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Conformity and truthful voting under different voting rules

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We induce conformity in a binary-decision voting game in which one of the options require certain support (majority, supermajority or unanimity) to be the adopted decision. We consider heterogenous types of voters in that each of them prefer a different outcome in the voting game. We demonstrate theoretically that truthful voting is the unique equilibrium without conformity for each possible voting rule. Introducing conformity enlarges the set of equilibria, which includes voting profiles in which agents do not necessarily vote for their preferred option. If we account for the presence of non-conformist honest voters that vote truthfully for their preferred option, truthful voting is more pervasive for conformist voters in equilibrium. In our setting, the effects of conformity and honest voters on the likelihood of voting truthfully depend on the voting rule that determines whether or not voters are in a decisive group to implement one of the decisions. We provide empirical support for our theoretical predictions by means of a laboratory experiment. Our findings indeed suggest an interplay between the voting rule and the willingness to conform.

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  1. In a binary-decision voting game, one agent instrumentally prefers A to B if she gets the highest possible payoff when option A is adopted.

  2. Agents can have incentives to form coalitions and coordinate their votes; see, e.g., Morelli (2004), Eguia (2011) and the references therein.

  3. We focus on the idea of normative conformity as the willingness to conform in our model stems from a desire to ’fit in’ or be liked. The literature on conformity considers also the possibility that agents follow others because they want to be correct in their decision (informational conformity). Our paper departs from this view because our agents have instrumental preferences over the two options in a way that each type of agent prefers one of the alternatives; i.e., there is no correct decision that will make it optimal for everyone to vote one of the options. Readers interested in informational conformity in voting can consult, among others, Anderson and Holt (1997), Morton and Williams (1999, 2000), Callander (2007), Morton et al. (2012, 2015), Hung and Plott (2001), or Goeree and Yariv (2015).

  4. This resembles the idea in Wright (1990) that “it may be ok to back the loser in a close battle because one has plenty of support in one’s position [but voting] for the loser in a landslide could leave the respondent feeling vulnerable and isolated”.

  5. In a context with private information, Feddersen and Pesendorfer (1998) or Battaglini et al. (2010) refer to these agents as partisan voters. In their setting, partisan voters will ignore any signal about the relevant state of the world to vote for their preferred option in an election. As voters do not receive any signal in our model, we avoid using their terminology.

  6. Importantly, we do not intend to test the existence or the type of conformity that agents may possess motivations to conform; e.g., ethical preferences or a desire to vote for the winner.

  7. Other papers that induce preferences over outcomes in a voting game include, among others, Gerber et al. (1998), Morton and Williams (1999), Kube and Puppe (2009), Battaglini et al. (2010), Bassi et al. (2011) or Van der Straeten et al. (2010, 2013, 2016).

  8. The participation decision in an election is not only affected by the pivot probability (Feddersen and Sandroni 2006; Levine and Palfrey 2007; Duffy and Tavits 2008) but can also be influenced by the willingness to conform (Blais and Hortala-Vallve 2016, 2017; Agranov et al. 2017).

  9. One might think that the preferred choice of agents (i.e., their instrumental preference) is to maximize their material payoff, while the alternative (i.e., their expressive preference) is to maximize the total payoffs or minimize inequality. Tyran and Sausgruber (2006) show that accounting for inequality aversion can explain voting in redistribution problems.

  10. There may be several ways of defining conformity (see Moreno and Ramos-Sosa 2017). For models that assume that agents experience a benefit or cost depending on whether they vote with the majority or for the winner of the election see, among others, Luzzati (1999), Hung and Plott (2001), Callander (2007),Morton et al. (2012), Battaglini et al. (2010), Bassi et al. (2011), Michaeli and Spiro (2015). In Supplementary Appendix B, we develop a simple model in which agents may want to conform for efficiency motives (Feddersen et al. 2009) and discuss the extent to which this model reconciles with the observed behaviour. Overall, we find that the efficiency motive is not the main determinant to conform, but voters may have a tendency to vote for the winning option.

  11. Moreno and Ramos-Sosa (2017) provide the number of honest agents that should vote truthfully within a group to guarantee the truthful outcome. Their results hold for any voting rule \(q\in \{1,n\},\) any number of agents n and any list of agents’ types t.

  12. We decided to have two subjects instead of the computer in the role of honest voters to avoid any concern about social preferences; e.g., type-A agents can vote differently depending on whether they impose an externality on the computer or on another human subject. For the effects of social preferences on bandwagon voting, see Morton and Ou (2015) or Corazzini and Greiner (2007).

  13. For the role of strategic uncertainty see also Bouton et al. (2017a).

  14. The reported p values refer to one-sided alternative. Our findings are robust to other statistical analyses; e.g., test of proportions, Mann–Whitney–Wilcoxon test or robust rank-order test (Feltovich 2003).

  15. This result is robust when we perform the analysis at the individual level (see Supplementary Appendix C) and it is much in line with the comment made by Charles Plott to the authors in the sense that “the votes under majority-rule institutions are typically overwhelming majorities because the minority, when anticipating a loss on the vote, just go along with the majority.”

  16. We cannot rule out the possibility that some type-A agents fail to vote truthfully in the BL treatment because there is noise in our data. We believe, however, that our finding that more than 70% of the type-A agents vote for their preferred option in the BL provide enough support for the hypothesis of truthful voting, especially when we compare these figures with the behaviour of subjects in other voting experiments; e.g., in a simultaneous-voting game, Esponda and Vespa (2014) find that nearly 80% of subjects fail to behave optimally, because they have problems to anticipate the behavior of other voters. Van der Straeten et al. (2010) also find evidence of irrational behavior or noise in that some subjects fail to vote for the closest candidate to their position in the second round of the election in a two-round majority voting rule.

  17. Type-B agents are in the majority group, thus all of them will receive 100 ECUs if option B is elected. The remaining 50 ECUs are obtained by type-A agents under different conditions. For example, type-A agents get the 50 ECUs in BL, regardless of their votes. If \(q=3\), each type-A agent in CON can obtain the 25 ECUs if they both vote truthfully or if they both conform. If \(q=5\), then type-A agents need to conform to attain the maximum possible payoff for the group. If one of the agents votes for A, type-A agents will get 75 or 100 ECUs, but type-B agents will be worse off and the total surplus will not be maximized.


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We would like to thank two anonymous referees for their valuable feedback that really helped to shape the exposition of the paper. We also benefited from comments and suggestions provided by seminar and conferences participants at the Social Choice and Mechanism Design Workshop in Manchester, Middlesex University London, University of Hamburg (UHH). Special thanks to Aniol Llorente-Saguer, Matthias Weber, Paul J. Ferraro, Leeat Yariv, Charlie Plott, Rebecca B. Morton, Daniel Müller, Moti Michaeli, Gary Bolton, Ben Greiner, Collin Raymond, David Hugh-Jones, and Jonathan Lafky who provided very useful references and stimulated discussion through the ESA Group. Financial support from Junta de Andalucía (SEJ-5980) and the Spanish Ministry of Science and Technology (ECO2014-53767-P and ECO2014-58297-R) is gratefully acknowledged. Ismael Rodriguez-Lara wants to thank financial support from FEDER and the Ministerio de Economia y Competitividad under the project CO2017-87245-R.

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Correspondence to María del Pino Ramos-Sosa.

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Moreno, B., Ramos-Sosa, M.d.P. & Rodriguez-Lara, I. Conformity and truthful voting under different voting rules. Soc Choice Welf 53, 261–282 (2019).

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