Method
Power analysis
We preregistered our intention to recruit a total of 450 participants. We estimated this sample size through a priori power simulations of binomially-distributed data, based on the effect size observed in Balafoutas et al’s10 original study –i.e., a reduction in the probability of third-party punishment of 40% between the PUN condition (50%) and the CPUN condition (10%); for details about the simulation, see Supplementary Material. Given that we expected smaller differences between our new APUN condition and the PUN and CPUN conditions, respectively, we took as a reference effect size a difference of 20% in third-party punishment rates. Specifically, the simulations indicated that 150 participants per condition would guarantee sufficient statistical power to detect a reduction of third-party punishment from 50 to 30% (i.e., 1 - β = .87) and from 30 to 10% (i.e., 1 - β = .96) in a χ² test, assuming α = .05.
Participants and design
In total, we recruited 487 German participants, mainly university students, from the Bonn ECON lab’s participant pool. We excluded from analyses the data of 16 participants who did not complete all parts of the study, 5 participants who did not provide informed consent, 10 participants who participated multiple times, 8 participants whose anonymous identifier did not match in both parts of the study, and 5 participants who failed the comprehension questions of the 3PPG. The final sample consisted of 443 participants (Mage = 26.86, SDage = 7.13, 39.50% male, 59.37% female, 1.11% diverse/did not answer). All participants were at least 18 years old and either native speakers of or very good at German.
The study followed a three-cell between-subject design, with participants being randomly assigned to one of the three experimental conditions (i.e., PUN, CPUN, or APUN).
Procedure
The study was conducted in two parts to avoid any potential carry-over effect between the exploratory dispositional measures and the participants’ decisions in the 3PPG. In the first part, participants answered to the dispositional measures, intended to gauge antagonism aversion (i.e., aversion to interpersonal conflict, agreeableness, fear of negative evaluation) and other exploratory interindividual differences, as well as participants’ demographics.
One day later, participants received the link to participate in the second part, where they completed the 3PPG in one of the three conditions (PUN, CPUN, or APUN). After reading the respective instructions (see Supplementary Materials), they answered three comprehension questions, tapping into important elements of the 3PPG (e.g., “How much money will Person B have at the end of the task?”). If participants failed a question, the instructions and the respective comprehension question were repeated. Those participants who consecutively failed a question three times were excluded from the study, whereas those who answered correctly continued to the decision-making stage of the 3PPG. Once completed, participants finished the study by answering the post-experimental questionnaire.
Third-party punishment game (3PPG). Our 3PPG was an adapted version of Balafoutas et al’s10 paradigm, with the following minor modifications.
First, we changed the payoff structure of the 3PPG in order to optimize resources, and thus, guarantee the estimated sample size. Specifically, we halved the payoff structure relative to Balafoutas et al’s10 3PPG. Thus, Person A (i.e., the potential victim) received an endowment of 4 euros, while they played a passive role. In turn, Person B (i.e., the potential perpetrator) received an endowment of 6 euros, and could decide to take 2.50 euros from Person A. Person C (i.e., the third party) received an endowment of 5 euros. In the case that Person B took money from Person A, Person C could decide to incur a cost of 0.50 euros to punish Person B by deducting 1.50 euros from the latter’s endowment.
Additionally, we exchanged the lottery ticket that Person C received in Balafoutas et al’s10 study for a voucher worth 6.25 euros –i.e., 4 times less than the expected value of Balafoutas et al’s10 lottery ticket. We opted for a voucher in order to eliminate the lottery as a source of uncertainty, and thus, to rule out any possible confound between this uncertainty and the possibility of counterpunishment on third-party punishment. In any case, as part of our battery of exploratory measures, we included a measure of intolerance to uncertainty to examine any potential moderation effect.
For the decision-making stage, we used a strategy vector method 25. Different from Balafoutas et al.10, each participant made sequential decisions in the roles of Person C (i.e., the third party) and Person B (i.e., the potential perpetrator). Since our main measure of interest was third-party punishment, we asked participants to decide as Person C first and as Person B second. Once we completed data collection, we randomly grouped participants in triads, assigned them to one of the three roles (Person A, B or C) and paid them accordingly to their decisions in the role they got assigned to and the decisions of the other members of the triad.
