Following previous literature and the discussion in this section so far, we can formulate specific hypotheses to be tested by the experiment. Unless explicitly stated, all hypotheses apply to both treatments and are tested separately and between subjects.

It is a weakly dominant strategy for subjects in both treatments to choose the game they truly prefer, a necessary assumption for the identification strategy. The individual game choice never influences who becomes the group leader: the game preference of a subject remains private information during the election in ID, and leaders are chosen randomly in RD. Hence, there is no incentive to misrepresent game preferences for the sake of becoming group leader, and the game choice is strategy-proof in that regard. Furthermore, the optimal choice between the games does not depend on the treatment.

Which game is preferred depends on a subject’s beliefs about the other group members’ actions in the coordination game and their own player type. Following previous literature on the public goods game – which presents a social dilemma situation like the prisoners’ dilemma – as surveyed by Chaudhuri (Reference Chaudhuri2011), we can assume there to be three player types: unconditional cooperators who always play A, conditional cooperators who prefer to play A if they believe their opponent will do the same and B otherwise, and defectors who play B regardless. Most studies found that the majority of subjects are conditional cooperators. It is thus a reasonable assumption for subjects of all three types to believe that they are paired with conditional cooperators. In the prisoners’ dilemma, the behavior of conditional cooperators will depend on their actual group composition: if there are other (un-)conditional cooperators in the group, the outcome (A,A) may be played, even though there is the constant temptation to deviate to the dominant strategy of playing B, which the defectors certainly choose. If a conditional cooperator is paired with one or more defectors, she will reciprocate by playing B as well.Footnote ⁵ Therefore, the likelihood of observing cooperative behavior in stage 1 decreases disproportionately in the number of defectors in each group. As DFP (2010) note, whether or not a subject prefers to modify the payoffs for stage 3 depends on what equilibrium they expect to coordinate on in the coordination game. A defector is weakly better off in the prisoners’ dilemma: since she always plays B, in equilibrium she will have the same payoff in both games, but can expect a higher gain off equilibrium should she meet a cooperating subject. On the contrary, all conditionally and unconditionally cooperative subjects at least weakly prefer the coordination game over the prisoners’ dilemma as it turns mutual cooperation into an equilibrium.

Hypothesis 1

A subject who is cooperative in stage 1 is more likely to have a preference for payoff modification than an uncooperative subject.

The experiment is able to test three factors influencing cooperative behavior that are identified in the literature on the effects of elected leadership: selection of more cooperative leaders, intrinsic motivational changes of elected leaders’, and changes in voter behavior in response to the decision-making process (Drazen and Ozbay, Reference Drazen and Ozbay2019). While the emphasis is on the latter, which includes the democracy premium phenomenon, the former two aspects are also testable using the experimental design at hand.

First, according to the selection factor, it is to be expected that groups in ID elect the most cooperative subject as representative (Hamman et al., Reference Hamman, Weber and Woon2011). It follows directly from Hypothesis 1 that the highly cooperative subjects should vote for another cooperative subject. Subjects who are conditional cooperators and play equilibrium strategies in which they defect in the prisoners’ dilemma but cooperate in the coordination game are better off under the modified payoffs and should thus vote for a more cooperative subject as well. Only subjects who always defect can have a weak preference for another non-cooperative subject as representative under the assumption that she will not modify payoffs and that there are some other subjects in the group who cooperate off the equilibrium path. In short, only off-equilibrium beliefs justify having strong preferences for either the unmodified payoffs or an uncooperative representative.

Hypothesis 2

In treatment ID, cooperative players are more likely to be elected as representatives.

Second, elected leaders have been shown to act less selfishly than randomly chosen leaders (Drazen and Ozbay, Reference Drazen and Ozbay2019). This can be tested via a comparison between the two treatments.

Hypothesis 3

In stage 3, leaders in ID behave more cooperatively than leaders in RD.

