sci Rev (to appear)

    Google Scholar 

  3. Bartholdi JJ III, Tovey CA, Narasimhan L (1990) Recognizing majority-rule equilibrium in spatial voting games. Soc Choice Welfare 8: 183–197

    Google Scholar 

  4. 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 

  5. Bartholdi JJ III, Tovey CA, Trick MA (1989) The computational difficulty of manipulating an election. Soc Choice Welfare 6: 227–241

    Google Scholar 

  6. Brams SJ (1982) The AMS nominating system is vulnerable to truncation of preferences. Notices Am Math Soc 29: 136–138

    Google Scholar 

  7. Brams SJ, Fishburn PC (1991) Alternative voting systems. Preprint from the Department of Politics, New York University, New York, NY 10003. In: Maisel LS (ed) Encyclopedia of American political parties and elections. Garland, New York

    Google Scholar 

  8. Chamberlin JR (1985) An investigation into the relative manipulability of four voting systems. Behav Sci 30: 195–203

    Google Scholar 

  9. Doron G, Kronick R (1977) Single transferable vote: an example of a perverse social choice function. Am J Polit Sci 21: 303–311

    Google Scholar 

  10. Dummet M (1984) Voting procedures. Clarendon Press, Oxford

    Google Scholar 

  11. Fishburn PC (1982) Monotonicity paradoxes in the theory of elections. Disc Appl Math 4: 119–134

    Google Scholar 

  12. Fishburn PC, Brams SJ (1983) Paradoxes of preferential voting. Math Mag 56: 207–214

    Google Scholar 

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

    Google Scholar 

  14. Garey MR, Johnson DS (1979) Computers and intractability: A guide to the theory of NP-compleness. WH Freeman, San Francisco

    Google Scholar 

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

    Google Scholar 

  16. Hill ID, wichmann BA, Woodall DR (1987) Single transferable vote by Meek's method. Comput J 30: 277–281

    Google Scholar 

  17. Holzman R (1989) To vote or not to vote: what is the quota? Disc Appl Math 22: 133–141

    Google Scholar 

  18. Janofsky M (1990) No clear favorite in search for site. NY Times (Sports Sect) September 16, 1990

  19. Mill JS (1861) Considerations on Representative Government (1962 reprinting by Henry Regnery Company, Chicago of the original edition published in Londen by Parker, Son, and Bourn in 1861)

  20. Moulin H (1988) Axioms of cooperative decision making. Cambridge University Press, Cambridge

    Google Scholar 

  21. Moulin H (1988) Condorcet's principle implies the no-show paradox. J Econ Theory 45: 53–64

    Google Scholar 

  22. Muller E, Satterthwaite MA (1977) The equivalence of strong positive associate and strategy-proofness. J Econ Theory 14: 412–418

    Google Scholar 

  23. Newland RA (1972) Only half a democracy. The electoral reform society of Great Britain and Ireland, London

    Google Scholar 

  24. Nitzan S (1985) The vulnerability of point-voting schemes to preference variation and strategic manipulation. Publ Choice 47: 349–370

    Google Scholar 

  25. Nurmi H (1990) Probability models in constitutional choice. Eur J Polit Econ 6: 107–117

    Google Scholar 

  26. Saari DG (1990) Susceptibility to manipulation. Publ Choice 64: 21–41

    Google Scholar 

  27. Saijo T (1987) On constant Maskin monotonic social choice functions. J Econ Theory 42: 382–386

    Google Scholar 

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

    Google Scholar 

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Bartholdi, J.J., Orlin, J.B. Single transferable vote resists strategic voting. Soc Choice Welfare 8, 341–354 (1991). https://doi.org/10.1007/BF00183045

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