1. Introduction
Group identities matter in elections and often lead to an electorate divided along group lines (Huddy, Reference Huddy2001; Eifert et al., Reference Eifert, Miguel and Posner2010; Michelitch, Reference Michelitch2015). Intuitively, the mechanism by which individuals with the same group identity align their behavior is rooted in shared preferences or other group-related considerations, such as concern for group status or group conformity (Akerlof and Kranton, Reference Akerlof and Kranton2000; Dickson and Scheve, Reference Dickson and Scheve2006). Which candidate the group chooses to support collectively, however, varies significantly with context, such as the distribution of policy preferences within the group or the competition among candidates who offer group-targeted benefits—i.e., club goods—in exchange for the group's electoral support.
The relationship between politicians and voters in many societies is frequently characterized as clientelistic, a trade off beneficial policies for electoral support (Kitschelt and Wilkinson, Reference Kitschelt and Wilkinson2007). Such policies that exclusively benefit non-universal social groups are a standard feature of politics, even if their “purchase” in Western democracies is not acknowledged by stakeholders as explicitly as it is in patronage systems. Voters reward incumbents for targeted policies (Weghorst and Lindberg, Reference Weghorst and Lindberg2013; Carlson, Reference Carlson2015; Harding, Reference Harding2015) and politicians strategically engage in providing group-targeted, excludable benefits to particular social groups to create and sustain reciprocal relationships (Gottlieb et al., Reference Gottlieb, Grossman, Larreguy and Marx2019) if possible (Ichino and Nathan, Reference Ichino and Nathan2013).
In this paper, I provide a theoretical account of exactly how voters coordinate with other members of their social group to secure group-targeted benefits. I show how they trade off their preferences over policies benefiting them at the individual-level against group-level benefits from a club good. In particular, I model the relationship between within-group heterogeneity in policy preferences and the groups’ ability to coordinate on one candidate to secure a group-targeted benefit. I then implement a laboratory experiment to test the model's predictions. Experimental treatments pinpoint which electoral alternative draws members of one social group with variation in within-group heterogeneity in preferences over individual-level benefits or priming of the individual-level versus group-targeted benefits offered by candidates.
The experiment operationalizes the main dimension of political conflict as a distribution of income with a larger social group comprising mostly wealthy members; a smaller social group that is mostly poor; and two candidates, one proposing redistribution of income and the other a status-quo distribution. The group-targeted benefit is represented by a club good that the social group can secure for all of its members but only if the group represents a majority of supporters of the winning candidate.Footnote 1 To mimic group identities, I induce minimal groups that have been shown to trigger awareness of group membership and formation of identity-contingent beliefs about others’ behavior, e.g., Eckel and Grossman (Reference Eckel and Grossman2005).Footnote 2
The experiment confirms the models’ prediction that when within-group heterogeneity is low, voters mostly coordinate on the equilibrium where they vote for a candidate who benefits most members of the group individually while securing the group-targeted benefit from the winning candidate. Such equilibrium behavior is observationally equivalent to following a group-majoritarian decision heuristic, vote for the candidate whose platform is individually beneficial to most members of the group. Interestingly, in more heterogeneous groups, for which voting for this candidate is not an equilibrium, I find group-majoritarian coordination as well. To a larger extent however, more heterogeneous groups converge on an equilibrium candidate who imposes individual-level costs on most members of the group but delivers the club good. Experimentally priming voters’ individual-level benefit makes coordination on that equilibrium candidate less likely, driven by those group members who would incur reduced individual-level benefits from switching to equilibrium play. Finally, I provide evidence that more heterogeneous groups converge to the equilibrium candidate who is individually costly to most members of the group because of voters’ increased awareness of what their fellow group members and other groups might do. This finding demonstrates the existence of a strong strategic rationale behind the formation of group-based electoral coalitions.
By delineating mechanisms by which voters coordinate on a specific candidate, this study makes three contributions: it adds to the political behavior literature that investigates group identities as political identities (for an overview see Huddy (Reference Huddy, Huddy, Sears and Levy2013)) highlighting the role strategic considerations play in the formation of electoral coalitions; it extends the literature on ethnic politics investigating the mechanisms behind census voting (Chandra, Reference Chandra2004); and it provides a micro-foundation for the beliefs-relevant effects of social group membership, going beyond the seminal framework of Akerlof and Kranton (Reference Akerlof and Kranton2000) for conceptualizing group identity.
2. Group-targeted benefits and electoral coalition formation
In elections where group identities matter, their influence on individuals’ preferences is the most commonly considered mechanism explaining individuals’ group-contingent decision-making. Voters give more weight to group-related concerns than in elections without group divisions, where this shift is attributed to general in-group favoritism (Chen and Li, Reference Chen and Li2009), emotional gains from conforming to group norms (Goette et al., Reference Goette, Huffman and Meier2006; Suhay, Reference Suhay2015), or group status (Shayo, Reference Shayo2009; Klor and Shayo, Reference Klor and Shayo2010), but also to emotional losses from failing to concede to peer pressure (White et al., Reference White, Laird and Allen2014). Akerlof and Kranton (Reference Akerlof and Kranton2000) prominently introduced such group-driven preferences into models of individual decision-making as an additive term in agents’ utility function.