Third, the response of the voters to the implementation process is at the heart of the paper. Rational choice would predict subjects to be indifferent between the decision-making procedures as long as the outcome, including the information revealed about other players’ preferences, remains constant. However, as discussed in Sect. 2, numerous empirical studies have rejected this null hypothesis in the case of direct democratic decision-making. We could therefore expect endogenous policy selection to lead to more cooperation than the exogenously imposed policy in both treatments (between-subjects comparison of cooperation rates in stage 3). Regarding the difference between direct and representative democracy, the direct process seems to be seen as carrying higher legitimacy (Olken, Reference Olken2010; Towfigh et al., Reference Towfigh, Goerg, Andreas Glöckner, Llorente-Saguer, Bade and Kurschilgen2016). Therefore, we can expect the democracy premium to be smaller in the present setting compared to DFP, (2010).

Hypothesis 4

There is a democracy premium, i.e. cooperation rates are higher when a policy is democratically introduced.

Finally, the treatments ID and RD serve to improve the understanding of the sources of the democracy premium. Two candidate transmission channels shaping compliance with the outcome of a decision-making procedure are legitimacy and authority. On the one hand, legitimacy can be narrowly defined as being derived from the consent of the governed through elections (Locke, Reference Locke1983). More specifically, institutions which are responsive to citizens by allowing participation in the decision-making process carry input legitimacy (Schmidt, Reference Schmidt2013). On the other hand, authority is concentrated political power, regardless of its source. If the two coincide, a feeling of mutual responsibility arises. This is the case in a representative democracy, where authority stems from the figure of the representative herself and legitimacy from her democratic election. A random dictator has authority but no legitimacy from an election process. Compliance is described as a crucial consequence of political legitimacy (Ham et al., Reference van Ham, Thomassen, Aarts and Andeweg2017). Thus, depending on which treatment corresponds to higher cooperation rates following the decision-making process, we can isolate the more important transmission channel of the democracy premium between the two factors authority and legitimacy, leading to two competing hypotheses.

Hypothesis 5.a

(Legitimacy) The democracy premium is larger in ID than RD

Hypothesis 5.b

(Authority) There is no difference between the democracy premia in ID and RD.

The following sections examine the experimental data in the light of the hypotheses formulated in the previous section. Unless indicated otherwise, p-values are derived from non-parametric statistical tests, i.e. the Wilcoxon rank-sum test for within- and the Mann-Whitney-U-test for between-subjects comparisons.

Average cooperation in the first stage, in which all groups played the regular prisoners’ dilemma, amounts to 32 percent in the ID treatment and 36 percent in RD (see left panel of Fig. 3). The difference is small and not statistically significant. The general pattern of positive but decreasing cooperation is well-known from previous experiments using the prisoners’ dilemma (Cooper et al., Reference Cooper, DeJong, Forsythe and Ross1996).

Fig. 3

Cooperation Rates in stages 1 and 3. Depicted are the shares of subjects choosing to cooperate in each round, separated by treatment (RD and ID) and game. In stage 1, all subjects play the prisoners’ dilemma

In the vote stage, 64 percent of subjects in ID and 65 percent in RD chose to modify the payoffs in case they became group leader ( $p=0.803$ ). Table 3 shows linear probability models (LPM) and Probit estimates of voting for modification regressed on variables covering experiences from stage 1 and personal characteristics. Own cooperation is positively related to a preference for the coordination game and significant in every specification. A player who cooperated in all of the first ten rounds has a probability to favor the coordination game that is almost 50 percentage points higher than that of someone who did not cooperate at all. Furthermore, partners’ cooperation has a significantly negative influence, which is intuitive since a subject with cooperative group members in stage 1 would see less necessity to switch to the coordination game to increase cooperation. Cognitive reflection, as measured by the variable logic, is significantly positively correlated with a preference for modification. A subject who was able to answer all three cognitive reflection questions correctly has a probability of voting for modification that is 30 percentage points higher compared to one who gave no correct answer. The treatment dummy variable random dictator is not significant, which supports the conjecture that modification preferences are formed independent of treatment. Overall, the data lends support to Hypothesis 1, implying that cooperative actors self-select into matching institutions.

