Flocks of starlings fill the skies above our heads and schools of fish paint the waters of our oceans and lakes with mesmerizing patterns. These collective motions make for some of the most iconic moments of animation in cinematic history – the wildebeest stampede in The Lion King and the bat swarms in Batman.
In the physical world, crowds are a fundamental part of everyday life: We pass through them, and become part of them, on our way to work, at school, and running errands.
Whether they are made up of pixels or pedestrians, however, the complex behaviors exhibited by crowds depend on a fairly simple set of psychological processes that make coordinated movement possible, APS Fellow William Warren of Brown University writes in Current Directions in Psychological Science.
Similar to how physicists have yet to discover a “unified theory of everything” that might bridge the gap between their understanding of “very large” and “very small” elements of the universe, psychological scientists have yet to establish a model of collective behavior that successfully bridges the gap between the local behavior of individuals and the global behavior of the groups that contain them, Warren said.
“The problem is that people and animals are more complicated than particles,” he explained. “We have energy supplies on board, can make decisions, there are multiple principles on which we operate.”
On the microlevel, the attraction-repulsion framework holds that individuals move toward neighbors who are far away, away from neighbors who are nearby, and match the speed and direction of those in between.
Other computational models look at groups on the macro-level, treating crowds as a fluid, Warren explained. Approximating a crowd’s viscosity, density, and speed of movement based on a few parameters can work when you have a vast number of individuals, such as the more than 2 million Muslims who make the 5-day Hajj pilgrimage to Mecca each year, he continued. But the model begins to break down when it comes to predicting individual behavior.
In the end, it may not be possible to create a single integrated model of collective motion that functions on both levels, Warren said. In the meantime, psychological scientists, mathematicians, physicists, and computer scientists, among many others, are collaborating to make crowds safer everywhere from concert halls to disaster zones.
Cauldrons, Clutters, Colonies, and Caravans
Prickles of porcupines, scurries of squirrels, and coalitions of cheetahs may be little more than a vestige of England’s aristocratic hunting culture, but the fact remains that different kinds of animals move differently.
“There are some very general principles that govern behavior at all levels and across all species, from bacteria to humans,” Warren said. “They aggregate, they swarm, they form flocks and schools, so there must be some general principles that these systems operate by, but the local rules might be slightly different from species to species.”
Humans, for example, only tend to coordinate movement with “metric neighbors” who are within a few meters of us. Some species of birds such as starlings, on the other hand, don’t seem to care about distance, focusing instead on their seven closest “topological neighbors,” no matter how far away they are, Warren explained.
Crowds consisting of humans and other animals demonstrate many of the same basic physical phenomena (such as clogging up bottlenecks) and stimulus-response behaviors (such as steering and flocking), said Anna Sieben, a social psychology researcher at Ruhr University Bochum in Germany. But goal- and norm-oriented “collective actions” that build on these foundations such as intention-building and ethical decision making are, in many ways, uniquely human. Although physics-based models of collective phenomena predict lane creation even among plasmas and other particles, for example, no other species of animal would consciously self-organize into a queue or take a group vote on where they want to go next.
Even in less clear cut situations, humans tend to fall back on a dynamic set of generally accepted norms and behaviors, Sieben said. As part of a 2013 federal study of crowd safety at large-scale events such as concerts, a research team led by Armin Seyfried, a professor of computer science studying pedestrian behavior at the University of Wuppertal in Germany, studied more than 2,000 people as they participated in a 4-day series of scenarios involving crowds of up to 1,000 individuals per experiment. Their personal goal, participants were told, was to be one of the first people through a pair of turnstiles that would allow them to exit the experiment.
When participants were assembled around the entrance to the imaginary concert hall in a loose semi-circle with no guiding barriers, the crowd became denser, resulting in a constriction effect that limited entry and slowed the crowd’s movement to a crawl – just 2 centimeters per second.
When barriers were used to create a corridor, however, participants created a queue, an unprompted collective action that reduced crowd density and allowed the throng of participants to move at a rate of 8.3 centimeters per second, four times faster than they could in the previous free-for-all.
In a follow-up analysis of these studies, Sieben and colleagues had a group of 60 participants evaluate overhead images and videos of the semi-circle and barrier conditions from the point of view of someone in the crowd trying to get one of just 100 tickets to see their favorite band.