All these effects on vote choice from membership in a social group provide rationales to do what is “best” for one's group or to vote in conformity with one's group. However, groups are often heterogeneous, inter-group competition is complex, and voting for the group's best interest or following a group norm is not always obvious. Group decision-making, where outcomes have consequences with respect to individual- and group-targeted benefits, presents a coordination problem (Bornstein, Reference Bornstein2003). Faced with that problem, individuals as group members intuitively may align their vote choice with what fellow group members are most likely to do.
In the context of ethnic politics, Chandra (Reference Chandra2004) articulates an important argument that provides a starting point for guiding our thinking about how identities may serve as group coordination devices: we see coordination of vote choice along ethnic lines when co-ethnics represent a large enough electoral coalition to help the candidate win; the candidate, then, provides group-targeted benefits.Footnote 3 The question still arises: On which candidates do voters of the same group coordinate? Do they choose a co-ethnic candidate; but what if such a candidate is not running? Do they pick a candidate who offers club goods; but how do they chose when there are several candidates campaigning on group-targeted benefits? We may expect group members in such circumstances to coordinate by aligning with and supporting the apparent policy preferences of the majority of group members; they would assess those preferences by considering which alternative would give most group members a higher utility. The definition of group-majoritarian coordination follows accordingly: groups coordinate on the electoral alternative that is preferred by most members of that group.
Take a group whose membership mostly comprises wealthy individuals but also includes some poor individuals. According to group-majoritarian coordination, all members of the group should vote against income redistribution regardless of whether the individual voter is poor. A vote for a wealth-preserving status quo policy against redistribution would generate higher individual-level benefits for a majority of group members but imposes cost on the fewer poorer members.Footnote 4
Is there a strategic rationale that could justify a group attempt to coordinate on the electoral alternative that leads to a loss in individual-level benefits for most of its members instead? Suppose that most members of a society with two social groups would benefit from income redistribution (the median income is below the mean income), but most members of a larger social group are disproportionately wealthy, and those in a smaller, minority social group are mostly poor. When that larger social group is rather heterogeneous in preferences over individual-level benefits or when campaign appeals prime the necessity for a group to coordinate their vote for securing group-targeted benefits, members’ awareness of the preferences of their social group as a group, of the diversity of preferences over the individual-level benefit within their group, and of the preferences of the poorer minority social group may increase. Subsequently, members of the larger social group will be more aware of the fact that the poorer minority social group prefers redistribution. At this point, given that the minority social group together with the poorer members of the larger social group may represent an electoral majority of votes in this society, the politician who offers a higher level of redistribution becomes a viable candidate to win the election. The wealthier members of the larger social group may now realize the appeal of voting for more redistribution, since voting jointly with fellow group members allows them to at least secure the club good for their group. The definition of equilibrium coordination follows accordingly: groups support the electoral alternative that may not be individually beneficial to most group members but secures group-targeted benefits.
Before I describe results from an experiment that tests which coordination mechanism is prevalent, it is necessary to verify that the behavior underlying both mechanisms is rationalizable by characterizing equilibrium play in a model of electoral competition.
3. A simple model of electoral competition
Electoral competition is modeled in a complete information environment and I provide equilibrium predictions accordingly. Consider a society of N = 5 voters where voter i is characterized by two distinct attributes. The first attribute is her level of income ωi distributed according to F(ωi). The second attribute is a binary group identity attribute, which, given N odd, induces a division of voters into two groups, {MI, MJ}, where MJ is the larger (majority) social group (N MJ = 3) and MI is the smaller (minority) social group (N MI = 2).
The political competition is a majority-voting contest between two candidates, C = {P, R}. Candidate P's platform is to provide a public good, which voters value at V, at the cost of a tax τ to finance it. Candidate R is the anti-redistribution candidate whose platform is to maintain the existing income levels without redistributive public good provision. Both candidates offer group-targeted benefits to the group, MJ or MI, which most strongly supports them electorally.Footnote 5 Voter i chooses which of the candidates to vote for, a i ∈ A i = {P, R}.
Voter i's utility has two components. One component, denoted $U_i^C$
, is the individual-level benefit dependent on ωi and induced by which candidate wins the election:
The second component is the utility derived from the group-targeted benefit, denoted I, which depends on whether agent i is a member of the social group, MI or MJ, that represents an electoral majority of voters who supported the winning candidate. Formally,
where n MJ is the number of voters in MJ who voted for the winning candidate, n MI is the number of voters in the MI who voted for the winning candidate, and ${\cal I}> 0$
. Voter i's utility is thus, given as $u_i = U_i^C + I.$
The fact that only the latter requires enough voters sharing the same group identity attribute to vote for the same candidate to receive the benefit differentiates individual-level and group-targeted benefit. Voters receive the individual-level benefit provided in the platform of the winning candidate no matter who elected that candidate; a poor voter, for example, benefits from candidate P's platform independent of who helped P win, poor or rich voters.
I can be seen as a club good, the reward given to members of the social group that forms the electoral majority support for the victorious contender, representing the allocation of a scarce resource exclusively to that group. In the real world, such policies may allocate funds to an industry that is located where a critical mass of a supportive social group resides or protect an exclusive right valued by that social group.Footnote 6
Even when i does not vote for the winning candidate, she may receive the group benefit—if her group casts the most votes for the winning candidate. Suppose voter i is the member of MJ and the two other members of MJ as well as one member of MI vote for P but voter i herself votes for R. Then, MJ casts the most votes for the winning candidate, and all members of MJ, including voter i, receive the group benefit.