Table 3

Individual Determinants of Institutional Preferences

Dependent variable: preference for the coordination game
	LPM		Probit
	(1)	(2)	(3)	(4)
Own	0.049 ${}^{\ast \ast \ast }$	0.048 ${}^{\ast \ast \ast }$	0.137 ${}^{\ast \ast \ast }$	0.152 ${}^{\ast \ast \ast }$
Cooperation	(0.013)	(0.012)	(0.040)	(0.042)
			[0.048] ${}^{\ast \ast \ast }$	[0.049] ${}^{\ast \ast \ast }$
Partners’	−0.035 ${}^{\ast \ast \ast }$	−0.032 ${}^{\ast \ast }$	−0.097 ${}^{\ast \ast }$	−0.097 ${}^{\ast \ast }$
Cooperation	(0.013)	(0.012)	(0.039)	(0.040)
			[−0.035] ${}^{\ast \ast \ast }$	[−0.032] ${}^{\ast \ast }$
Logic		0.105 ${}^{\ast \ast \ast }$		0.311 ${}^{\ast \ast \ast }$
		(0.027)		(0.081)
				[0.101] ${}^{\ast \ast \ast }$
Random		−0.007		−0.014
Dictator		(0.050)		(0.151)
				[−0.004]
Female		−0.066		−0.235
		(0.062)		(0.192)
				[−0.076]
Age		−0.011 ${}^{\ast }$		−0.034 ${}^{\ast \ast }$
		(0.006)		(0.017)
				[−0.011] ${}^{\ast \ast }$
Economics		0.058		0.158
Student		(0.053)		(0.164)
				[0.051]
Constant	0.597 ${}^{\ast \ast \ast }$	0.717 ${}^{\ast \ast \ast }$	0.249 ${}^{\ast \ast }$	0.673
	(0.045)	(0.170)	(0.121)	(0.515)
$N$	280	272	280	272
$R^2$	0.055	0.154
Pseudo $R^2$			0.043	0.128

The dependent variable is equal to one if a subject chose the coordination game. Own and partners’ cooperation range from 0 to 10 for each round of cooperation in stage 1. Logic ranges from 0 to 3 for each correct cognitive reflection question. Marginal effects in brackets. Subjects who did not specify their gender are excluded in (2) and (4)

Standard errors (in parentheses) clustered at group level. ${}^{\ast }$ $p<0.10$ ${}^{\ast \ast }$ $p<0.05$ , ${}^{\ast \ast \ast }$ $p<0.01$

Result 1

Cooperative individuals and those with a higher cognitive ability have an increased preference for the coordination game.

In the representative democracy treatment, nearly half of the participants (43 percent) declared in the questionnaire they had voted for a group member because it had appeared cooperative in the first stage. But in fact the elected representatives cooperated less than the other players in stage 1 (on average 2.5 versus 3.5 out of 10 rounds, $p=0.022$ ). There is neither a significant difference in modification preference nor in cooperation in stage 3 between the elected representatives and the rest of the subjects ( $p=0.363$ and $p=0.790$ , respectively).

Result 2

Elected representatives are not more cooperative than other subjects.

Regarding the difference in leadership behavior between the treatments, contrary to Hypothesis 3, the randomly appointed leaders in RD cooperate on average 6.3 out of 10 times in stage 3. The elected representatives in ID cooperate 5.8 out of 10 times and the difference is not significant ( $p=0.363$ ). The results thus fail to confirm the findings by Drazen and Ozbay (Reference Drazen and Ozbay2019). However, leaders in both treatments considerably increase their average cooperation rate between the two stages. Cooperation of leaders in stage 3 goes up by 90 percent in the RD treatment and by 130 percent in ID.

Result 3

Elected representatives are not more cooperative than randomly appointed group leaders.

The right panel of Fig. 3 shows that cooperation rates in both treatments are higher and more stable in the coordination game than in the prisoners’ dilemma ( $p<0.01$ , two-sided t-tests). The payoff modification is therefore effective in fostering cooperative behavior as subjects respond to the changed incentive structure of the game and mostly coordinate on the more efficient equilibrium.

But what is the effect of the endogenous modification? Table 4 shows cooperation rates and subject numbers separated by vote stage outcomes and subjects’ game preferences for both treatments in the first round after the vote. The leaders’ decision was considered for 31 groups (or 124 subjects) in total. Out of those, 12 leaders in ID and 10 in RD modified the payoffs to play the coordination game with their group. The remaining 9 leaders (6 in ID and 3 in RD) chose to remain with the prisoners’ dilemma. In the exogenous condition, the payoffs were modified for 8 of the 17 groups in ID and 11 of the 22 groups in RD.

