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Costly voting: a large-scale real effort experiment

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Abstract

We test the turnout predictions of the canonical costly voting model through a large-scale, real effort experiment. We recruit 1200 participants through Amazon’s Mechanical Turk and employ a \(2\times 2\) between subjects design encompassing small (\(N=30\)) and large (\(N=300\)) elections, as well as close and lopsided. As predicted, participants with a higher opportunity cost are less likely to vote; turnout rate decreases as the electorate size increases in lopsided elections and increases the closer the election is in large elections. However, in the large lopsided election the majority turns out to vote at a higher rate than the minority. We rationalize these results as the equilibrium outcome of a model in which voters obtain a small non-monetary utility if they vote and their party wins.

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Notes

  1. See, for instance, Riker and Ordeshook (1968), Morton (1991), Castanheira (2003), Feddersen and Sandroni (2006), Evren (2012), Myatt (2012), and Faravelli et al. (2015).

  2. Two notable exceptions are Coate et al. (2008) and Gerber et al. (2017). However, both of these papers find little support for the pivotal voter model.

  3. See also, as examples of laboratory experiments on the pivotal voting model, Schram and Sonnemans (1996), Cason and Mui (2005), Grosser and Schram (2006), Duffy and Tavits (2008), Grosser and Schram (2010), Herrera et al. (2014) and Agranov et al. (2018).

  4. A typical HIT may involve data cleaning, processing photos or videos, translations or transcription of podcasts.

  5. Although this platform is relatively new, the number of social science and economics experiments that use MTurk is rapidly increasing (see, for instance, DellaVigna and Pope 2017, as an example of a recent real effort experiment). Various studies find no significant differences when comparing MTurk behavior with laboratory behavior (Mason and Suri 2012). See also Horton et al. (2011) and Suri and Watts (2011), who replicate classical results from prisoner’s dilemma games (Cooper et al. 1996) and public goods games (Fehr and Gaechter 2000), respectively. Moreover, as documented in Mason and Suri (2012), the internal consistency of self-reported demographics on MTurk is high.

  6. We are also fully confident of their thorough understanding of the instructions, as we devised an extremely rigorous screening process. Each one of our subjects correctly answered a set of 5 questions regarding different pivotal situations. If at any point a participant made a mistake she would be taken back to the first question for another attempt. Only 4 attempts (i.e., 3 mistakes) were permitted. Almost 60% of our subjects passed the quiz at the first attempt and 81% took at most two attempts. The probability of randomly answering correctly all 5 questions at the first attempt is \(1.7\times 10^{-5}\).

  7. A potential disadvantage of using a real effort task is the lack of control over the cost function. Nonetheless, adopting an incomplete information setting with regards to preferences allows us to obtain equilibrium uniqueness for a rich class of cost distributions as well as the same comparative statics that we are interested in. For more details see Sect. 2.3 and “Appendix 1” in electronic supplementary material.

  8. Morton and Ou (2015) call this phenomenon bandwagon abstention effect, as opposed to bandwagon vote choice, which refers to a situation in which “the knowledge that one candidate is more likely to win leads supporters of the loser to switch their support for the winner” (Morton and Ou 2015, 226). As in our experiment a subject is not allowed to vote for the other group, bandwagon vote choices cannot occur. Thus, we will refer to the majority voting with a higher turnout rate than the minority simply as bandwagon, always meaning bandwagon abstention.

  9. We opted for 0.49 instead of 0.50 to avert the focal feature of perfect symmetry, as some participants may perceive 0.50 to be an equal split of the population between A members and B members in realization.

  10. The maximum amount of time a requester can allow a worker to complete a HIT on MTurk cannot be less than 2 h.

  11. Instructions are reported in “Appendix 3” (Electronic supplementary material).

  12. All subjects were made aware of this from the start. The percentage of subjects who made 0, 1, 2 and 3 mistakes is, respectively, 58.5%, 22.5%, 11.2%, and 7.8%.

  13. For purely practical reasons to do with payment procedures, those who started Stage 2 but did not complete it were discarded from the subject pool and are not part of the experiment. Subjects were informed beforehand that they would not receive any payment if they left Stage 2 half way through.

  14. Note that the participants can use any device with an internet browser such as phones, tablets or laptops to complete the experiment. In Sect. 3.1, we use the heterogeneity generated by the use of different devices to estimate the time to complete the task and use this estimate as a proxy for the cost of voting.

  15. See also Goeree and Großer (2007) as an example of aggregate uncertainty about group sizes, although the cost of voting is common knowledge.