Thus, in the PUN condition, participants firstly decided as Person C whether they would punish Person B if the latter had taken money from Person A. Then, they decided as Person B if they would take money from Person A. In the CPUN condition, participants made the same decisions as in PUN, with the difference that, when acting as Person B, they could further decide whether they would counterpunish Person C by withdrawing the latter’s voucher if Person C had punished them. Note that in Balafoutas et al’s10 study, Person B could counterpunish even if Person C had not punished. We removed this possibility to make the CPUN condition comparable with our third APUN condition.
In the APUN condition, participants, in the role of Person C, learnt that if they decided to punish Person B, an algorithm would randomly determine whether their voucher was withdrawn. The probability with which the algorithm determined this was unknown to participants (parallel to the CPUN condition, where arguably the probability of counterpunishment was unknown as well). However, in order to keep CPUN and APUN comparable, we made the algorithm use the frequency of counterpunishment in the CPUN condition (i.e., 55%) as the probability to determine whether each participant got their voucher withdrawn in the APUN condition.
For a summary and a comparison of experimental conditions across studies, see Table 1.
Measures
Third-party punishment
We used participants’ dichotomous decision as Person C (0 - No punishment, 1 - Punishment) as the measure of third-party punishment.
Exploratory measures
Antagonism aversion
We employed three measures as indicators of antagonism aversion. First, we developed a four-item scale to capture aversion to conflict with other people (e.g., “I find it upsetting that others might get mad at me.”, Cronbach’s α = .83). Second, we included 10 items from the HEXACO-60 scale26 to measure agreeableness –e.g., “When people tell me that I’m wrong, my first reaction is to argue with them.” (reversed), α = .75. Third, we used the 5-item fear of negative evaluation scale27 (e.g., “I am concerned about the impression I am making on someone”, α = .89).
Intolerance to uncertainty
We assessed dispositional intolerance to uncertainty as an exploratory moderator of the hypothesized effects. We used six items from the short German version of the intolerance of uncertainty scale28 (e.g., “It frustrates me not having all the information I need.”; German version29,30, α = .77).
Post-experimental questionnaire
To further explore the psychological mechanisms potentially underlying the effect of counterpunishment on third-party punishment, we included a post-experimental questionnaire. We developed 15 items to measure different motives that might play a role when participants decide (not) to punish as Person C. Six items were intended to gauge antagonism aversion (e.g., “When I made my decision in the role of Person C, I wanted to avoid conflict with Person B.”, α = .83) and three items, intolerance to uncertainty (e.g., “When I made my decision in the role of Person C, I found it aversive to not know the exact consequences of my decision.”, α = .71). Furthermore, two items measured participants’ concerns about avoiding potential costs (e.g., “I was afraid of losing my voucher”). Additionally, we included one item asking participants how likely they thought they were to lose the voucher by punishing Person B (0–0% probability to 10–100% probability). For the complete post-experimental questionnaire, see Supplementary Material.
Results
Main analyses
The frequencies of third-party punishment, taking behavior and counterpunishment per condition are displayed in Table 2.
Table 1
Summary of differences across experimental designs between Balafoutas et al’s original study, Study 1 and Study 2.