Regarding cooperation rates, round 11 as shown in Table 4 provides the most conservative results because it is the first round in which the institutional change has come into effect. Over time, behavioral differences between the outcomes could self-reinforce and inflate the estimates. The lowest cooperation rates in both treatments are observed in EndoNot, where only a quarter and a third of subjects cooperate in ID and RD, respectively. ExoNot induces cooperation rates that are more than twice as high as in EndoNot in the ID treatment. This demonstrates the flip side of democracy: endogenously chosen non-cooperative institutions lead to large-scale defection. In the coordination game, cooperation is highest in EndoMod for both treatments. Subjects cooperate more if the payoffs were modified by the group leader compared to an exogenous modification, and the difference is much larger for the elected representatives (16.6 percentage points) compared to the random dictators (0.5 percentage points).

Table 4

Cooperation Rates By Vote Outcome

Cooperation Rates in Round 11 (in %)
	EndoMod	EndoNot	ExoMod	ExoNot
Individual vote
Representative democracy (ID)
No	64.29	23.08	40.00	46.67
	[14]	[13]	[10]	[15]
Yes	94.12	27.27	81.82	61.90
	[34]	[11]	[22]	[21]
All	85.42	25.00	68.75	55.56
	[48]	[24]	[32]	[36]
Random dictator (RD)
No	80.00	22.22	66.67	44.44
	[10]	[9]	[12]	[18]
Yes	80.00	66.67	84.44	84.62
	[30]	[3]	[32]	[26]
All	80.00	33.33	79.55	68.18
	[40]	[12]	[44]	[44]

Number of subjects in brackets

While cooperation rates in all four vote stage outcomes are significantly different from zero (see regression results in Table 5), there are not always significant differences between the outcomes, especially when controlling for modification preferences (see p-values and sharpened q-values in Table 6). Behavior under ExoNot is statistically indistinguishable from ExoMod in both treatments, even though there are two different payoff schemes at play. The difference between EndoMod and ExoMod is significant at the 10-percent level in ID. Thus, the implementation procedure through the elected representative versus the computer is of relevance to subjects. In RD, no significant effect can be found between EndoMod and ExoMod; the behavior is virtually identical in both outcomes.

However, the simple difference between cooperation rates in EndoMod and ExoMod is not an appropriate measure of the effect of the democratic policy selection. Because the leaders actively choose their games in the endogenous condition, the treatment assignment is not random. As reported in Result 1, cooperative subjects are more likely to prefer the coordination game. Therefore, the difference between the endogenous and exogenous conditions is potentially biased by self-selection. Table 4 shows that the yes-voters cooperate more than the no-voters. It is thus necessary to account for differences in group composition between the outcomes when comparing cooperation rates and deriving the effect of the endogenous policy choice.

Table 5

The Effect of Democracy

Dependent variable: cooperation in round 11
	(1)	(2)	(3)	(4)
	ID	RD	ID	RD
EndoMod	0.854 ${}^{\ast \ast \ast }$	0.800 ${}^{\ast \ast \ast }$
	(0.063)	(0.069)
EndoNot	0.250 ${}^{\ast \ast \ast }$	0.333 ${}^{\ast \ast \ast }$
	(0.090)	(0.126)
ExoMod	0.688 ${}^{\ast \ast \ast }$	0.795 ${}^{\ast \ast \ast }$
	(0.078)	(0.066)
ExoNot	0.556 ${}^{\ast \ast \ast }$	0.682 ${}^{\ast \ast \ast }$
	(0.073)	(0.066)
EndoModn			0.643 ${}^{\ast \ast \ast }$	0.800 ${}^{\ast \ast \ast }$
			(0.114)	(0.133)
EndoNotn			0.231 ${}^{\ast }$	0.222
			(0.118)	(0.140)
ExoModn			0.400 ${}^{\ast \ast \ast }$	0.667 ${}^{\ast \ast \ast }$
			(0.135)	(0.121)
ExoNotn			0.467 ${}^{\ast \ast \ast }$	0.444 ${}^{\ast \ast \ast }$
			(0.110)	(0.099)
EndoMody			0.941 ${}^{\ast \ast \ast }$	0.800 ${}^{\ast \ast \ast }$
			(0.073)	(0.077)
EndoNoty			0.273 ${}^{\ast \ast }$	0.667 ${}^{\ast \ast \ast }$
			(0.129)	(0.243)
ExoMody			0.818 ${}^{\ast \ast \ast }$	0.844 ${}^{\ast \ast \ast }$
			(0.091)	(0.074)
ExoNoty			0.619 ${}^{\ast \ast \ast }$	0.846 ${}^{\ast \ast \ast }$
			(0.093)	(0.082)
$N$	140	140	140	140
$R^2$	0.71	0.74	0.73	0.77

OLS results, dependent variable equal to one for cooperation. Independent variables are binary indicators for vote stage outcomes. Models estimated without constant. Suffixes denote interactions with individual preferences for (-y) or against (-n) modification

Standard errors in parentheses.