I assume that the distribution F(ωi) is contingent on identity group membership. There are three critical values in the income-space that will play an important role in the analysis. Let ωL ≡ (V − I/τ), ωM ≡ (V/τ), and ωH ≡ (V + I/τ) where ωL < ωM < ωH. I will refer to incomes below ωL as very poor, those between ωL and ωM as moderately poor, those between ωM and ωH as moderately rich, and those above ωH as very rich. Throughout the main analysis, I will assume that ωi < ωM for all members of MI and one member of MJ and that ωi > ωM for the other two members of MJ. In words, all members of MI are either moderately or very poor while MJ is composed of one poor and two rich members.Footnote 7
Finally, I assume when i is indifferent between voting for candidate P and candidate R, holding fixed the rest of the strategy profile, i votes for the candidate that would give i a higher $U_i^C$
.
Equilibrium Analysis
I will define equilibrium strategy profiles of this game to be inclusive of mixing strategies and denote them by $\alpha ^\ast = ( \alpha _1^{\ast \text {MJ}},\; \alpha _2^{\ast \text {MJ}},\; \alpha _3^{\ast \text {MJ}};\; \alpha _1^{\ast \text {MI}},\; \alpha _2^{\ast \text {MI}})$
, where $\alpha _i^{\ast G}\in \Delta A_i$
with G ∈ {MI, MJ} assigns non-negative weights to the two elements of A i such that the weights sum to 1 for each i. In pure strategy equilibria, these weights are degenerate.
I focus on Nash equilibria in weakly undominated strategies. In particular, every equilibrium strategy $\alpha _i^{\ast G}$
of this game satisfies two conditions for every i, G:
(1) There exists no $\alpha _i^G\, \in \Delta A_i$
, $\alpha _i^G\neq \alpha _i^{\ast G}$ such that $u_i( \alpha _i^G,\; {\boldsymbol \alpha }_{-i}) \geq u_i( \alpha _i^{\ast G},\; {\boldsymbol \alpha }_{-i}) \, \forall \, {\boldsymbol \alpha }_{-i}\in {\bf \Delta}{\boldsymbol A}_{-i}$ with strict inequality for some α−i ∈ ΔA−i.(2) There exists no $\hat {\alpha _i}^G\neq \alpha _i^{\ast G}$
such that $u_i( \hat {\alpha _i}^G,\; {\boldsymbol \alpha }_{-i}^\ast ) > u_i( \alpha _i^{\ast G},\; {\boldsymbol \alpha }_{-i}^\ast )$.
Below I will refer to $\alpha ^\ast$
that meet these conditions as “equilibria.”
Proposition 1 The only pure strategy equilibria possible are of the form (P, P, P; P, P) and (R, R, R; P, P). The (P, P, P; P, P) equilibrium always exists. The (R, R, R; P, P) equilibrium and an equilibrium in mixed strategies of the form $( \alpha _1^{\ast MJ}( P) ,\; \alpha _2^{\ast MJ}( P) ,\; \alpha _3^{\ast MJ}( P) ;\; P,\; P) ,\;$
where $( \alpha _1^{\ast MJ}( P) ,\; \alpha _2^{\ast MJ}( P) ,\; \alpha _3^{\ast MJ}( P) )$
are probabilities of playing P for players i = {1, 2, 3} ∈ MJ respectively, exist if and only if all members of MJ are not very poor, i.e., if their incomes are higher than ωL = (V − I/τ).Footnote 8
There are multiple Nash equilibria in pure strategies satisfying equilibrium conditions (1) and (2). For convenience, I will refer to the (P, P, P; P, P) equilibrium (where P wins the election) as P-equilibrium and the (R, R, R; P, P) equilibrium (where R wins the election) as R-equilibrium. Proposition 1 provides a clear prediction if at least one member of MJ is very poor: in the P-equilibrium, members of MJ solve the trade-off between the individual-level and group-targeted benefit by all voting for the redistributive candidate P even though this imposes a large cost on the rich members of MJ not made up for by securing the group-targeted benefit I. If no member of MJ is very poor, Proposition 1's equilibrium prediction for members of MI is also unambiguous, vote for the redistributive candidate P, but for MJ multiple equilibrium sub-profiles exist. Still, there is a group-welfare ordering of these equilibrium sub-profiles: MJ's welfare is maximized when all members vote for the wealth-preserving candidate R. Note, both coordination mechanisms, equilibrium coordination on candidate P and group-majoritarian coordination where MJ votes for R and MI for P, correspond to equilibria of the simple model of electoral competition but the latter only exists if no member of MJ is very poor.
4. Experimental design
The experiment varies the distribution of income within groups (group heterogeneity treatments) to tests whether behavior congruent with equilibrium predictions arises. It also introduces primes of either the individual-level or group-targeted benefit component of voters’ utility function (appeal treatments) to assess the robustness of equilibrium play and to identify voters’ decision-making mechanism, group-majoritarian or equilibrium coordination.
