INTRODUCTION
Institutions are one of the most important factors determining political outcomes. Institutions, however, are not exogenous: they are themselves political outcomes. Recognizing this fact, a recent but already significant literature, both in economics and in political science, has proposed positive theories of how political institutions are chosen.Footnote 1 At the core of most of these theories, there is the implicit assumption that political actors are rational, selfish versions of the proverbial “homo economicus.” On the other hand, history is full of examples in which groups entrusted with significant power choose to share it with others for what appear to be, perhaps superficially, purely idealistic reasons. Recent experimental evidence, moreover, shows that humans can behave in surprisingly altruistic ways; and that humans do not only care about what is decided, but also about how decisions are made.Footnote 2 This suggests a number of open research questions: to what extent are institutions the result of Machiavellian calculations of convenience; and, conversely, to what extent are they shaped by other behavioral factors? In this paper, we make a first step in addressing these issues by presenting a laboratory experiment.
In our experiment, a population of citizens is divided in two groups, the “blues” and the “yellows.” The entire population collectively decides between alternative payouts through an election. Before the election is held, the yellows are endowed with the constitutional power to choose the voting rule that determines the outcome of the election. They can choose between a majoritarian system and a system in which the policy outcome is determined by the groups in proportion to their size. We study the yellows’ choice under conditions where the yellows are expected to be the majority and the blues have varying degrees of retaliatory power.
We find three results of note. First, a small but significant fraction of the yellows vote for a decision rule that favors the blues in the baseline treatment. Second, despite the fact that retaliation is never optimal in equilibrium, punishment occurs; the possibility of punishment by the minority, moreover, induces a significant increase in the fraction of majority members voting for the proportional rule. Third, the choice of the voting rule changes the way the minority punishes the majority: an unfavorable outcome is punished more under a rule that allocates proportional power to the two groups than under the majoritarian rule (that allocates all the power to the majority).
This indicates that procedural factors are important: the choice of the voting rule affects players’ expectations and hence their reference point with regard to the resulting payoff allocation. Based on these findings, we conclude that institutions are the result of both behavioral factors and self-serving calculations that interact in interesting ways.
THE EXPERIMENT
Our experiment implements three different games of collective decision making. In all three games, one of the two groups has exclusive constitutional power to choose the decision rule.
The Benchmark Game (TBase)
There are six players. Nature randomly assigns the color yellow or blue to each player. With probability
$\frac{9}{10}$
, there are four yellow and two blue players in the group, and with the remaining probability
$\frac{1}{ 10}$
, the group consists of two yellow and four blue players. Players observe their type but they do not know whether their type constitutes the majority. However, they know the probabilities of that occurring.Footnote
3
The players play a game with two stages:
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• In the constitutional stage, the yellows, regardless of whether they hold the majority, privately choose between two voting rules, rule 1 and rule 2. One yellow’s choice is randomly drawn with equal likelihood and implemented. Then, all players are informed about which rule the yellows have implemented.
-
• In the voting stage, all players participate in an election. They privately vote for either alternative Y or alternative B (abstention is not allowed). Alternative Y assigns a high payoff α + 5 to each yellow and a low payoff α to each blue player; and alternative B does the reverse. The rule chosen in the previous stage will determine the result.
Under rule 1, one of the six players is randomly drawn with equal probability and his decision implemented. Under rule 2, the alternative with the highest number of votes is implemented.Footnote 4 Thus, rule 1 is the random-dictator rule and rule 2 the simple-majority rule.Footnote 5 As is well known, there is no widely accepted model of proportional electoral systems. An established literature has modelled power sharing typical of proportional systems by allowing the policy outcome to be determined by different constituencies in proportion to their size (see, for example, Sahuguet and Persico (Reference Sahuguet and Persico2006)) as in rule 1.Footnote 6 Following this literature, we interpret rule 1 as representing a proportional system.
At the end of the game, all players learn whether alternative Y or B has been implemented and earn their resulting payoff. In the unique Perfect Bayesian equilibrium of this game, the yellows choose rule 2 and vote for Y, whereas the blues vote for B. Outcome Y is implemented whenever the yellows are the majority and B is implemented whenever the blues are the majority.
Treatments with Punishments (TPunish, TExit)
We consider two additional treatments in which the minority can punish the majority.
The Ex-post Punishment Game (TPunish)
The ex-post punishment game differs only in one respect from the benchmark game: it adds a punishment stage following the voting stage. On the punishment stage, each blue player privately chooses between accepting (keep) and changing (change) the final outcome of the election, i.e., Y or B. One blue player in the group is randomly drawn, and his choice is implemented. (All blue players are equally likely to be selected).
