Do descriptive social norms drive peer punishment?

Conditional punishment strategies and their impact on cooperation

Peer punishment is widely considered a key mechanism supporting cooperation in human groups. Empirical evidence shows that many people are willing to punish those who free ride on the cooperation of others, even if punishment is costly and cannot lead to future benefits. The threat of punishment makes free riding less attractive and can thereby help support cooperation at high levels.


Given this important role of peer punishment, it is critical to understand what factors influence people’s willingness to punish. Laboratory studies investigating punishment behavior typically focus on factors specific to the interaction at hand, such as peers’ cooperation decisions and the cost and impact of punishment, and abstract away from the broader social context. Cross-cultural experiments do show that people from different societies use peer punishment in systematically different ways, but because societies differ from each other in many ways, these studies have limited ability to identify causal pathways. As a result, little is known about how punishment decisions are impacted by the social context.

In our paper, we investigate an important way in which the social context may influence the punishment of free riding: by indicating ‘descriptive norms’ specifying what behavior is typical in the current interaction setting.


For the decision to punish a free riding peer, two descriptive norms may be important. First, punishment decisions might be guided by the descriptive norm of cooperation: is free riding the typical action in the population? It has been shown that people often infer injunctive norms (what one ought to do) from descriptive norms (what most people actually do). People tend to judge behaviors that are less common in a population to be less socially appropriate (or ‘moral’) and consequently more deserving of punishment. If people use descriptive norms of cooperation to form moral judgments in this manner, they will judge free riding more harshly when it is atypical, which will increase their willingness to punish.


Second, punishment decisions might be guided by the descriptive norm of punishment: is punishment a typical reaction to free riding? Descriptive norms of punishment can signal a ‘principle of social proof’ that free riding is disapproved of, and that punishment is an appropriate and legitimate reaction. Conformity to these norms would lead people to punish free riding if others do so as well.


Examining the impact of these two descriptive norms on sanctioning behavior increases our understanding of how the social context can affect individuals’ punishment of free riding and thereby influence the emergence and maintenance of cooperation.



We conducted two large-scale incentivized experiments in which participants (N=999) could punish their free-riding partner conditional on either the level of cooperation or the level of punishment in a pay-off irrelevant reference group.

Our results demonstrate that, on aggregate, people’s willingness to punish their free riding partner increases both with the level of cooperation (CC experiment) and with the level of punishment (CP experiment) in the reference group.


Interestingly, we observe substantial heterogeneity in how people react to descriptive norms. Although many participants punish independently of levels of cooperation or punishment, a substantial portion is affected by the social norms:

  • When participants can condition their punishment on the fraction of cooperators in the reference group, many participants punish free riding more severely when cooperation is more common (‘norm enforcement’).

  • When participants can condition their punishment on the level of punishment in the reference group, a substantial portion of participants punishes free riding more severely when free riding is more severely punished by others (‘conformist punishment’).

Although behavior in reference group had only modest effects on the aggregate level of punishment, the subset of participants who engaged in norm enforcement and conformist punishment strongly reacted to the level of cooperation and punishment in the reference group.


Theoretical model

To examine the possible long-term implications of the experimentally observed conditional punishment strategies, we develop a simple dynamic model in which a population of agents recurrently interact in a social dilemma game with punishment similar to our experiments. We use analytical methods and agent-based simulations to evaluate how the experimentally observed punishment strategies can shape cooperation in a population.

Here, I will focus on the simulations where we consider the dynamics of cooperation in situations where independent punishers are not sufficiently frequent in the population to sustain cooperation. The figures below show how the level of cooperation (y-axis) develops over time (x-axis) in the presence of different punishment strategies. In each panel, black lines show mean cooperation rates over time across 100 simulation runs; grey lines show individual runs, with a representative run highlighted in green.

We first confirm that in our simulation, if independent punishers alone are too rare to support cooperation on their own, and neither of the conditional punishment strategies is present in the population, cooperation never emerges in our simulations (a and b).


Next, we consider cases where independent punishment is complemented with conditional punishment strategies, raising the overall frequency of punishers. The presence of norm enforcement has a strong stabilizing effect once high levels of cooperation have been achieved (c). However, it might take considerable time for cooperation to emerge (d). These dynamics are driven by a positive feedback loop between norm enforcement and cooperation, locking a population into a state of either high or low cooperation, making it hard to transition from one state to the other.


By contrast, in the presence of conformist punishers cooperation readily emerges, but is not stable (e and f). The population alternates between states with low and high levels of cooperation, with rapid shifts between these states. These dynamics are driven by another positive feedback loop: when levels of cooperation and punishment are low, some agents may punish their free riding partner by mistake. In turn, these stochastic events may prompt other conformist punishers to punish as well, thereby increasing the levels of cooperation and punishment even more, and possibly tipping the population to high levels of cooperation and punishment. However, similar stochastic processes may also cause cooperation to suddenly break down when conformist punishers stop punishing because they happen to underestimate the level of punishment in the population.


When both conformist punishers and norm enforcers are present in the population—but keeping the overall frequency of conditional punishers the same—cooperation rapidly emerges and remains stable at high levels (g and f). Conformist punishers still amplify the impact of stochasticity when cooperation is low, facilitating the emergence of cooperation. Subsequently, norm enforcement locks the population into a state of high cooperation. This result highlights that the concerted action of conformist punishment and norm enforcement can efficiently support cooperation.


These results indicate that different conditional punishment strategies can promote cooperation in different ways: conformist punishment facilitates the emergence of cooperation; norm enforcement helps to maintain it after its emergence.

The figure below confirms these insights. When a population starts from a state of low cooperation, the presence of conformist punishment (green line), rather than norm enforcement (red line), can strongly increase the rate at which it shifts to a state of high cooperation (a). Conversely, the presence of norm enforcement (red line) can substantially extend the time that a population remains in a state of high cooperation (b).



Our experiments provide behavioral evidence that punishment of free riding in social dilemmas is shaped both by descriptive norms of cooperation and by descriptive norms of punishment. While many participants punish independently of levels of cooperation or punishment, a substantial portion punishes free riding more severely when cooperation is more common (‘norm enforcement’), or when free riding is more severely punished by others (‘conformist punishment’).

Our dynamic model demonstrates that conditional punishment strategies can substantially promote cooperation. In particular, conformist punishment helps cooperation to gain a foothold in a population, and norm enforcement helps to maintain cooperation at high levels. Our results thus provide both solid empirical evidence of conditional punishment strategies and illustrate their possible implications for the dynamics of human cooperation.


Our results give pointers for efficiently promoting desirable behaviors, such as voting, tax compliance, or energy conservation. In particular, facilitating the observability of (or accessibility to) information about other people’s behavior may be effective when the majority of the population displays the desired behavior: this information can boost norm enforcement, ensuring that adherence to the present norm remains high.

Conversely, when a majority of the population shows the undesired behavior, it may be more effective to provide people with information that informs them that many people disapprove of the undesirable behavior. Such information may trigger conformist punishment and shift the population towards the more desirable outcome.

The paper is joint work with Lucas Molleman and Xueheng Li, and is available on (open access) on the website of Evolution & Human Behavior .

Dennie van Dolder
Assistant Professor