After viewing the videos, participants reported perceiving two distinct sets of social norms, one for each of the conditions. In the semicircle set up, there were “no rules,” resulting in a “first come, first served” and “right of the strongest” mentality. In the corridor, meanwhile, people were expected to queue and behave in an orderly fashion, as pushing and shoving were “forbidden.” In line with these norms, 40.6% of participants reported that many or all people in the semicircle condition exhibited inappropriate behavior, such as pushing, shoving, and jostling, compared with just 5.1% in the corridor condition.
Not all of participants’ perceptions held up to objective measurement, however. While the majority of participants correctly reported that the crowd in the corridor condition moved more quickly than in the semi-circle condition , and found lining up to be more comfortable, it may not have been as equitable a situation as many believed. The tendency toward queueing in corridors creates the perception of fairness, the authors explained, but it also provides ample space for opportunistic individuals to violate the assumed norm and cut the line. Despite the more aggressive behavior observed in the semicircle set up, people were so tightly packed together that they could little more than wait for their turn to pass through the turnstile.
“In the semicircle setup, people’s options to act are strongly limited after the constriction has taken place because it is too dense,” the authors wrote. “Thus, natural and social psychology truly complement each other in their perspective on crowd dynamics.”
Computing Complex Crowds
Physicists and psychological scientists aren’t alone in their curiosity about the complexities of crowd movement, however — computer scientists have also been getting in on the action. Mehdi Moussaïd, a researcher studying adaptive rationality at the Max Planck Institute of Human Development in Berlin, is using his background in the computational and cognitive sciences to create simulations and virtual reality programs that account for the parallels between animal swarms, fluid dynamics, and human crowds.
“Crowd research is a bit of everything,” Moussaïd said. “It’s interdisciplinary in essence.”
While complementary, the relevance of cognitive science-based and physics-based models of crowd behavior can vary based on the density of a system, he added. Moussaïd’s cognitive science approach suggests that pedestrians in relatively open areas navigate their visual environment based on two behavioral heuristics:
They choose the direction that allows the most direct path to their destination, taking into account the presence of obstacles, including other people; and
They determine their walking speed based on the amount of time it would take to avoid those obstacles.
One of the primary differences between this and physical models of crowd movement is that rather than being repelled by their neighbors, individuals are characterized as actively seeking a free path through the crowd, Moussaïd and colleagues wrote in Proceedings of the National Academy of Sciences. In one of several tests of the heuristic pedestrian model, which accounts for speed, pressure, and body compression, computer simulations found the mathematical model closely matched recordings of participants passing each other in a hallway over the course of 200 trials.
Crowd movement isn’t always so predictable, though. When an area becomes overcrowded — typically at a density above four to five people per square meter — it becomes important to distinguish between intentional movements resulting from the above heuristics and unintentional movements resulting from body collisions, which are better described by a physics-based model, Moussaïd said.
Crowds are often modeled as a collection of isolated individuals, he continued, but that is rarely the case – in a 2010 study of more than 4,500 pedestrians, Moussaïd and colleagues found that over half of people observed walking in two areas of Toulouse, France were with at least one other person. Analyzing the speed and spatial organization of these 1,353 groups of pedestrians also allowed the researchers to account for the role of crowd density in group behavior.
In a low-density public space, groups of four or fewer individuals tended to walk side-by-side. On a higher density commercial street, though, group behavior wasn’t what you might expect – rather than bending backward into a more “aerodynamic” shape to cut through the crowd, pedestrian groups tended to bend forward into a ‘V’ or ‘U’-shaped formation.
Using data gleaned from recordings of these pedestrians, Moussaïd was then able to create a series of computer simulations using the social force model, a mathematical model that describes pedestrian motion as a combination of an individual’s motivations and their interactions with other pedestrians and the environment. In addition to simulating the same collective walking patterns observed on the streets of France, the mathematical model also allowed the researchers to identify a particular variable that may be responsible for pedestrians’ tendency to bend forward in densely populated areas: the strength of a groups’ desire for social interaction.
When the variable was set to 0, simulated groups were found to form the more practical ‘V’-shape, whereas setting the variable higher caused groups to reverse that formation, slowing themselves down to support better communication, the authors wrote.
“Crowd dynamics is not only determined by physical constraints induced by other pedestrians and the environment, but also significantly by communicative, social interactions among individuals,” Moussaïd said.
In cases of severe overcrowding, however, these physical interactions begin to take over, Moussaïd continued.
When these denser crowds encounter a bottleneck, such as a limited number of exits from a building, this can cause the coordinated motion of pedestrians to break down, creating uncontrollable patterns of fluctuating movement known as crowd turbulence. This results in a buildup of pressure around the bottleneck, which is eventually released from the system through the “earthquake-like” displacement of pedestrians. This can result in people falling, trampling over others, and suffering injuries, as seen in crowd disasters like the 2010 Love Parade disaster in Germany and the 2015 Hajj stampede.