If the selected choice is “keep”, then the payoffs of this round remain unchanged. If it is change, each yellow player loses 7 points, the blue player whose choice was implemented loses 1 point, and the payoffs of the other blue player(s) remain unaffected. Hence, when the yellows are indeed punished, the blue who is responsible for it, gets one point more than the yellows, while the other blue player(s) get(s) 2 points more.Footnote 7 All players are informed whether “change” or “keep” was implemented in the group. Punishments in this treatment are not sub-game perfect, so the unique equilibrium coincides with the equilibrium of TBase.
The Interim Punishment Game (TExit)
The interim punishment game moves the punishment stage up the game tree: directly after the voting rule has been chosen and revealed to all players, the blues have to decide between continue and exit. Again, one blue player is randomly drawn and his choice implemented. If it is continue, the game proceeds as in the benchmark game. But if it is exit, the game ends immediately, without the voting stage being reached, and payoffs are as follows: each yellow in the group earns α − 2, the blue player whose choice has been implemented earns α − 1, and the other blue player(s) earn α. Thus, the payoffs after exit in TExit are the same as those after change in TPunish when the electoral outcome has been Y. If exit is not implemented, the subjects get the same feedback as in TBase.
The difference between TPunish and TExit is that in TPunish the blues can condition their punishment behavior both on the voting rule and the outcome (Y or B), but in TExit punishment can only be conditioned on the voting rule. Here too punishments are not sub-game perfect, so the unique equilibrium remains unchanged from TBase.
Hypotheses
Our three games can be seen as collective-decision variations of the dictator and ultimatum game. Similar to the experimental literature on these games, it is reasonable to expect systematic deviations from the predictions of the perfect Bayesian equilibrium. First, we know from the literature on dictator games that under standard conditions subjects tend to share their payoffs to reduce inequality. In our setting, subjects can only reduce inequality in expected payoffs; this can be done by implementing the proportional rule on the constitutional stage. Second, the literature on ultimatum games strongly suggests that recipients react to disadvantageous inequality (if better options have been available) by choosing to punish the proposer even though this is not sub-game perfect. In our setting, the blues are those confronted with disadvantageous inequality, and they have access to punishment in the two control treatments. In particular, we expect that the yellows are willing to choose a less favorable voting system in order to leave some power to the blues; and that the blues are willing to pay a price to punish opportunistic behavior by the yellows. The willingness to choose a less favorable outcome, moreover, may depend on the possibility of punishments, despite the fact that punishments are never sub-game perfect. Similarly, the willingness to punish may depend on the policy outcome and voting rule with which it is chosen.
Motivated by these considerations, we test the following four hypotheses:
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H1. The yellows choose the proportional rule (rule 1) with positive probability in the benchmark game.
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H2. The yellows (i) select the proportional rule more often in the two punishment games and (ii) vote for B more often in the ex-post punishment game than in the benchmark game.
-
H3. In the ex-post punishment game, the blues (i) punish more often afterYthan after B; (ii) and they punish more under the simple-majority rule than under the proportional rule (both (a) in general and (b) conditional on a given outcomeY or B).
-
H4. In the interim punishment game, the blues punish more under the simple-majority rule than under the proportional rule.
In contrast with dictator and ultimatum games, there is no obvious “fair” ex-post allocation of payoffs in our model,Footnote 8 pro-social behavior at the constitutional stage cannot be exclusively attributed to concerns about the fairness.Footnote 9 Indeed, our results suggest that perceived fairness of the final allocation depends on how it is achieved, in particular on the voting system chosen in the “constitutional” phase.
Experimental Procedure
We conducted three experimental treatments, one for each game.Footnote 10 Each treatment had six sessions. In each session, the game had 18 subjects. In each round, players were divided in three groups of six to play the game at hand. Subjects were randomly rematched into groups and roles between rounds.Footnote 11 Thirty rounds of the game at hand were played. We randomly varied α across rounds.Footnote 12 One round was randomly drawn and the payoffs were paid out to the participants in cash.
RESULTS
We first report the results from the constitutional stage and the voting stage in all three games. We then present our results regarding the punishment behavior of the blues in the two punishment games.
When Do Subjects Share Power?
The upper part of Table 1 displays standard t-tests of whether the proportion of yellows voting for the proportional rule is significant in our three treatments.