${}^{\ast }$ $p<0.10$ , ${}^{\ast \ast }$ $p<0.05$ , ${}^{\ast \ast \ast }$ $p<0.01$

Table 6

The Effect of Democracy: p-values and q-values

	(1)	(2)	(3)	(4)
	ID	RD	ID	RD
p-values
EndoNot = ExoNot	0.009***	0.015**
EndoMod = ExoMod	0.099*	0.962
EndoMod = EndoNot	0.000***	0.001***
ExoMod = ExoNot	0.219	0.223
EndoNotn = ExoNotn			0.146	0.198
EndoModn = ExoModn			0.171	0.460
EndoModn = EndoNotn			0.013**	0.003***
ExoModn = ExoNotn			0.702	0.485
EndoNoty = ExoNoty			0.031**	0.159
EndoMody = ExoMody			0.293	0.683
EndoMody = EndoNoty			0.00***	0.601
ExoMody = ExoNoty			0.128	0.983
Sharpened q-values
EndoNot = ExoNot	0.015**	0.024**
EndoMod = ExoMod	0.071*	0.423
EndoMod = EndoNot	0.001***	0.006***
ExoMod = ExoNot	0.123	0.175
EndoNotn = ExoNotn			0.166	0.857
EndoModn = ExoModn			0.166	1.000
EndoModn = EndoNotn			0.049**	0.028**
ExoModn = ExoNotn			0.295	0.857
EndoNoty = ExoNoty			0.066*	1.000
EndoMody = ExoMody			0.265	1.000
EndoMody = EndoNoty			0.001***	1.000
ExoMody = ExoNoty			0.166	1.000

p-values and sharpened q-values (to account for multiple hypothesis testing, see Benjamini et al. (Reference Benjamini, Krieger and Yekutieli2006), Anderson (Reference Anderson2008)) of Wald tests for differences between vote stage outcomes based on regression results reported in Table 5

How can the effect of the endogenous policy choice on cooperation be identified? DFP (2010) propose an identification strategy that breaks down the differences in cooperation rates between the vote stage outcomes while accounting for differences in the distribution of Yes- and No-voters. The strategy allows to estimate the increase in cooperation in response to the decision-making procedures in ID and RD that cannot be explained by the payoff change or differences in group composition. This unbiased estimate is called the democracy premium. It can be used to break down the total policy effect of endogenously changing the game to a selection effect, the exogenous treatment effect, and the democracy premium. This is done by using weighted averages of the individual cooperation rates and voter shares after the vote stage in Table 4 (the detailed calculation can be found in the Electronic Supplementary Material). The weighting by modification preferences accounts for differences in group composition: as modification preference and cooperation are positively correlated, a group with more yes-voters can be expected to have higher cooperation rates. Therefore, the estimation approach by DFP (2010) holds voter shares constant across vote stage outcomes.

Table 7 gives an overview of the decomposed treatment effects in ID and RD. The total effect of the policy – the endogenous change from one game to another – is given by the difference between EndoMod and EndoNot and amounts to 60 percentage points in ID and 47 in RD. The effect of endogenously switching to the coordination game is thus substantially larger for the representative democracy. Comparing the cooperation difference in the endogenous condition to the one in the exogenous condition, we find that the total policy effect is highly significant in both treatments.

The selection effect captures the higher cooperation that would be observed in the EndoNot condition if the share of yes-voters was the same as in the EndoMod groups. Under the assumption that yes-voters cooperate more, the group composition matters for the observed cooperation rates. Using the voter shares from EndoMod – where more yes-voters are present – to reweigh the average cooperation in EndoNot corrects for the self-selection of voter types into the different games. The selection effect is then the difference between the observed cooperation rates in EndoNot and the reweighted average. The difference in the proportion of player types that leads to differences in behavior is insignificant in both treatments.

