Experimental evidence that quorum rules discourage turnout and promote election boycotts


Many democratic decision making institutions involve quorum rules. Such rules are commonly motivated by concerns about the “legitimacy” or “representativeness” of decisions reached when only a subset of eligible voters participates. A prominent example of this can be found in the context of direct democracy mechanisms, such as referenda and initiatives. We conduct a laboratory experiment to investigate the consequences of the two most common types of quorum rules: a participation quorum and an approval quorum. We find that both types of quora lead to lower participation rates, dramatically increasing the likelihood of full-fledged electoral boycotts on the part of those who endorse the Status Quo. This discouraging effect is significantly larger under a participation quorum than under an approval quorum.

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  1. 1.

    Available at: http://www.idea.int/uid/fieldview.cfm?field=327.

  2. 2.

    Think, for example, of the April 2001 referendum on the Mississippi official flag or the British Columbia sales tax referendum of 2011, as well as the large number of local tax ballot measures voted across the US outside general election days.

  3. 3.

    In fact, there are countries where holding national referenda and general elections simultaneously is explicitly precluded, as in the cases of Canada (under the Referendum Act) or Portugal (under the Constitution), for example.

  4. 4.

    Previous papers by Schram and Sonnemans (1996), Morton and Tyran (2011), Battaglini et al. (2010), and Groβer and Schram (2006 and 2010) have provided laboratory evidence on strategic abstention.

  5. 5.

    See Dhillon and Peralta (2002) and Fedderson (2004) for reviews of the strengths and weaknesses of the rational-choice approach, as well as of other approaches like group-based, expressed, or bounded rationality voting models.

  6. 6.

    Unlike Levine and Palfrey (2007), we consider a game involving aggregate uncertainty, as in Börgers (2004) and Coate et al (2008). Although this implies an added degree of complexity, uncertainty about the actual percentages for and against the measure under consideration is a realistic feature of most voting situations.

  7. 7.

    Like Levine and Palfrey (2007), we assume that each option wins with 50 % probability in case of a tie, provided that the quorum is met.

  8. 8.

    These values were chosen because they imply, according to the no-quorum equilibrium predictions, relatively high turnout rates in the absence of a quorum. By choosing a high turnout equilibrium to start with, we are giving a chance that the quorum is not a binding constraint and that does not distort incentives. Had we started with low turnout rates in the no-quorum case, then quorum busting strategies would be very easy to implement and become the only equilibria (see the first scenario in Table 1). In such case, it would not be surprising to conclude that quora had deleterious effects.

  9. 9.

    Given that quorum rules modify both the incentive structures and the set of results that correspond to Status Quo victory, we want to make the latter as similar as possible between quora in order to concentrate on the effects of the incentive structure. Choosing PQ = 4 and AQ = 3 accomplishes that. With 9 electors, there are 55 possible results. Of these, there are only two possible results that have different outcomes. If the Status Quo receives 0 votes and Change receives 3, then, with AQ = 3, Change wins and with PQ = 4 Status Quo wins. The other result is a 2–2. In that case, with AQ = 3, Status Quo wins, while with PQ = 4, Status Quo wins only with 50 % chances. Except for the trivial case of AQ = 1 and PQ = 1, in which the two quora are equivalent, the difference between the two Status Quo sets is minimized for these particular choices. For example, had we considered an AQ = 2 and the Status Quo set would be a strict subset of the Status Quo region with PQ = 4, meaning that the approval quorum threshold would undoubtedly be less restrictive than the participation quorum threshold. On the other hand, had we considered AQ = 4, and the opposite would happen, with the approval quorum Status Quo region being a strict superset of the Status Quo region in the participation quorum case.

  10. 10.

    See Online Appendix 1 for a derivation of this probability function.

  11. 11.

    It is difficult to estimate λ in our treatments with quora, because of the existence of multiple equilibria. That is so because it is difficult to distinguish a low λ from players playing different equilibria. Using data from our no quorum treatments our estimates suggest that λ is between 0.03 and 0.035, which is close to the estimates of Levine and Palfrey. Table 2 would be very similar if we had considered λ = 0.03 instead.

  12. 12.