  16. Taylor and Yildirim (2010) prove equilibrium uniqueness under a condition on the parameter values that is only satisfied in our large close election. Therefore, we check equilibrium uniqueness using several distribution functions. For the normal distribution, we check for every value of every combination of mean and standard deviation between 0.1 and 5 with 0.1 increments. We performed a similar exercise for the uniform, Pareto, exponential, half-normal, log-normal, and Chi square distributions. We always obtain a unique equilibrium for every value of \(\gamma\) when fixing \(N=30\) and \(N=300\). We also checked equilibrium uniqueness for additional values of \(N=10,\ 50,\ 100,\ 600\).

  17. We adopt the simplifying assumption that participants have common knowledge about the cost distribution. We take the classical position within economic theory to justify common knowledge of certain parameters within a theoretical model. In our case, even if the experimenter does not have access to the cost distribution of the MTurk population, we believe that it is reasonable to assume that subjects do have common knowledge about it by virtue of being experienced MTurk workers (only MTurk workers with at least 500 completed HIT’s and 97% completion rate are allowed to participate in the experiment, and this fact is common knowledge among the subjects). Thus, each participant has a long history of observations of hourly wages for HIT’s of different types offered within MTurk, and these wages contain information about such a cost distribution. Furthermore, the main comparative statics of the model should be robust to small deviations from this informational assumption.

  18. We expressed Hypothesis (2), (3) and (4) in terms of turnout rate for ease of exposition. Note, however, that this boils down to the individual ex ante probability to vote and can also be expressed in these terms. For this reason, each participant’s decision constitutes an observation of our analysis, for a total of 1200 observations.

  19. Furthermore, when looking at the competition effect, we observe that turnout is always an increasing function of \(\gamma\) (see “Appendix 1” in electronic supplementary material for details). We verified that (2) is true using \(N=10,\ 30,\ 50,\ 100,\ 300,\ 600\).

  20. Note, however, that we are conducting 30 pairwise comparisons and that the significance threshold we use (5%) is not corrected for multiple comparisons. For example, the Bonferroni corrected significance threshold would be 0.16%; if we use this threshold, the difference in annual income when comparing pairwise the four treatments is not significant. Similarly, significance tests using the Benjamini–Hochberg procedure for a false discovery rate of up to 25% show no significant difference for any of the five background statistics across all four treatment conditions (Benjamini and Hochberg 1995). Also note that, as we will report, turnout rate is lowest in the large lopsided election. If participants in this treatment have, on average, a lower income, this result, which is in accordance with the theoretical predictions, is even stronger considering that the opportunity cost of time is positively correlated with income.

  21. Results are qualitatively similar when we use a logistic regression. We report linear regressions as the coefficients are easier to interpret.

  22. See Sect. 4 for a discussion.

  23. To be precise, we acknowledge that Stage 1 also includes the instructions, besides the practice task; this, potentially, adds some noise to our estimation.

  24. We work out a rough estimate of a participant’s per minute income by dividing her gross annual income by 120,000 (2000 h per year times 60 min).

  25. Sonnemans et al. (1998) experimentally study a step-level public good game and report subjects’ satisfaction from different outcomes. In a similar vein, subjects experience less disutility form a wasteful contribution when the threshold is already reached than when it is not.

  26. Callander (2007, 2008) deals with the problem of information aggregation in a common value election.

  27. Agranov et al. (2018) adopt the same approach to explain their experimental results. They estimate the parameter v individually and find that the two best-fitting values are \(\$0.11\) and \(\$0.5\). Setting \(v=\$0.1\) is in line with their more conservative estimate.

  28. We should bear in mind that any comparison with previous lab experiments should be taken with appropriate care. There are two substantial differences. Firstly, we conduct the experiment as a one shot game, which does not allow learning over time. Secondly, we are interested in large elections, a case for which, with the exception of Morton and Tyran (2012), there exist no comparable results in the literature.

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Acknowledgements

We thank Randall Walsh for preliminary discussions. We also thank Steven Callander, Martin Dumav, David Gill, Miguel Fonseca, Ed Hopkins, Tatiana Kornienko, David Levine, César Martinelli, Massimo Morelli, Joep Sonnemans, Jean-Robert Tyran, Haishan Yuan, and seminar participants at Monash University, UNSW, The University of Queensland, and The University of Edinburgh. Marco Faravelli’s and Carlos Pimienta’s research was supported by the Australian Research Council’s Discovery Projects funding scheme (Project Number DP140102426). Kenan Kalayci acknowledges financial support from Australian Research Council Grant DE160101242.

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  1. School of Economics, University of Queensland, Brisbane, Australia

    Marco Faravelli & Kenan Kalayci

  2. School of Economics, UNSW Business, University of New South Wales, Sydney, Australia

    Carlos Pimienta

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  1. Marco Faravelli
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Faravelli, M., Kalayci, K. & Pimienta, C. Costly voting: a large-scale real effort experiment. Exp Econ 23, 468–492 (2020). https://doi.org/10.1007/s10683-019-09620-3

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