| Balafoutas et al. (2014) |
| PUN | CPUN |
Roles/Endowments | Person A (Victim) – 8€ Person B (Perpetrator) – 12€ Person C (Third party) – 10€ + lottery ticket (1/8 of 200€) | Person A (Victim) – 8€ Person B (Perpetrator) – 12€ Person C (Third party) – 10€ + lottery ticket (1/8 of 200€) |
Decisions | Norm violation: Person B may take 5€ from Person A Third-party punishment: Person C may reduce 3€ from Person B at a cost of 1€ | Norm violation: Person B may take 5€ from Person A Third-party punishment: Person C may reduce 3€ from Person B at a cost of 1€ Counterpunishment: Person B may withdraw the lottery ticket from Person C |
| Study 1 |
| PUN | CPUN | APUN |
Roles/Endowments | Person A (Victim) – 4€ Person B (Perpetrator) – 6€ Person C (Third party) – 5€ + voucher (6.25€) | Person A (Victim) – 4€ Person B (Perpetrator) – 6€ Person C (Third party) – 5€ + voucher (6.25€) | Person A (Victim) – 4€ Person B (Perpetrator) – 6€ Person C (Third party) – 5€ + voucher (6.25€) |
Decisions | Norm violation: Person B may take 2.50€ from Person A Third-party punishment: Person C may reduce 1.50€ from Person B at a cost of 0.50€ | Norm violation: Person B may take 2.50€ from Person A Third-party punishment: Person C may reduce 1.50€ from Person B at a cost of 0.50€ Counterpunishment: Person B may withdraw the voucher from Person C | Norm violation: Person B may take 2.50€ from Person A Third-party punishment: Person C may reduce 1.50€ from Person B at a cost of 0.50€ Algorithm: Algorithm randomly determines whether the voucher from Person C is withdrawn |
| Study 2 |
| PUN | disproportionate-CPUN | equivalent-CPUN | equivalent-APUN |
Roles/Endowments | Person A (Victim) – 4€ Person B (Perpetrator) – 6€ Person C (Third party) – 5€ + voucher (6.25€) | Person A (Victim) – 4€ Person B (Perpetrator) – 6€ Person C (Third party) – 5€ + voucher (6.25€) | Person A (Victim) – 4€ Person B (Perpetrator) – 6€ Person C (Third party) – 5€ + voucher (6.25€) | Person A (Victim) – 4€ Person B (Perpetrator) – 6€ Person C (Third party) – 5€ + voucher (6.25€) |
Decisions | Norm violation: Person B may take 2.50€ from Person A Third-party punishment: Person C may reduce 1.50€ from Person B at a cost of 0.50€ | Norm violation: Person B may take 2.50€ from Person A Third-party punishment: Person C may reduce 1.50€ from Person B at a cost of 0.50€ Counterpunishment: Person B may withdraw the voucher from Person C | Norm violation: Person B may take 2.50€ from Person A Third-party punishment: Person C may reduce 1.50€ from Person B at a cost of 0.50€ Counterpunishment: Person B may reduce 1.50€ from the value of the voucher from Person C | Norm violation: Person B may take 2.50€ from Person A Third-party punishment: Person C may reduce 1.50€ from Person B at a cost of 0.50€ Algorithm: Algorithm randomly determines whether the value of the voucher from Person C is reduced by 1.50€ |
Table 2
Observed rates of third-party punishment, taking behavior and counterpunishment per condition - Study 1.
| PUN | APUN | CPUN |
Punishment | 0.40 | 0.07 | 0.07 |
Taking | 0.62 | 0.63 | 0.51 |
Counterpunishment | | | 0.55 |
n | 148 | 148 | 147 |
To determine whether third-party punishment decreased under the possibility of counterpunishment (H1), we conducted a χ2-test between third-party punishment rates in the PUN vs. CPUN condition. As expected, we found third-party punishment rates to be significantly lower in the CPUN condition compared to the PUN condition, χ2(1, N = 295) = 43.16, p < .001, V = 0.38. Specifically, the frequency in which third parties punished was almost six times less when counterpunishment was possible. For exploratory purposes, we further checked if differences in taking rates existed between the two conditions. The χ2-test between taking rates in the PUN vs. CPUN condition was not significant, χ2(1, N = 295) = 3.29, p = .07, thus, we could not infer that participants decided to take more often, despite their chance to counterpunish the third party.