Table 1 Behaviour of the Yellows
*** p < 0.01, **p < 0.05, *p < 0.1, 95% Confidence Interval
Note– proportional is a dummy variable and equals 1 if the proportional rule is chosen. A one sample t-test against a one-sided alternative is used. To account for the clustered data structure, the tests are conducted on the proportion of Yellows choosing the proportional rule. In the upper part of the table, the average over groups is calculated first. Then the average over sessions is calculated. Hence, we are left with six independent data points per treatment. In the middle part of the table, the average over groups is tested. In the lower part of the table, the proportion of how often an individual votes for Outcome B when she is Yellow is tested. With 6 sessions per treatment and 18 individuals per session, we are left with 108 individuals per treatment
Result 1. (i) Supporting hypothesis H1, on average 12% of the decisions made by yellow players in TBase are in favor of the proportional rule; this proportion is highly significant. (ii) A higher average of roughly 26% (TPunish) and 29% (TExit) of the decisions made by yellow players in the two punishment treatments are in favor of the proportional rule; again, these proportions are highly significant.
Comparing TBase with TPunish and TExit, we find: (1) the share of players who always or nearly always choose the majoritarian rule (95% or more of their opportunities to do so) is more than halved under the threat of punishment; and (2) the share of players who often choose the proportional rule (95% or more of their opportunities to do so) is more than doubled (not shown in the tables).Footnote 13
As a first step toward testing whether these differences are significant, we used a Random Effect logit model as displayed in Table 3. To visualize this result, we took a closer look at the distribution of constitutional choices over individual players and estimated the cumulative distribution functions of yellows choosing the proportional rule in our three treatments (Figure 1). Interestingly, the distributions in TPunish and TExit are similar and they both first-order stochastically dominate the corresponding distribution in TBase. This difference is statistically significant.Footnote 14 We conclude:
Figure 1 Treatment Effects on Rulechoice
Result 2. Supporting our hypothesis H2(i), the average number of yellow players choosing the proportional rule increases significantly under the threat of punishment, both when punishment occurs ex post (TPunish) and when it occurs on the interim stage (TExit).
To test for learning effects, we ran logit regressions as displayed in Table 2.Footnote 15 We find that learning in TBase is highly significant, but small in magnitude.Footnote 16
Table 2 Logit Regression of Rulechoice in TBase
*** p < 0.01, **p < 0.05, *p < 0.1
Note– rulechoice is the dependent dummy variable and equals 1 if the simple majority rule is chosen. Coefficients estimated using logit regressions. In model (1) Standard Errors are clustered on session level.
Do Subjects Vote for Giving Others More Than Themselves If Threatened?
As shown in the lower part of Table 1, the average frequency of voting for alternative B when yellow (Y_vote_B) is slightly below 2% and 5% in TBase and TExit, respectively; but much higher, 13.8%, in TPunish. This difference is intuitive: it is only in TPunish that the blues can condition their punishment on the alternative, which the yellows seem to anticipate. All three means are significantly different from zero.
We tested for treatment differences by running a logit regression (Table 3(3)); and we conclude:
Result 3. Supporting hypothesis H2(ii), the share of yellow votes for alternative B is significantly higher in TPunish than in TBase.
Table 3 Treatment Effects on the Behaviour of the Yellows
*** p < 0.01, **p < 0.05, *p < 0.1
Note– Regression estimated using a Random Effect Logit model rulechoice is the dependent dummy variable in model (1) and (2) and equals 1 if the simple majority rule is chosen. Y_vote_B is the dependent dummy variable in model (3) and equals 1 if the Yellow votes for outcome B. Germany is a dummy variable indicating that the sessions were conducted in Berlin rather than in Princeton. TPunish and TExit are dummy variables as well, indicating the Treatment.
(How Much) Do the Blues Punish?
Consider TPunish first. The upper panel of Table 4 reveals that the blues punish significantly more after outcome Y; they also punish less frequently under the simple-majority rule, although this latter effect is not statistically robust.Footnote 17
Table 4 Logit Regression of Change
*** p < 0.01, **p < 0.05, *p < 0.1
Note– decide is a dummy variable and is 1 if the outcome Y. rule is equal to 1 if the simple majority rule is chosen and 0 otherwise. Coefficients estimated using logit regressions. Model (3) and (4) estimated using pooled data. Standard Errors are clustered on session level.