In the experiment, I simulate vote choice between two candidates and if chosen by electoral majority, one candidate implements redistribution, while the other implements a status-quo distribution. Following the model presented in Section 3, I will refer to the former as “candidate P” and the latter as “candidate R.” On the subject screens in the experiment, candidate P is referred to neutrally as Alternative A and candidate R as Alternative B as to not add a priming effect. The winning candidate rewards the group that casts the most votes for her among all voters who support her by implementing a policy that will disproportionally allocate a scarce resource to that group. Voters are characterized by two social attributes: individual “income” and membership in a “social group.” While income outside of the laboratory could constitute membership in a social group (e.g., the poor, middle class, etc.), social group membership here is defined by the attribute that determines receipt of the group-targeted benefit. I will refer to membership in that social group as group identity, and to the other as individual-level attribute (assigned income).
Each experimental session unfolds in two stages: (1) group identity inducement stage and (2) voting game stage. The voting game stage runs for 40 rounds.Footnote 9
Group identity inducement stage
At the beginning of each experimental session, subjects are assigned to be a Klee or a Kandinsky following standard procedure for inducing group identities in experiments.Footnote 10 This assignment constitutes their membership in a social group and a groups’ status as majority MJ or minority MI is randomly assigned to the social groups of Klees and Kandinskys.
In the subsequent voting game stage, the identities of all subjects with whom individual subjects interact are displayed for them on the screen, making the artificially induced group identities salient. Group membership is directly payoff relevant adding to the salience of group identities in the experiment and implying a potential experimenter demand effect. I account for some consequences of such demand effects in the analysis but note that other demand effects are a desired feature of the experimental design to model campaign appeals calling voters to consider fellow group members’ preferences and behaviors.Footnote 11
Voting game stage
The voting game proceeds as follows:
(1) Subjects are randomly assigned to a five-person society at the beginning of the session and that assignment stays fixed until the end of the experiment.
(2) In each round, subjects are randomly assigned their income from an underlying set of fixed income distributions without replacement.
(3) Subjects are informed about income and group identities of all subjects in their society.
(4) Subjects are asked to make a choice between two candidates, P and R. Whichever candidate receives the most votes in their society becomes the winning candidate of that society.
(5) The winning candidate is announced to the members of the society and subjects are privately informed about their round payoffs.
In this experiment, τ = 1/2, V = 25, and ${\cal I} = 10$
, which ensures existence of equilibria described in Section 3 and allows for easily comprehendible cut-points in the income space. The round payoff to subject i when P wins is given by
The round payoff to subject i when R wins is given by
It is made clear to subjects that there are two distinct parts to their round payoff: the individual-level benefit that depends on their assigned income and the group-targeted benefit that is determined by whether i's group holds a majority among the supporters of the winning candidate.
In what follows (but not on the subjects’ screen within the experiment), voters are defined as “very poor” if they are assigned the three lowest possible values of income (10, 22, or 27), “moderately poor” if they have the next two income values (38 or 44), “moderately rich” if they are assigned the two following values (56 or 62), and “very rich” if they have one of the two highest income values (73 or 90). Three out of five voters in a society are either very or moderately poor with an assigned income below 50, but two out of three members of MJ are moderately or very rich with an assigned income above 50.
The payoffs in the game are structured so that the loss in individual-level benefit for a moderately poor (rich) voter when R (P) wins is more than offset when her group secures the group-targeted benefit but the very rich and the very poor voters would prefer receiving the individual-level to the group-targeted benefit if only one is to be had.
Treatments
Group heterogeneity treatments vary the distribution of assigned income within groups (within subject-design). Appeal treatments vary whether the individual-level or group-targeted benefit component in subjects’ utility function is visually primed on the subjects’ screen. Appeal treatments are assigned on the sessions-level (between subject-design).
I implement three main group heterogeneity treatments that vary the level of income heterogeneity in the larger social group MJ. In the low group heterogeneity treatment, MJ is composed of one very rich, one moderately rich, and one moderately poor voter while in the smaller social group MI there is always one moderately poor and one very poor voter. In the medium group heterogeneity treatment, the poorest voter in MJ is very poor and in the high group heterogeneity treatment, that poorest voter's income is much lower and income of the richest voter in MJ is much higher than in the medium or low group heterogeneity treatments. Figure 1 summarizes the variation induced by the treatments in MJ; the distribution of incomes in MI is constant.Footnote 12
Figure 1. Distribution of income in majority MJ and minority MI (gray markers) within societies by group heterogeneity.
In the no appeal treatment there is no priming, in the group appeal treatment the necessity to coordinate with fellow group members to secure the group-targeted benefit is highlighted, and in the income appeal treatment voters’ individual-level attribute income is primed. Appeals are shown to subjects on their computer screens while they are making their voting decisions. The statement representing a group appeal, depending on Klee [Kandinsky] group membership, reads: Remember you are a KLEE [KANDINSKY]! Should you vote with other Klees [Kandinskys], you may receive a higher identity payoff. The income appeal reads: Remember your income is below 50! Should you vote for Alternative A, you may receive a higher decision payoff. Footnote 13 The income appeal treatment provides a clear behavioral prescription contingent on income while the group appeal treatment only reminds subjects that the groups’ coordination would be necessary to secure the group-targeted benefit but the treatment does not name the target of such coordination.
For robustness checks and for additional tests to identity treatment effects, I implement a series of supplemental treatments that are described in the results section once referenced.
