What proportion of sincere voters guarantees efficiency?

  • Yasunori OkumuraEmail author
Original Paper


This study considers a hybrid voting model where some of the voters sincerely vote but the others may not. By using the model, we discuss several voting rules: the plurality rule, Borda rule, and others. In each rule, we derive the threshold number such that a Pareto efficient alternative is always chosen if and only if the ratio of the sincere voters is more than the number. Further, we show that in any rule that satisfies strategy-proofness, a Pareto inefficient alternative may be chosen if even one voter insincerely votes.



  1. Barberà S (2010) Strategy-proof social choice. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 2. chap 25. Elsevier, Amsterdam, pp 731–832CrossRefGoogle Scholar
  2. Ballester MÁ, Rey-Biel P (2009) Does uncertainty lead to sincerity? Simple and complex voting mechanisms. Soc Choice Welf 33(3):477–494CrossRefGoogle Scholar
  3. Black D (1976) Partial justification of the Borda count. Public Choice 28:1–15CrossRefGoogle Scholar
  4. Börgers T, Smith D (2014) Robust mechanism design and dominant strategy voting rules. Theor Econ 9(2):339–360CrossRefGoogle Scholar
  5. Dutta B, Peters H, Sen A (2007) Strategy-proof cardinal decision schemes. Soc Choice Welf 28:163–179CrossRefGoogle Scholar
  6. Farkas D, Nitzan S (1979) The Borda rule and Pareto stability: a comment. Econometrica 47:1305–1306CrossRefGoogle Scholar
  7. Fishburn PC, Gehrlein WV (1976) Borda’s rule, positional voting, and Condorcet’s simple majority principle. Public Choice 28:79–88CrossRefGoogle Scholar
  8. Forsythe R, Myerson RB, Rietz TA, Weber RJ (1996) An experimental study of voting rules and polls in three-way elections. Int J Game Theory 25:355–383CrossRefGoogle Scholar
  9. García-Lapresta JL, Marley AAJ, Martínez-Panero M (2011) Characterizing best–worst voting systems in the scoring context. Soc Choice Welf 34:487–496CrossRefGoogle Scholar
  10. Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601CrossRefGoogle Scholar
  11. Gibbard A (1977) Manipulation of schemes that mix voting with chance. Econometrica 45(3):665–681CrossRefGoogle Scholar
  12. Hylland A (1980) Strategy proofness of voting procedures with lotteries as outcomes and infinite sets of strategies. University of Oslo, Institute of EconomicsGoogle Scholar
  13. Kawai K, Watanabe Y (2013) Inferring strategic voting. Am Econ Rev 103(2):624–662CrossRefGoogle Scholar
  14. Majumdar D, Sen A (2004) Ordinally Bayesian incentive compatible voting rules. Econometrica 72(2):523–540CrossRefGoogle Scholar
  15. Moulin H (1988) Condorcet’s principle implies the no show paradox. J Econ Theory 45:53–64CrossRefGoogle Scholar
  16. Okumura Y (2018) Rank-dominant strategy and sincere voting. Mimeo. Accessed 8 Nov 2018
  17. Rietz TA, Myerson RB, Weber RJ (1998) Campaign finance levels as coordinating signals in three-way experimental elections. Econ Polit 10(3):185–217CrossRefGoogle Scholar
  18. Saari DG (2010) Strategy-proof social choice. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 2. chap 27. Elsevier, Amsterdam, pp 897–945Google Scholar
  19. Satterthwaite MA (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217CrossRefGoogle Scholar
  20. Spenkuch J (2014) (Ir)rational voters? Mimeo. Accessed 8 Nov 2018
  21. Young HP (1974) An axiomatization of Borda’s rule. J Econ Theory 9:43–52CrossRefGoogle Scholar
  22. Zeckhauser R (1973) Voting systems, honest preferences, and Pareto optimality. Am Polit Sci Rev 67:934–946CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Logistics and Information EngineeringTUMSATTokyoJapan

Personalised recommendations