To test whether the blues punish more when they get outcome Y under the proportional rule and more when they get outcome B under the majoritarian rule, as suggested by the descriptive statistics,Footnote 18 we split the sample into two subsamples, one with outcome B ((3) in Table 4) and one with outcome Y ((4) in Table 4). There seems to be a significant effect of the voting rule on the acceptability of outcome Y: in the subsample in which B was the electoral outcome, the blues do not punish the yellows significantly more under any of the two rules. By contrast, in the subsample in which Y was the outcome of elections, the blues punish the yellows significantly less under the simple-majority rule. Overall, we can conclude that:
Result 4. Supporting part (i) of H3 the blues punish more after Y than after B. There is however weak evidence supporting the hypothesis that the blues generally punish less under the simple-majority rule than under the proportional rule (contrary to (ii.a) of H3). Moreover, conditioning on aYoutcome, the blues punish more under the proportional rule, contrary to (ii.b) of H3.
A plausible explanation for the fact that the blues are more inclined to punish for a Y outcome under rule 1 is that the choice of the voting rule affects the reference point according to which the blues evaluate the outcome of the vote: the blues feel more entitled to expect a more favorable outcome under the proportional rule than under the majoritarian rule.
Consider now the treatment TExit. To test whether the blues punish the yellows for choosing the simple-majority rule, we ran a logit regression of the dummy exit on rule. We obtain:Footnote 19
Result 5. Supporting our hypothesis H4, the blues choose “exit” significantly more often under the simple-majority rule than under the proportional rule.
Is the behavior of the yellows optimal given the actual punishing behavior of the blues? In Table 5, we report the average frequency of punishment after the four possible combinations of voting rule and voting outcome. These frequencies allow us to verify that it is not worth it for the yellows to “appease” the blues by choosing the proportional rule or by voting for B. Given the empirical frequencies of Y, B, and punishment, and conditioning on pivotality, the yellows’ expected utility of voting for Y is E[α] + 2.641 after rule 2 and E[α] + 1.759 after rule 1; the expected utility of voting for B is E[α] − 0.833 after rule 2 and E[α] − 0.399 after rule 1; the expected utility of voting for rule 1 is approximately E[α] + 0.86 and the expected utility of voting for rule 2 is approximately E[α] + 1.60.Footnote 20
Table 5 Frequency of Punishment
*** p < 0.01, **p < 0.05, *p < 0.1, 95% Confidence Interval
Note – A one-sample t-test against a one-sided alternative is conducted. To account for the clustered data structure, the test is conducted on the calculated mean over groups. Relative Frequency refers to the relative frequency of the outcome after the Yellows chose the rule. For example, we observed overall 540 group decisions and from that 137 groups chose the proportional rule. When the proportional rule was chosen, 80 group decisions had Y as the outcome, so the relative frequency of outcome Y under the proportional rule is 58.4%.
CONCLUSION
While there is a vast experimental literature on sharing money, our paper presents the first experimental study on sharing constitutional power between groups. Our results clearly show that some (but not all) insights from the experimental literature on the dictator and ultimatum game carry over to our games of power sharing between groups: the privileged group (i.e., the majority) shares power voluntarily only to a small extent. Thus, the prevalent determinant of their constitutional choices is self-interest. They react—or even overreact—to an anticipated punishment threat by becoming more inclined to share power, even though the punishment is not consistent with equilibrium predictions.
To see what can be learned from our findings, note that our study is the first that complements the theoretical literature on endogenous constitutional design with a behavioral perspective. Our experiment suggests that even if a cool-minded cost-benefit analysis would prevent structural minorities from using costly punishment against the structural majority, behavioral motives can nonetheless trigger them to do so, and the majority is quick to understand and even overreact to this. Moreover, the results from the baseline treatment in our experimental study suggest that the majority is sometimes (although rather rarely) willing to share its political power with the minority in the absence of threats even if self-interest would dictate not to. Another contribution of our paper is the clear prediction concerning the effect of endogenous voting rules on the acceptability of electoral outcomes, a nexus completely ignored by the existing literature. We show that punishment is conditioned both on the voting rule and the electoral outcome, and the group with constitutional power understands this and often votes against their immediate interests in order to appease the other group. Importantly, the group without constitutional power is more inclined to accept an unfavorable electoral outcome (i.e., to refrain from retaliation) if they are disempowered by the electoral rule. From this, we conclude that the majority faces a trade-off: on the one hand, sharing power increases the likelihood of electoral outcomes in favor of the underprivileged, thus decreasing the risk of punishment. On the other hand, sharing power increases the risk of punishment if the electoral outcome does not favor the underprivileged.
Overall, our experimental study suggests that behavioral determinants both directly affect how endogenous constitutions are designed and influence the way in which those constitutions shape collective decision making.
SUPPLEMENTARY MATERIALS
For supplementary material for this article, please visit Cambridge Journals Online. http://dx.doi.org/10.1017/XPS.2015.2.