Table 1. Number of societies, subjects, and subject-round observations for appeal and group heterogeneity treatment conditions
The appeal treatments are subtle but are perceived by subjects to influence the behaviorFootnote 14 and treatment conditions are balanced in observables. The number of independent observations in the study is equal to the number of societies of five voters and accounted for in the statistical analysis accordingly (see Table 1). While the order of rounds in which a particular level of group heterogeneity (low or medium) occurred was randomly drawn, the order remained the same during all sessions with high group heterogeneity being implemented in the last four rounds to maximize statistical power of the more subtle effects of the appeal treatments; in this way, order effects may arise.
Hypotheses
Testing for the prevalence of different equilibria derived in Section 3, I facilitate variation in the distribution of income assigned to members of MJ as induced by the group heterogeneity treatments.
HYPOTHESIS 1 (Equilibrium predictions)
When group heterogeneity of the majority MJ of a society is medium or high, all voters will always support the redistributive candidate P and P wins the election (P-equilibrium). When group heterogeneity of the majority MJ is low, the majority MJ also votes for the wealth-preserving candidate R while the minority MI still chooses P (R-equilibrium).
In both cases, MJ receives the group-targeted benefit, but in the latter, the P-, R-, and mixed-strategy equilibrium exists. Given the parameters implemented in the experiment, in the mixed-strategy equilibrium, the moderately poor member of MJ chooses candidate R with a probability of 0.38, the moderately rich member with a probability of 0.62, and the very rich member with a probability of 0.74, and MI chooses candidate P for sure.
I empirically assess hypothesis 1 at the society-level where the equilibrium strategy profile is defined and compute the relative frequency of the possible strategy profiles and compare their occurrences across group heterogeneity treatments.Footnote 15 Observations on the presented statistics across levels of group heterogeneity come from repeated measurements taken within each society.Footnote 16 While variation in group heterogeneity leads to clear hypotheses with respect to which equilibrium should be prevalent, identifying how robust equilibria are to the ways voters trade off individual-level and group-targeted benefit components of their utility function is less straightforward. A unique equilibrium exists when group heterogeneity in MJ is medium, but playing that P-equilibrium and securing the group-targeted benefit imposes hefty costs on the rich members of MJ. The same equilibrium prediction applies for the high heterogeneity treatment, but the potential loss in individual-level benefit when voting for P as the richest member of MJ increases even more. Are those rich voters always willing to accept a loss in the individual-level dimension to win the club good as predicted in the equilibrium? Here is where the appeal treatments allow for identification.
With an income appeal, should the appeal be effective, the R-equilibrium is less likely to occur because the poor member of MJ is more prone to deviate to P. Recall that the income appeal gives a specific behavioral prescription based on subjects’ level of assigned income: vote for candidate R if you are rich and vote for candidate P if you are poor. The P-equilibrium however, will not arise more often because the rich members of MJ are at least as likely, if not even more likely, to vote for candidate R. Further, an increased propensity to vote with fellow group members upon receiving a group appeal is conceivable as long as the target of coordination is not ambiguous. Regarding the prevalence of equilibrium play, this means that because the P-equilibrium is the unique equilibrium, it is more likely to be played in the group appeal than in the no appeal treatment. When group heterogeneity of MJ is low, multiple equilibria exist with different behavioral prescriptions for members of MJ, and no clear effect of priming the benefits of group coordination arises.
The hypothesis below aggregates the predictions about the effects of appeal treatments:
HYPOTHESIS 2 (Appeal treatment effects) Priming the individual-level benefit splits voters by income therefore decreasing the prevalence of any equilibrium. Appealing to consider the group-targeted benefit makes all voters more prone to vote for redistributive candidate P when group heterogeneity in the majority is not low and increases the likelihood that the P-equilibrium is played.
To evaluate hypothesis 2, I test for changes in the relative frequency of equilibrium profiles played and changes in the vote share of candidate R across appeal treatments. Additionally, looking at vote share captures marginal changes in support for candidates—even those that do not imply that societies switch to or away from an equilibrium. When testing for group appeal treatment effects, observations on the presented statistics come from measurements taken in independent samples of societies assigned to the different treatment conditions.
What is left to ask is by what mechanism do voters coordinate with their fellow group members? In both pure strategy equilibria, MJ wins the club good, but the P-equilibrium proves more costly to the rich majority of members of MJ. This implies a group welfare ordering of equilibria favoring coordination on the R-equilibrium.Footnote 17 Such coordination on the R-equilibrium that maximizes MJ's group welfare represents behavior that follows the logic of group-majoritarian coordination, as introduced earlier. Following the heuristic of group-majoritarian coordination however, can also arise in non-equilibrium play in the form of the strategy profile (R, R, R; P, P) when group heterogeneity in MJ is medium or high; it only requires voters to choose what is best for the group defined as voting for the candidate whose platform is beneficial to most members of the group. Whether equilibrium coordination happens with group appeals is identified when voters coordinate on candidate P and when their vote for P is caused by voters forming the expectation that fellow group members and the members of the other group will vote for P.
HYPOTHESIS 3 (Coordination mechanism) Group appeals trigger equilibrium coordination if voters coordinate on voting for the redistributive candidate P and make their decisions in response to the expectations that other voters will also vote for P. They trigger group-majoritarian coordination if voters in the majority MJ coordinate on voting for the wealth-preserving candidate R independent of their income and the level of group heterogeneity.