Situations like these are often said to result in “mass panic,” a theory rooted in the idea that becoming part of a crowd strips people of their ability to respond reasonably to an emergency, wrote John Drury, a professor of social psychology at the University of Sussex in England, in Resilience. Although 19th century social psychologists such as Gustave Le Bon dismissed crowds as impulsive, “hypnotized” individuals incapable of reason, Drury’s research suggests that, in many disaster situations, crowds may instead serve as a source of psychosocial resilience.
“There’s a long history of saying that in crowds people become mad because look at the destructive things that they do, but, in reality, what that crowd gives you is power,” Drury said. And the key to unlocking this power may lie in shared identity.
How Crowds Keep Calm and Carry On
More often than not, family, friends, or tightknit communities come together when faced with natural disasters and other calamities, Drury said. But most contemporary terrorist attacks take place in urban environments where victims have few existing relationships to rely on.
Take the perpetrators of the London bombings in 2005, which resulted in over 700 injuries and 56 deaths, the largest casualty count in the United Kingdom since World War II . The attack targeted morning commuters on the city’s bus and subway systems. Many survivors of the attacks were left stranded underground in the dark with no way of knowing when they would be rescued, or even if there would be another explosion.
Despite the fact that most survivors were surrounded by strangers, Drury’s analysis of publicly available personal accounts and researcher-led interviews with survivors suggest that the sense of shared fate created by danger and disaster may create a psychological crowd, pushing us to overcome our fears in favor of helping others. In fact, while Drury and colleagues identified three reports of selfish behavior in coverage of the attacks – for example, people elbowing each other to escape a bombed bus – they found 214 instances of survivors and witnesses reassuring each other, pulling people from wreckage, and supporting the wounded as they evacuated.
This “collective resilience,” as Drury calls it, was present in first-hand accounts and interviews as well. Of the 90 survivors and 56 witnesses involved in the study, only a handful reported observing or experiencing any kind of selfish behavior or panic in the aftermath of the bombings. Far more often, crowds of survivors were described as outwardly calm, helpful, and united despite the majority of victims reporting they either anticipated their own death or that those around them seemed to do so.
“My initial feelings of anxiety did turn to being scared early on,” said one interviewee, “but when it became obvious that I would have to ensure my colleague got home, the challenge of that overtook any feelings of worry or fear I had.”
Survivors seem to have engaged in widespread helping behavior despite the unpredictably dangerous situation created by the unexpected explosions, Drury wrote. While not everyone has such prosocial aims in an emergency, this interview and observational data suggests that, instead of creating yet another hurdle for survivors, crowds have the potential to be a valuable psychosocial resource, he explained.
“Being part of a psychological crowd increases individuals’ chances of physical survival and psychological recovery,” Drury continued. “The crowd enables them practically to realize goals they cannot achieve alone, including organizing the world around them to minimize the risks of being exposed to further trauma.”
While we often think about how to stand out from the crowd, Drury’s research suggests that we may not want to be so quick to separate ourselves from the pack. When it comes to the psychological science of crowd movement and behavior, other people aren’t just obstacles between us and where we want to be — they’re what gets us there.
Drury, J., Cocking, C., Reicher, S. (2009). The nature of collective resilience: Survivor reactions to the 2005 London bombings. Resilience, 27(1), 66-95. doi:10.1080/21693293.2013.765740
Drury, J., Novelli, D., & Stott, C. (2013). Representing crowd behaviour in emergency planning guidance: ‘mass panic’ or collective resilience? Resilience, 1(1), 18-37. doi:10.1080/21693293.2013.765740
Moussaïd, M., Helbing, D., & Theraulaz, G. (2011). How simple rules determine pedestrian behavior and crowd disasters. Proceedings of the National Academy of Sciences, 108(17), 6884-6888. doi:10.1073/pnas.1016507108
Moussaïd, M., Perozo, N., Garnier, S., Helbing, D., & Theraulaz, G. (2010). The walking behaviour of pedestrian social groups and its impact on crowd dynamics. PLOS ONE, 5(4). doi:10.1371/journal.pone.0010047
Sieben, A., Schumann, J. & Seyfried, A. (2017). Collective phenomena in crowds. Where pedestrian dynamics need social psychology. PLOS ONE, 12 (6).
Warren, W. H. (2018). Collective motion in human crowds. Current Directions in Psychological Science, 27(4), 232-240. doi:10.1177/0963721417746743