The change in cooperation caused by an exogenous payoff modification is given by the exogenous treatment effect. It is given by the weighted difference between the two exogenous conditions ExoMod and ExoNot. Again, the difference is reweighted using the voter proportions of the EndoMod condition to account for potential self-selection and allow a comparison of the effects. The weighted exogenous treatment effect is again statistically insignificant in both treatments. Thus, an exogenous modification has little influence on cooperative behavior in both treatments.

Lastly, subtracting the selection effect and the exogenous treatment effect from the total policy effect, the democracy premium remains. This part of the total policy effect is the increase in cooperation not explicable by self-selection or the payoff modification itself. This residual accounts for 47 percentage points in ID and 19 in RD. The representative democracy thus induces an increase in cooperation that is more than twice that of the random dictator. This democracy premium in ID is significant and to a large extent driven by a pronounced reaction from the no-voters, who cooperate much more after endogenous modification than with the exogenous modification. The “nudge” towards cooperation from the elected group representative has a much stronger influence on behavior than modification through the computer. The more legitimate decision-making process of democratic choice seems to be especially powerful in combination with the focal figure of an elected representative. The RD democracy premium is positive as well, but not statistically significant. The democracy premium here is rather driven from the opposite direction: a significant decrease in cooperation in EndoNot. If anything, as opposed to the elected representative, the endogenous decision by a random dictator can have a negative impact on cooperation. Subjects do not seem to appreciate an unelected – and therefore potentially illegitimate– leader.

Table 7

Treatment Effects – Decomposing Cooperation Rates

	Representative Democracy (ID)	Random Dictator (RD)
Total policy effect	60.42*** (10.61)	46.67*** (13.84)
Selection effect	1.05 (4.35)	22.22 (14.02)
Exogenous treatment effect	12.16 (10.51)	5.42 (5.38)
Democracy premium	47.21** (15.58)	19.07 (21.74)

Standard errors in parentheses

As a robustness check, an additional estimation approach. for the democracy premium is conducted: Bó et al. (Reference Dal Bó, Foster and Kamei2019) introduce an alternative identification strategy to estimate the size and significance of the effect of endogenous decision-making by using weighted averages of voting behavior instead of the individual voting decisions. The cooperation rates in the endogenous conditions are reweighted according to the yes- and no-voter shares of the exogenous conditions. In both treatments the subjects in favor of the modification are overrepresented in EndoMod compared to the exogenous conditions (70.8 The difference between the weighted average cooperation rates gives the democracy effect (see Table 8). In ID, the estimated democracy effect is positive with the modified payoffs – albeit smaller than in the decomposition analysis discussed above–and significant at the 10-percent level. The democracy effect in the modified payoffs in RD is economically and statistically insignificant. There is, however, a highly significant negative democracy effect in both treatments: subjects are much less cooperative if the payoffs are endogenously unmodified, and the effect is almost twice as large in ID than in RD. The alternative identification strategy thus yields qualitatively the same result as the decomposition: There is a strong effect of endogenous procedures if the group leader was democratically elected.

Table 8

Treatment Effects–Weights-Based Analysis

Weighted average cooperation rates in round 11
Treatment	Payoffs	Endo	Exo	Democracy effect	Standard Error (p-Value)
ID	Mod	83.2	68.8	14.4	8.16
		[48]	[32]		(0.078)
	Not	25.7	55.6	-29.8	8.30
		[24]	[36]		( $<0.001$ )
RD	Mod	80.0	79.5	0.45	6.11
		[40]	[44]		(0.941)
	Not	51.5	68.2	-17.9	7.05
		[12]	[44]		(0.011)