Observing equilibrium coordination is equivalent to observing the P-equilibrium, while observing group-majoritarian coordination requires the strategy profile (R, R, R; P, P) to be played (whether in equilibrium or not). Identifying group-majoritarian coordination empirically is straightforward—a positive treatment effect of group appeals (over no appeals) on the likelihood that MJ votes for candidate R independent of assigned income and level of group heterogeneity. The empirical test for the existence of equilibrium coordination, in contrast, is composed of two steps: First, I must identify MJ groups likely to vote for P and, second, evaluate whether the decisions of members of such MJ groups are based on forming beliefs about others’ choices.
5. Results
In the analysis of experimental data to follow, I first characterize the relative frequency of equilibrium play as a function of the group heterogeneity treatments. Second, I provide average treatment effects of the appeal treatments on the relative frequency of equilibrium play as well as on the average vote share of candidate R. Finally, I provide evidence for the mechanism behind the effects of group appeals (identifying equilibrium and group-majoritarian coordination).
5.1 Equilibrium predictions
When group heterogeneity of MJ is low, societies choose the R-equilibrium in 45 percent of elections. In this equilibrium all members of MJ vote for the redistributive candidate R, all members of MI vote for wealth-preserving candidate P, R wins the election, and MJ earns the group-targeted benefit I. The distribution of strategy profiles as well as the distribution of which candidate won the election is shown in Figure 2; observations for when group heterogeneity in MJ is low appear in the left panel. The relative frequency of the P-equilibrium where all voters choose P is shown on top (blue, darkest color); the strategy profile where MJ votes for candidate R and MI supports P is given at the bottom (red, second darkest color). The relative frequency of profiles in which P wins but are not the P-equilibrium is given in the lightest color (light blue); the profile where R wins, except (R, R, R; P, P), is shown in the second lightest color (light red). At this level of group heterogeneity, averaging across appeal treatments, only rarely do societies converge to the P-equilibrium (relative frequency 0.02), candidate R wins in 67 percent of elections, and MJ earns the group-targeted benefit in 72 percent of the elections (and shares it with MI in 12 percent).
Figure 2. Distribution of relative frequency of strategy profiles by group heterogeneity and appeal treatments.
When group heterogeneity in MJ is medium or high, the R-equilibrium does not exist and, unsurprisingly, the strategy profile where all members of MJ coordinate on candidate R and all members of MI vote for candidate P occurs significantly less often (at a rate of 0.16 and 0.06, respectively). The relative frequency of the P-equilibrium, however, increases significantly; from 0.02 when group heterogeneity in MJ is low, to 0.19 when it is medium, and to 0.23 when it is high. When group heterogeneity in MJ is medium or high, candidate R wins the majority in only 31 percent and 12 percent of elections, which is a significant drop of 37 percent and 56 percent from when group heterogeneity in MJ is low, respectively. MJ receives the full group-targeted benefit only in 57 percent and 45 percent of elections, a decline of 15 percent and 27 percent, respectively.
I do not find evidence that societies not playing a pure strategy equilibria, choose congruent with the mixed strategy equilibrium instead; in particular the moderately poor and the moderately rich member of MJ in such societies vote for candidate R significantly too often (at a rate of 0.67 and 0.75, in contrast to the predicted 0.38 and 0.62, respectively).
RESULT 1 When group heterogeneity is low, the majority MJ is more likely to coordinate on the wealth-preserving candidate R, helping R win, and taking the group-targeted benefit. When group heterogeneity is medium or high, the majority MJ tends to fully coordinate on candidate R or the redistributive candidate P at similar rates, but given a higher frequency of split votes and because the minority MI always votes for P, candidate P wins most elections.
5.2 Appeal treatment effects
When group heterogeneity is low, the relative frequency of the R-equilibrium does not vary significantly across appeal treatments: it is 0.42 with no appeals, 0.52 with group appeals, and 0.38 with income appeals. In societies where group heterogeneity in MJ is medium or high, the non-equilibrium strategy profile (R, R, R; P, P) is played more often in income (p = 0.11) and significantly more often in group appeal than no appeal treatment (difference 0.09 each).
In the income appeal treatment, the vote share of candidate R among the poor member of MJ is by 0.11, 0.24, and 0.28 lower than among rich members when group heterogeneity is low, medium, and high, respectively (where the difference between poor and rich is significant for the latter two levels). The difference between poor and rich in MJ, however, is stable across all appeal treatments; see Figure 3, which shows the vote share of candidate R across group heterogeneity and appeal treatments for rich MJ (black bars), poor MJ (white bars), and MI (gray bars).
Figure 3. Vote share of the wealth-preserving candidate R by group heterogeneity and appeal treatments for majority MJ and minority MI. Confidence bars are computed from a subject-level clustered bootstrap.
The vote share of candidate R in MI is low throughout but falls significantly in the group appeal over the no appeal treatment when group heterogeneity is medium or high.
RESULT 2 Income and group appeal treatments do not affect the frequency of equilibrium play. When group heterogeneity in the majority MJ is medium or high, both appeals increase the likelihood of the wealth-preserving candidate R winning with the support of the majority MJ while the minority MI still votes for the redistributive candidate P with strongest support upon receiving a group appeal.