    By definition, this table is sensitive to the particular choice of λ. As we explained before, if λ is very high, say 1, then the predictions are almost equivalent to SBNE, then as we consider lower and lower values for λ, de number of equilibria decreases and, as λ approaches zero, then agents will vote with 50 % probability no matter what. See Online Appendix 2, to see how Table 2 changes for different values of λ.

  13. 13.

    Subjects were recruited using the online recruitment system ORSEE (Greiner 2004). The experiment was programmed using the software z-Tree (Fischbacher 2007). Students came from various disciplines (approximately 45 % economics, 20 % other social sciences, 10 % natural sciences, 25 % humanities). 45 % of our subjects were female.

  14. 14.

    Subjects were not explicitly informed that they would repeatedly interact with the same set of participants. It is important to note that despite this “fixed matching” scheme, subjects were randomly assigned to the two “teams” at the beginning of each round.

  15. 15.

    A potential drawback of this (strategy) method is that it forces participants to use a cutoff strategy, as predicted by theory. If our goal was to test this aspect of the theory, this would be an inappropriate design choice. However, our aim is to investigate the effects of the quorum rules on participation, and not to test the use of cutoff strategies. Still it is important to note that Levine and Palfrey do find that “to a reasonable approximation individuals followed consistent cutpoint rules” (2007, p. 152). Therefore we are confident that forcing subjects to use cutoff strategies did not restrict their behavior significantly. See Brandts and Charness (2011) for a more general discussion of the strategy method and how it compares to the direct response method.

  16. 16.

    This method of payment was chosen as a good compromise between avoiding paying all rounds (introducing wealth effects) and paying only one round (introducing additional risk). See Morton and Williams (2010, p. 399) for a discussion of this methodological choice.

  17. 17.

    I all sessions, the probability of favoring change cycled deterministically as follows: 3/9, 6/9, 4/9, 5/9. The sequence of no quorum/quorum conditions was counterbalanced. In half of the sessions, the sequence was: 8 rounds with quorum, 4 without, 8 with, etc. In the other sessions, we began with 4 rounds no quorum, 8 with, etc. (We conduct twice as many rounds with quora because in that case the game is not symmetric and so we acquire fewer observations when distinguishing between supporters and opponents.) All random team assignments were drawn once prior to the first session and kept constant in all sessions. i.e. the realized numbers of Supporters and Opponents were the same in all treatments.

  18. 18.

    Considering a model with individual fixed effects yields almost identical results, showing that any individual and group effects are very well controlled for, with the random effects model. Also, given the bounded nature of the dependent variable, one could have on model of fractional response variables a la Papke and Wooldridge (2008). The results were nearly identical, so there is no obvious advantage in using this more complicated framework.

  19. 19.

    Take, for example, the 3/6 case. This means that for Supporters there is a clear majority against Change. For Opponents, there is a clear majority for Change.

  20. 20.

    Even in the only case in which the 95 % confidence interval includes zero, Table 4, in the second to the last column, tells us that the effect is still statistically significant at 10 %.

  21. 21.

    The third order polynomial was statistically non-significant.

  22. 22.

    To compute the probability of boycott and the marginal effects, we considered Round number = 25.


  1. Aguiar-Conraria, L., & Magalhães, P. C. (2010a). Referendum design, quorum rules and turnout. Public Choice, 144(1), 63–81.

    Article  Google Scholar 

  2. Aguiar-Conraria, L., & Magalhães, P. C. (2010b). How quorum rules distort referendum outcomes: Evidence from a pivotal voter model. European Journal of Political Economy, 26(4), 541–557.

    Article  Google Scholar 

  3. Battaglini, M., Morton, R. B., & Palfrey, T. R. (2010). The swing voter’s curse in the laboratory. The Review of Economic Studies, 77(1), 61–89.

    Article  Google Scholar 

  4. Blais, A. (2000). To vote or not to vote?. Pittsburgh: University of Pittsburgh Press.

    Google Scholar 

  5. Blais, A., & Rheault, L. (2011). Optimists and skeptics: Why do people believe in the value of their single vote? Electoral Studies, 30, 77–82.

