Collective action in violent conflicts and other highly uncertain situations

Individuals are reluctant to cooperate for public goods, especially for risky ones that involve violent confrontations where they may get hurt while others freeride on their efforts. Cooperation can be fostered by norms, incentives, reputations, and training for risky situations, which take time to develop and depend on monitoring and reliable information transmission through a group’s network. Nevertheless, untrained amateurs engage in impromptu street fights, rescue victims at disasters, and participate in protests against oppressive regimes, largely without these mechanisms. An Ising model that reflects asymmetric payoffs of cooperation and defection demonstrates that under high uncertainty, agitation by situational turmoil such as aggressing opponents is sufficient to get cooperation started. At a critical level of turmoil, just a few accidental cooperators entail a burst of cooperation among the rest. If the proportion of unconditional defectors is above a critical threshold, however, bursts do not occur, which is confirmed by video data of street violence. The model also explains why in larger groups, violent subgroups are typically small whereas larger groups have a better chance to win. In the end we discuss how the model can be generalized by incorporating the usual mechanisms to explain cooperation without turmoil. Why would one contribute to a public good if one runs the risk of being exploited by freeriders, especially if one also runs the risk of getting hurt? Police, fire brigades, ambulance staff, and armies specialize in these situations, receive professional training, have leadership, and internalize effective ∗Jeroen Bruggeman and Don Weenink: Department of Sociology, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, Netherlands. Corresponding author: j.p.bruggeman@uva.nl. 1 ar X iv :2 11 2. 05 08 8v 1 [ ph ys ic s. so cph ] 9 D ec 2 02 1 norms. Ordinary citizens who face sudden disasters or violent opponents, in contrast, are less prepared or not prepared at all. Nevertheless, on numerous occasions, citizens save others at disasters, engage in or deescalate street fights, and join protests. For many participants, these situations are unfamiliar, daily routines and norms do not apply, information is incomplete, uncertainty is high, and payoffs are vaguely known at best. In general, high uncertainty makes people less, not more, cooperative [1], which renders cooperation even more puzzling. To explain cooperation for public goods under high uncertainty, we present an Ising spinglass model and apply it to video recorded street fights, where the public good is the defeat of or the defense against opponents. If people collectively want to help or hurt, they face a dilemma of collective action [2, 3, 4, 5, 6]. To visualize the dilemma, think of two individuals, each with the behavioral options to defect or cooperate [7]. They may both defect, which avoids exploitation but does not yield any public good, and leaves the participants somewhat dissatisfied. Alternatively one individual may cooperate while being exploited by the freeriding other, which yields only half of the public good and results in higher average dissatisfaction. Finally, they may both cooperate at a cost, which maximizes the public good and minimizes average dissatisfaction. Fig. 1 plots the dilemma as a hill that stands in the way to proceed from full defection on the left to full cooperation on the right, with average dissatisfaction [8] on the vertical axis. It is drawn for a group of two and a clique (fully connected network) of five. The literature presents mechanisms to solve the dilemma centered around individual rewards and punishments, called selective incentives [5]: Norms about (in)appropriate behavior [9] in a given situation, as well as monitoring of the participants [10], and reliable transmission of information (i.e., gossip) through a fairly stable network lead to reputations [11] that feed back through incentives and cooperators breaking ties with or excluding defectors. All of these have to be developed over time, which may not be available at impromptu trouble. We argue that even without selective incentives, people can cooperate collectively if they are sufficiently agitated by turmoil, for example the sight of victims or provocations by opponents [12]. Turmoil consists of (noisy) signals that agitate individuals who are sensitive to them. This can be due to their awareness of its (potential) consequences, of opportunities, or simply a physical response. Agitation is manifested by “trembling hands” [13], which means that some participants may accidentally cooperate. We do not assume the presence of initiative takers or leaders, in contrast to well known theories on thresholds [14], cascades [7], and critical mass [15]. If there are initiative takers or leaders [16, 17], however, we can accommodate them in our model,