5.3 Coordination mechanism
Two interesting observations emerge from the analysis so far: (1) high frequency of the R-equilibrium when group heterogeneity in MJ is low and the P-equilibrium also exists, and (2) strong support for candidate R when group heterogeneity MJ is medium or high and only the P-equilibrium (P, P, P; P, P) exists. In a decision situation with multiple equilibria (i.e., when group heterogeneity in MJ is low), behavior congruent with the simple heuristic provided by group-majoritarian coordination arises unsurprisingly; but why do we observe behavior equivalent to using such heuristic when the behavior is not congruent with equilibrium play? And, which of the societies playing the P-equilibrium truly follow equilibrium coordination?
To identify group-majoritarian and equilibrium coordination, I look at instances of medium or high group heterogeneity in MJ and I define MJ with a propensity to coordinate on R by when MJ shows an average rate of voting for candidate R that is higher than the one by all MJ in a given treatment group. And, I define MJ with a propensity to coordinate on P by when MJ displays an average vote share of candidate R that is lower than the one by all MJ in a given treatment. I find sizable variation in MJ's coordination behavior even within treatment condition. In the no appeal treatment, 43 percent of MJ groups show a propensity to coordinate on R while that percentage grows to 50 percent in the income appeal treatment and 56 percent in the group appeal treatment.
The vote share of candidate R in MJ groups showing a propensity to coordinate on R in the no appeal treatment is by 0.46 significantly higher than the vote share of MJ groups with a propensity to coordinate on P; the difference is 0.50 in the group and income appeal treatments. MJ with a propensity to coordinate on R may follow the logic behind group-majoritarian coordination. MJ with a propensity to coordinate on P may engage in equilibrium coordination.
Figure 4 illustrates the effect of group and income appeal on MJ's coordination effort. Receiving the income appeal makes MJ's attempt to converge on candidate R fall apart toward the end of the experiment (right, bottom panel); the poorest member of MJ recognize the cost of converging with fellow group members on R leading to coordination failure. MJ with a propensity to coordinate on R behaves quite similar in appeal and group appeal treatment (left and middle, bottom panel), illustrating how powerful the heuristic behind group-majoritarian coordination is.
Figure 4. Vote share of the wealth-preserving candidate R for poor and rich members of the majority MJ by appeal treatment and coordination propensity (medium and high group heterogeneity). Confidence bars are computed from a subject-level clustered bootstrap.
Members of MJ, however, only truly choose according to group-majoritarian coordination if their support for candidate R, upon receiving a group appeal, is independent of their assigned income and the level of group heterogeneity. While the propensity to coordinate on candidate R certainly varies with assigned income, the group appeal treatment effect on vote choice remains the same in size and direction and is significantly different from zero at all levels of income (p < 0.1 for comparisons at income 10, 22, and 90). The true test of the existence of the group-majoritarian coordination heuristic is to evaluate whether the poorest member of MJ supports R at all levels of group heterogeneity. Only when the loss in individual-level benefit for the poorest member of MJ is not offset by the group-level benefit received from the wealth-preserving candidate R (i.e., group heterogeneity in MJ is medium or high), would a vote of that member be not congruent with equilibrium play but still driven by the group welfare heuristics behind group-majoritarian coordination. With low group heterogeneity in MJ, the poor member supports candidate R at a rate of 0.81. When group heterogeneity in MJ is medium or high, the vote share of the wealth-preserving candidate among the poorest member of MJ drops significantly to 0.40 and 0.27, respectively.
MJ members with a propensity to coordinate on P may follow equilibrium coordination on candidate P forming expectations about the behavior of other voters as a result of the group appeal and choose accordingly. Several pieces of evidence support such interpretation of the observed behavior:
First, the P-equilibrium not only keeps the rich members of MJ from deviating to higher levels of support for candidate R but also from quick convergence to voting for P. The top-middle panel of Figure 4 shows a significant time trend in average vote share of candidate R for MJ with a propensity to coordinate on P in the group appeal treatment, for rich and poor alike, while the average vote share of candidate R remains stable for MJ with a propensity to coordinate on R.Footnote 18
Second, priming subjects’ considerations of their individual-level attribute as implemented in the income appeal treatment should directly induce rich members of MJ to expect that the poorest member is likely to side with the poor MI in voting for candidate P. In turn, rich voters in MJ responding to that expectation vote for candidate P given that P is now more likely to be the vote winner. Indeed, when income is primed rich voters in MJ coordinate on candidate P as the experiment proceeds. Quick coordination with fellow group members on P, however, is harder to achieve in this treatment but happens eventually; the right panel in Figure 4 shows that rich members of MJ with a propensity to coordinate on P hold off longer with their support for the redistributive candidate than that is the case in the group appeal treatment.
Third, the Rich MI-Group appeal treatment, with only wealthy members in MI, removes any belief that MI is voting for candidate P. The wealth-preserving candidate now receives support at a rate of 0.92 because the poorest member of MJ no longer sees a reason to expect MI to vote for candidate P, and, in turn, the richer members of MJ are more certain that the poorest member coordinates with them on candidate R.
Finally, given that equilibrium coordination on the redistribution candidate P relies on the beliefs of members of MJ about their poorest member and the expectation of the poorest member of the poor MI's behavior, conditions for such coordination are most favorable when the poorest member is very poor and most likely to vote for the redistributive candidate P (assigned income of 10, 22, or 27 with medium and high group heterogeneity) instead of moderately poor (assigned income of 44 with low group heterogeneity). Indeed, the average rate of votes for candidate P in MJ is significantly higher in the former than the latter (difference is 0.34).