To test H2a and H2b, we conducted a logistic regression comparing third-party punishment rates in the PUN and CPUN condition to the APUN condition. The model included third-party punishment as criterion and two dummy-coded variables (CPUN: 0 = PUN, 0 = APUN, 1 = CPUN; PUN: 1 = PUN, 0 = APUN, 0 = CPUN) as predictors. The model’s intercept, that is, the estimated logit of third-party punishment in the APUN condition, was at − 2.62, 95% CI [–3.33, − 2.04]. As expected (H2a), we found a significant positive effect for PUN condition, b = 2.21, p < .001, 95% CI [1.53, 2.99], which indicated that third-party punishment was higher in the PUN condition compared to the APUN condition, where there was the risk of additional monetary costs. Contrary to our prediction (H2b), we did not find a significant negative effect for the CPUN term, b = 0.01, p = .99, 95% CI [–0.91, 0.93]. The risk of being counterpunished by a perpetrator (CPUN condition), in comparison to risk of incurring additional monetary costs determined by an algorithm (APUN condition) did not make a difference for third-party punishment rates in our experiment. Differences in predicted probabilities are displayed in Fig. 1.
Exploratory analyses
We explored interindividual differences in dispositional antagonism aversion and intolerance of uncertainty as predictors of the punishment decisions in the different experimental conditions. However, we did not find that antagonism aversion or intolerance to uncertainty moderated the differences found between experimental conditions (this was true for all measures of dispositional antagonism aversion; for further details on these analyses, see Supplementary Material).
Similarly, we investigated if the post-experimental ad-hoc measures of antagonism aversion, concerns over uncertainty, and cost avoidance were differentially associated with the punishment decision in the experimental conditions. We found that antagonism aversion negatively predicted punishment across conditions, but there was no significant interaction. For concerns over uncertainty, we found a significant interaction with the CPUN dummy-coded variable (CPUN: 0 = PUN, 0 = APUN, 1 = CPUN), which indicated that higher concerns over uncertainty reduced punishment rates, specifically in the CPUN condition, and not in the other conditions. Regarding cost avoidance, we found a significant negative main effect, but no interaction effects (for further details, see Supplemental Material).
Finally, we conducted a multiple regression analysis to look into differences in perceived probababilities of counterpunishment, i.e. how likely participants thought they were to lose their voucher across conditions. As predictors, we used dummy-coded variables for the comparisons between conditions: PUN (1 = PUN, 0 = APUN, 0 = CPUN) and CPUN (0 = PUN, 0 = APUN, 1 CPUN). Compared to an intercept of 6.76, p = < .001, 95% CI [6.45, 7.08], which represents the perceived probability in APUN condition, we found a significant negative effect for PUN, b = − 4.36, p < .001, 95% CI [–4.81, − 3.91]. The probability of losing the voucher was perceived lower in PUN than in APUN condition. Unexpectedly, however, we also found a significant positive effect for CPUN condition, b = 1.79, p < .001, 95% CI [1.34, 2.24], indicating that participants perceived it to be more likely to lose their voucher in CPUN compared to APUN (and PUN) condition.
Discussion
In Study 1, we replicated the results of Balafoutas et al.10, showing that the possibility of counterpunishment substantially discouraged third parties from punishing a norm violation. In addition, we observed that third parties got equally discouraged if the additional costs of punishment were applied by an algorithm (instead of by counterpunishment from the perpetrator). This finding suggests that the effect of counterpunishment in the 3PPG might not be inherently social by nature. Since the explicit interpersonal conflict, which counterpunishment entails, exerted the same effect as the additional costs applied by an algorithm, it seems that the effect of counterpunishment simply reflects a reaction to the potential high additional costs, and not to any social antagonism.
It seems important to consider that in both Balafoutas et al’s10 original design and in our Study 1, the costs that Person B (or in the APUN case, the algorithm) could impose on third parties by counterpunishing drastically exceeded the costs that third parties could impose on Person B as a punitive reaction to their norm violation. Higher ratios between the costs and the efficiency of third-party punishment had already been shown to discourage third-party punishment4. In the present experimental design, however, the drastic difference between the costs from the potential counterpunishment and the efficiency of third-party punishment could have exerted a disproportionate discouraging effect on third-party punishment that hindered the observation of nuances between experimental conditions. Specifically, the expected, yet unobserved differences between CPUN and APUN could have been overshadowed by the magnitude of the potential additional costs of third-party punishment. We aimed to address this issue in our next study.