Number of subjects in brackets. Bootstrapped standard errors

The differences between the vote stage outcomes become even more pronounced over the course of the third stage, where behavior is self-reinforcing within groups. Figures 4 and 5 show individual cooperation rates for all four vote stage results separated by individual voting behavior and treatment over the course of the entire experiment. It can be observed from the first panel of Fig. 4 that in ID the endogenous institution has a considerable effect on those who preferred modification and leads to almost full cooperation. For both conditions the change of payoff structure results in a striking increase in willingness to cooperate. The rates are much lower without modification, especially if it was endogenously determined. The lower panel shows only individuals who were against the payoff modification in ID. The no-voters who received the coordination game through their representative drastically change their behavior and display quite stable cooperation rates. In the exogenous condition both games induce remarkably similar behavior suggesting that the democratic procedure has a stronger behavioral impact than the change in monetary incentives. Such a strong effect on no-voters is in line with the findings of Gallier (Reference Gallier2020), but in contrast with DFP (2010), where the democracy premium was driven by those in favor of the policy. Figure 5 corroborates the result that the random dictator’s implementation of the coordination game did not increase cooperation more than the exogenous modification: the EndoMod cooperation rates are for both voter types for a large part closely below those in ExoMod. The authority to implement a policy decision does not seem to activate compliance in the absence of democratic legitimacy. The differences between treatments are statistically significant as well: cooperation rates in EndoMod compared to ExoMod are significantly different in ID ( $p<0.001$ ), but not in RD ( $p=0.818$ ). Furthermore, cooperation in EndoMod is 14

Result 4

Cooperation is higher if the policy is introduced by a representative (ID) and the size of the democracy premium is substantial. Payoff modification by an unelected group leader (RD) does not increase cooperation.

The treatment difference between ID and RD is informative regarding the source of the democracy premium as conjectured in Hypotheses 5a and b. The evidence from the experiment is clear in this regard: the positive increase in cooperation as a response to the group leader being considered is much larger in ID. In the RD treatment, the difference between EndoMod and ExoMod is small and statistically insignificant. The legitimacy created by the election process seems to be a necessary condition for the democracy premium; authority alone cannot foster cooperation in the same way. Therefore, we reject Hypothesis 5.b and support 5.a instead: perceived legitimacy is the transmission channel of the democracy effect.

Result 5

Representative democracy is associated with a significantly larger democracy premium than randomly appointed leadership.

As an additional robustness check and to further assess the channels through which the democracy premium works, we can consider the interactions between subjects’ preferences and the vote stage outcomes. One potentially relevant factor for subjects in the ID treatment is whether the elected representative was also the player that they themselves voted for. In Table 9, cooperation in the third stage is regressed on the individual modification preference, whether the individually preferred player won the election (variable candidate), and whether she was considered by the computer. Column (1) shows again that preferring the modification and receiving it democratically (EndoMod) both have a strongly positive influence on cooperation under the modified payoffs. It does not matter whether the preferred candidate was elected and there is no significant interaction effect between the variables. Column (2) shows that with unmodified payoffs, i.e. in the prisoners’ dilemma, the modification preference has no influence on cooperation. The endogenously chosen prisoners’ dilemma (EndoNot) is significantly negatively associated with cooperation. There is again neither a significant effect of having one’s preferred candidate elected nor of the interaction between the modification, candidate preference and endogeneity. These results corroborate the finding that it is the decision-making procedure itself that is driving for the democracy premium.

Table 9

Individual Leader Support and Cooperation in ID

Dependent variable: cooperation in periods 11 to 20
	(1)	(2)
	Modified payoffs	Unmodified payoffs
Modification	0.558 ${}^{\ast \ast \ast }$	−0.111
	(0.146)	(0.123)
Candidate	0.242	−0.092
	(0.142)	(0.091)
Modification*candidate	−0.305	−0.0100
	(0.234)	(0.087)
Endo	0.489 ${}^{\ast \ast }$	−0.391 ${}^{\ast \ast }$
	(0.185)	(0.178)
Modification*endo	−0.298	−0.065
	(0.195)	(0.127)
Candidate*endo	−0.0274	0.037
	(0.191)	(0.075)
Modification*candidate*endo	0.055	0.140
	(0.265)	(0.099)
Constant	0.225 ${}^{\ast }$	0.467 ${}^{\ast \ast }$
	(0.128)	(0.175)
$N$	800	600
$R^2$	0.242	0.158

OLS results, dependent variable equal to one for cooperation. Independent variables are binary indicators for individual modification preference (modification), own candidate’s success (align), and whether the representative was considered (endo). Standard errors (clustered at group level) in parentheses. ${}^{\ast }$ $p<0.10$ , ${}^{\ast \ast }$ $p<0.05$ , ${}^{\ast \ast \ast }$ $p<0.01$