    Article  Google Scholar 

  6. Börgers, T. (2004). Costly voting. American Economic Review, 94(1), 57–66.

    Article  Google Scholar 

  7. Brandts, J., & Charness, G. (2011). The strategy versus the direct-response method: a first survey of experimental comparisons. Experimental Economics, 14(3), 375–398.

    Article  Google Scholar 

  8. Coate, S., & Conlin, M. (2004). A group rule–utilitarian approach to voter turnout: Theory and evidence. American Economic Review, 94(5), 1476–1504.

    Article  Google Scholar 

  9. Coate, S., Conlin, M., & Moro, A. (2008). The performance of pivotal-voter models in small-scale elections: Evidence from Texas liquor referenda. Journal of Public Economics, 92(3–4), 582–596.

    Article  Google Scholar 

  10. Côrte-Real, P., & Pereira, P. T. (2004). The voter who wasn’t there: Referenda, representation and abstention. Social Choice and Welfare, 22(2), 349–369.

    Article  Google Scholar 

  11. Cox, G. W., & Munger, M. C. (1989). Closeness, expenditures, and turnout in the 1982 US house elections. American Political Science Review, 83(01), 217–231.

    Article  Google Scholar 

  12. Dhillon, A., & Peralta, S. (2002). Economic theories of voter turnout. The Economic Journal, 112, 332–352.

    Article  Google Scholar 

  13. Duffy, J., & Tavits, M. (2008). Beliefs and voting decisions: A test of the pivotal voter model. American Journal of Political Science, 52(3), 603–618.

    Article  Google Scholar 

  14. Fedderson, T. (2004). rational choice theory and the paradox of not voting. Journal of Economic Perspectives, 18, 99–112.

    Article  Google Scholar 

  15. Filer, J. E., & Kenny, L. W. (1980). Voter turnout and the benefits of voting. Public Choice, 35(5), 575–585.

    Article  Google Scholar 

  16. Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10, 171–178.

    Article  Google Scholar 

  17. Fréchette, G. (2012). Session-effects in the laboratory. Experimental Economics, 15, 485–498.

    Article  Google Scholar 

  18. Geys, B. (2006). Explaining voter turnout: A review of aggregate-level research. Electoral Studies, 25, 637–663.

    Article  Google Scholar 

  19. Greiner, B. (2004). An online recruitment system for economic experiments. In K. Kremer & V. Macho (Eds.), Forschung und wissenschaftliches rechnen 2003 (pp. 79–93). Datenverarbeitung: GWDG Bericht 63. Gesellschaft für Wissenschaftliche Datenverarbeitung Göttingen.

    Google Scholar 

  20. Groβer, J., & Schram, A. (2006). Neighborhood information exchange and voter participation: An experimental study. American Political Science Review, 100(2), 235–248.

    Article  Google Scholar 

  21. Groβer, J., & Schram, A. (2010). Public opinion polls, voter turnout, and welfare: An experimental study. American Journal of Political Science, 54(3), 700–717.

    Article  Google Scholar 

  22. Herrera, H., & Mattozzi, A. (2010). Quorum and turnout in referenda. Journal of the European Economic Association, 8(4), 838–871.

    Article  Google Scholar 

  23. Hizen, Y., & Shinmyo, M. (2011). Imposing a turnout threshold in referendums. Public Choice, 148(3), 491–503.

    Article  Google Scholar 

  24. International IDEA. (2008). Direct democracy: The International IDEA Handbook. Stockholm: International Institute for Democracy and Electoral Assistance.

    Google Scholar 

  25. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of of decision under risk. Econometrica, 47, 263–292.

    Article  Google Scholar 

  26. Kaufmann, B., Büchi, R., & Braun, N. (2008). Guidebook to direct democracy in Switzerland and Beyond. Marburg: Initiative & Referendum Institute Europe.

    Google Scholar 

  27. Laruelle, A., & Valenciano, F. (2012a). Majorities with a quorum. Journal of Theoretical Politics, 23(2), 241–259.

    Article  Google Scholar 

  28. Laruelle, A., & Valenciano, F. (2012b). Quaternary dichotomous voting rules. Social Choice and Welfare, 38(3), 431–454.

    Article  Google Scholar 

  29. LeDuc, Lawrence. 2003. The Politics of Direct Democracy: Referendums in Global Perspective. Toronto: Broadview Press.

