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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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.
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.
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.
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.
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.
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.
See Online Appendix 1 for a derivation of this probability function.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 %.
The third order polynomial was statistically non-significant.
To compute the probability of boycott and the marginal effects, we considered Round number = 25.
Aguiar-Conraria, L., & Magalhães, P. C. (2010a). Referendum design, quorum rules and turnout. Public Choice, 144(1), 63–81.
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.
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.
Blais, A. (2000). To vote or not to vote?. Pittsburgh: University of Pittsburgh Press.
Blais, A., & Rheault, L. (2011). Optimists and skeptics: Why do people believe in the value of their single vote? Electoral Studies, 30, 77–82.
Börgers, T. (2004). Costly voting. American Economic Review, 94(1), 57–66.
Brandts, J., & Charness, G. (2011). The strategy versus the direct-response method: a first survey of experimental comparisons. Experimental Economics, 14(3), 375–398.
Coate, S., & Conlin, M. (2004). A group rule–utilitarian approach to voter turnout: Theory and evidence. American Economic Review, 94(5), 1476–1504.
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.
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.
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.
Dhillon, A., & Peralta, S. (2002). Economic theories of voter turnout. The Economic Journal, 112, 332–352.
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.
Fedderson, T. (2004). rational choice theory and the paradox of not voting. Journal of Economic Perspectives, 18, 99–112.
Filer, J. E., & Kenny, L. W. (1980). Voter turnout and the benefits of voting. Public Choice, 35(5), 575–585.
Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10, 171–178.
Fréchette, G. (2012). Session-effects in the laboratory. Experimental Economics, 15, 485–498.
Geys, B. (2006). Explaining voter turnout: A review of aggregate-level research. Electoral Studies, 25, 637–663.
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.
Groβer, J., & Schram, A. (2006). Neighborhood information exchange and voter participation: An experimental study. American Political Science Review, 100(2), 235–248.
Groβer, J., & Schram, A. (2010). Public opinion polls, voter turnout, and welfare: An experimental study. American Journal of Political Science, 54(3), 700–717.
Herrera, H., & Mattozzi, A. (2010). Quorum and turnout in referenda. Journal of the European Economic Association, 8(4), 838–871.
Hizen, Y., & Shinmyo, M. (2011). Imposing a turnout threshold in referendums. Public Choice, 148(3), 491–503.
International IDEA. (2008). Direct democracy: The International IDEA Handbook. Stockholm: International Institute for Democracy and Electoral Assistance.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of of decision under risk. Econometrica, 47, 263–292.
Kaufmann, B., Büchi, R., & Braun, N. (2008). Guidebook to direct democracy in Switzerland and Beyond. Marburg: Initiative & Referendum Institute Europe.
Laruelle, A., & Valenciano, F. (2012a). Majorities with a quorum. Journal of Theoretical Politics, 23(2), 241–259.
Laruelle, A., & Valenciano, F. (2012b). Quaternary dichotomous voting rules. Social Choice and Welfare, 38(3), 431–454.
LeDuc, Lawrence. 2003. The Politics of Direct Democracy: Referendums in Global Perspective. Toronto: Broadview Press.
Levine, D. K., & Palfrey, T. R. (2007). The paradox of voter participation? A laboratory study. American Political Science Review, 101(1), 143–158.
Matsusaka, J. G. (1993). Election closeness and voter turnout: Evidence from California ballot propositions. Public Choice, 76(4), 313–334.
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.
Morton, R. B., & Williams, K. C. (2010). Experimental political science and the study of causality. New York: Cambridge University Press.
Palfrey, T. R. (2009). Laboratory experiments in political economy. Annual Review of Political Science, 12, 379–388.
Palfrey, T., & Rosenthal, H. (1985). Voter participation and strategic uncertainty. American Political Science Review, 79(1), 62–78.
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.
Qvortrup, M. (2005). A comparative study of referendums. Manchester UK: Manchester University Press.
Schiller, T. (2011). Local direct democracy in Europe. Wiesbaden: VS Verlag.
Schram, A., & Sonnemans, J. (1996). Voter turnout as a participation game: An experimental investigation. International Journal of Game Theory, 25(3), 385–406.
St-Vincent, S. L. (2013). An experimental test of the pivotal voter model under plurality and PR elections. Electoral Studies, 32, 795–806.
Suksi, M. (1993). Bringing in the people: A comparison of the constitutional forms and practices of the referendum. Dordrecht: Martinus Nijhoff Publishers.
Svensson, P. (1996). Denmark: The referendum as minority protection. In P. V. Uleri (Ed.), The referendum experience in Europe. Basignstoke: Macmillan.
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.
Verhulst, J., & Nijeboer, A. (2008). Direct democracy: Facts and arguments about the introduction of initiative and referendum. Brussels: Democracy International.
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.
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.
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
- Election design
- Participation quorum
- Approval quorum
- Laboratory experiment