RESULT 3 Group appeals trigger equilibrium coordination on the candidate who imposes costs on most members of their own group in individual-level benefit by making voters weigh their expectations about the behavior of fellow group members and of members of the other group more highly. Group-majoritarian coordination as decision heuristic arises only rarely.
An alternative mechanism, similar to the one behind equilibrium coordination, may better explain why MJ members often vote for candidate R despite such behavior being incongruent with an equilibrium profile: vote choice is determined by MJ's expectations about the behavior of its poorest member. The willingness of the poorest member of MJ to coordinate with richer fellow members and these richer members’ belief about the poorest member's willingness to coordinate is largest when the group-level benefit offsets the loss in the individual-level benefit (i.e., when group heterogeneity is low). Indeed, the richer members of MJ are by 0.30 significantly more likely to vote for candidate R when group heterogeneity in MJ is low than when it is medium or high.Footnote 19
6. Discussion and conclusion
I demonstrate how groups coordinate in elections to win group-targeted benefits. With increasing group heterogeneity, the candidate who is individually-beneficial to most members of the group loses support. Why? Voting is characterized by the opportunity to secure group-targeted benefits but individuals are required to make reasonable guesses about the responses of others to secure them. Individuals rely on focal points in decision under uncertainty. Group markers generate common knowledge about such focal points among the members of a group allowing for successful coordination similar to other more context-rich public signals, such as rituals (Chwe, Reference Chwe2013), symbols (Schnakenberg, Reference Schnakenberg2014), or information about political outcomes (Mebane and Sekhon, Reference Mebane and Sekhon2002).
Group identity serves as a low-cost information most valuable to individuals who are otherwise less informed (Bassi et al., Reference Bassi, Morton and Williams2011). The uncertainty about how other groups will behave, however, seems sufficient to steer voters away from this easily recognizable focal point. A group rationality now must emerge so the group finds an optimal strategy vis-a-vis the other group; that is more easily done when the group is appealed to (Bornstein et al., Reference Bornstein, Gneezy and Nagel2002). As an instance of such rationality, decision makers follow a mechanism—equilibrium coordination—by which joint group action arises from far less obvious considerations of the preferences and expected behaviors of fellow group members and the other group.
While the observed electoral outcomes in the experiment result from features of the game I implement, the mechanism by which subjects arrive at them is driven by a more fundamental response to a group appeal: decision makers become increasingly aware of the expectations of others, strategic uncertainties resolve and, ultimately, coordinated collective behavior of a group emerges. Group identities help to create common conjecture; they serve to persuade the individual that others will take a specific action, that others are similarly convinced that everyone else will also take this action, that others are certain that the individual will take this action, etc. My study provides clear evidence of the existence of common conjecture with group identities by a counterfactual: with income appeals the content of the common conjecture is muted and the resulting coordination changes with a different income distribution where the target of the group's joint action is shifted.Footnote 20
My study shows that even weak, context-free identities affect individuals’ beliefs and behaviors in group-driven political competition similar to what has been found outside of the laboratory (e.g., Michelitch (Reference Michelitch2015)). The group appeal treatment effect however, mostly speaks to effects on individuals’ beliefs. In my account, convergence of members of one social group on a particular electoral alternative should be seen as information-driven herding (Goeree and Yariv, Reference Goeree and Yariv2015) or as bandwagoning (Bartels, Reference Bartels1988), and not so much as a result of a saliency-triggered shift from personal to collective identity and an increased adherence to group norms (Huddy, Reference Huddy, Huddy, Sears and Levy2013). Nevertheless, the mechanism I identify differs from bandwagoning because it does not need the sequential nature of voting and the information provided therein (Morton and Williams, Reference Morton and Williams1999; Morton and Ou, Reference Morton and Ou2015).
Generally, I establish the existence of a coordination mechanism in the context of elections where voters respond to a call for coordinated group action by changing their behavior in response to how they expect the appeal to shape the actions of others. Indeed, such group appeal does not necessarily lead an individual to adhere to group norms or to value the overall welfare of the group. It makes it more likely that the voter considers the expected behavior of others and how everyone else might respond to the voters choice. Group identity primed in such way hastens coordination on the candidate most likely to be the electoral victor, leading some voters to abandon their “natural” electoral alternative given their preferences over individual-level benefits. Often, though, the intuitive effect to divide society along group lines persists even though those divisions may, as I show here, emerge from a strategic rationale.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/psrm.2020.53.
Acknowledgements
The research presented in this paper was supported by NSF Grant #SES-1124265 and the Wilf Family Department of Politics at New York University. Support through the ANR - Labex IAST is also gratefully acknowledged. I thank Dimitri Landa, Joshua Tucker, Catherine Hafer, Rebecca Morton, Eric Dickson, Tiberiu Dragu, Sönke Ehret, Sandy Gordon, Karine van der Straeten, Patrick Egan, Robert Johns, Catherine de Vries, Andre Blais, Christine Stedtnitz, Adam Peresman, and Rachel Schutte for their thoughtful comments and suggestions and Lorenz Kurrek for research assistance.