    Google Scholar 

  30. Levine, D. K., & Palfrey, T. R. (2007). The paradox of voter participation? A laboratory study. American Political Science Review, 101(1), 143–158.

    Article  Google Scholar 

  31. Matsusaka, J. G. (1993). Election closeness and voter turnout: Evidence from California ballot propositions. Public Choice, 76(4), 313–334.

    Article  Google Scholar 

  32. Morton, R. B., & Tyran, J. R. (2011). Let the experts decide? Asymmetric information, abstention, and coordination in standing committees. Games and Economic Behavior, 72(2), 485–509.

    Article  Google Scholar 

  33. Morton, R. B., & Williams, K. C. (2010). Experimental political science and the study of causality. New York: Cambridge University Press.

    Book  Google Scholar 

  34. Palfrey, T. R. (2009). Laboratory experiments in political economy. Annual Review of Political Science, 12, 379–388.

    Article  Google Scholar 

  35. Palfrey, T., & Rosenthal, H. (1985). Voter participation and strategic uncertainty. American Political Science Review, 79(1), 62–78.

    Article  Google Scholar 

  36. Papke, L., & Wooldridge, J. (2008). Panel data methods for fractional response variables with an application to test pass rates. Journal of Econometrics, 145, 121–133.

    Article  Google Scholar 

  37. Qvortrup, M. (2005). A comparative study of referendums. Manchester UK: Manchester University Press.

    Google Scholar 

  38. Schiller, T. (2011). Local direct democracy in Europe. Wiesbaden: VS Verlag.

    Book  Google Scholar 

  39. Schram, A., & Sonnemans, J. (1996). Voter turnout as a participation game: An experimental investigation. International Journal of Game Theory, 25(3), 385–406.

    Article  Google Scholar 

  40. St-Vincent, S. L. (2013). An experimental test of the pivotal voter model under plurality and PR elections. Electoral Studies, 32, 795–806.

    Article  Google Scholar 

  41. Suksi, M. (1993). Bringing in the people: A comparison of the constitutional forms and practices of the referendum. Dordrecht: Martinus Nijhoff Publishers.

    Google Scholar 

  42. Svensson, P. (1996). Denmark: The referendum as minority protection. In P. V. Uleri (Ed.), The referendum experience in Europe. Basignstoke: Macmillan.

    Google Scholar 

  43. Uleri, P. V. (2002). On referendum voting in Italy: Yes, no or non-vote? How Italian parties learned to control referendums. European Journal of Political Research, 41(6), 863–883.

    Article  Google Scholar 

  44. Verhulst, J., & Nijeboer, A. (2008). Direct democracy: Facts and arguments about the introduction of initiative and referendum. Brussels: Democracy International.

    Google Scholar 

  45. West, F. C. (1985). A crisis of the weimar republic: A study of the German referendum of 20 June 1926. Philadelphia PA: American Philosophical Society.

    Google Scholar 

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This work was carried out within the funding with the UID/ECO/03182/2013 reference with the FCT/MEC’s financial support through national funding and when applicable co-funded by the FEDER under the PT2020 Partnership Agreement.

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Correspondence to Luís Aguiar-Conraria.

Additional information

Previous versions of this paper have benefited from several comments. We thank the participants of the 50th Anniversary Conference of The Public Choice Society, New Orleans, and the European Political Science Association Meeting in Barcelona, 2013. We also thank the participants in seminars at Catholic University of Portugal (in Porto and in Lisbon), University of Puerto Rico, University of Aveiro, University of Minho and Nova School of Business and Economics. In particular we wish to thank the very helpful discussion with Miguel Portela, Anabela Botelho, Marieta Valente, and Pedro Robalo. Luís Sá provided great research assistance. The usual disclaimer applies.

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Aguiar-Conraria, L., Magalhães, P.C. & Vanberg, C.A. Experimental evidence that quorum rules discourage turnout and promote election boycotts. Exp Econ 19, 886–909 (2016). https://doi.org/10.1007/s10683-015-9473-9

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  • Election design
  • Participation quorum
  • Approval quorum
  • Laboratory experiment

JEL Classification

  • C91
  • D72
  • D02