Does uncertainty lead to sincerity? Simple and complex voting mechanisms


We ask whether the absence of information about other voters’ preferences allows optimal voting to be interpreted as sincere.We start by classifying voting mechanisms as simple and complex according to the number of message types voters can use to elect alternatives. We show that while in simple voting mechanisms the elimination of information about other voters’ preferences allows optimal voting to be interpreted as sincere, this is no longer always true for complex ones. In complex voting mechanisms, voters’ optimal strategy may vary with the size of the electorate. Therefore, in order to interpret optimal voting as sincere for complex voting mechanisms, we describe the optimal voting strategy when voters not only have no information but also have no pivotal power, i.e., as the size of the electorate tends to infinity.

This is a preview of subscription content, log in to check access.


  1. Apesteguia J, Ballester MA, Ferrer R (2008) On the justice of decision rules. Mimeo

  2. Arrow JK (1951) Social choice and individual values. Wiley, New York. Revised edition 1963

  3. Ballester MA, Rey-Biel P (2007) Sincerity in simple and complex voting mechanisms. Mimeo

  4. Brams SJ, Fishburn PC (1978) Approval voting. Am Political Sci Rev 72: 831–847

    Article  Google Scholar 

  5. Brams SJ, Fishburn PC (1981) Approval voting, Condorcet’s principle, and runoff elections. Public Choice 36: 89–114

    Google Scholar 

  6. Brams SJ, Sanver MR (2006) Voting systems that combine approval and preference. Mimeo

  7. Casella A (2005) Storable votes. Games Econ Behav 51: 391–419

    Article  Google Scholar 

  8. Costa-Gomes M, Crawford B, Broseta B (2001) Cognition and behavior in normal form games: an experimental study. Econometrica 68: 1193–1235

    Article  Google Scholar 

  9. Dellis A, Oak MP (2006) Approval voting with endogenous candidates. Games Econ Behav 54: 47–76

    Article  Google Scholar 

  10. Farquharson R (1969) Theory of voting. Yale University Press, New Haven

    Google Scholar 

  11. Fishburn PC (1973) The theory of social choice. Princeton University Press, Princeton

    Google Scholar 

  12. Fisher S, Myatt D (2002) Strategic voting experiments. Nuffield College politics working paper 2002. W4

  13. Goeree J, Holt C (2004) A model of noisy introspection. Games Econ Behav 46: 365–382

    Article  Google Scholar 

  14. Hoffman D (1982) A model for strategic voting. SIAM J Appl Math 42: 751–761

    Article  Google Scholar 

  15. Jackson M, Sonnenschein H (2007) Overcoming incentive constraints by linking decisions. Econometrica 75(1): 241–258

    Article  Google Scholar 

  16. Majumdar D, Sen A (2004) Ordinally Bayesian incentive compatible voting rules. Econometrica 72: 523–540

    Article  Google Scholar 

  17. McKelvey R, Palfrey T (1995) Quantal response equilibrium for normal form games. Games Econ Behav 10: 6–38

    Article  Google Scholar 

  18. Merrill S (1983) Making multicandidate elections more democratic. Princeton University Press, Princeton

    Google Scholar 

  19. Merrill S, Nagel J (1987) The effect of approval balloting on strategic voting under alternative decision rules. Am Political Sci Rev 81: 509–524

    Article  Google Scholar 

  20. Myerson RB, Weber RJ (1993) A theory of voting equilibria. Am Political Sci Rev 87: 102–114

    Article  Google Scholar 

  21. Niemi RG (1984) The problem of strategic behavior under approval voting. Am Political Sci Rev 78: 952–958

    Article  Google Scholar 

  22. Nurmi H (1987) Comparing voting systems. Theory and decision library. Series A: Philosophy and methodology of the social sciences. Reidel, Dordrecht

  23. Stahl D (1993) Evolution of smart players. Games Econ Behav 5: 604–617

    Article  Google Scholar 

  24. Stahl D, Wilson P (1994) Experimental evidence on players’ models of other players. J Econ Behav Organ 25: 309–327

    Article  Google Scholar 

  25. Stahl D, Wilson P (1995) On players’ models of other players: theory and experimental evidence. Games Econ Behav 10: 218–254

    Article  Google Scholar 

  26. Weber RK (1978) Comparison of voting systems. Cowles foundation discussion paper no. 498. Yale University

Download references

Author information



Corresponding author

Correspondence to Miguel Ángel Ballester.

Additional information

We are grateful to Jorge Alcalde-Unzu, Enriqueta Aragonès, Carmen Beviá, Tilman Börgers, Caterina Calsamiglia, Jon Eguia, Julio González-Díaz, Jordi Massó, Juan D. Moreno-Ternero and John Weymark for useful comments. Financial support from Ministerio de Ciencia y Tecnología (SEJ2005-01481/Econ, SEJ2006-00538, ECO08-04756 and Consolider-Ingenio CSD2006-00016) and the support of the Barcelona GSE Research Network and the Government of Catalonia (2005SGR-00454, 2005SGR-00836) is gratefully acknowledged.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ballester, M.Á., Rey-Biel, P. Does uncertainty lead to sincerity? Simple and complex voting mechanisms. Soc Choice Welf 33, 477–494 (2009).

Download citation


  • Vote Rule
  • Bijective Mapping
  • Strategic Vote
  • Approval Vote
  • Game Econ