Collective Behavior Algorithms and Group Size: dynamic choices are most accurate in small groups.

Collective behaviourGroup living is common across many species, and group sizes range from small (e.g., the Elephant herd and Lion pride) to very large (e.g., bird flocks or fish schools). Different species evolved varying group sizes under different environmental conditions but, one way or another, group living evolved because of its many benefits – a critical one being that the offspring of group members stand a better chance at survival due to the collective behavior of the group.

Group survival dynamics operate across a variety of collective behavior algorithms (i.e., rules that group members follow in different contexts).  These algorithms are often shared and naturally vary across species, and their successful operation is often a function of group size (Sumpter, 2006).  Some algorithms work better for large group sizes, while others work better for small group sizes.  For example, herbivores living in large groups receive protection against predators through strength in numbers and, more specifically, by applying simple collective behavior algorithms that sustain distributed collective attention and vigilance to threats. Naturally, sustained vigilance can be exhausting, particularly if you have to sustain vigilance all on your own–but it’s much easier to sustain vigilance if everyone in a larger group takes their turn (and then rests).  Akin to the algorithm that drives a Mexican wave at a football match, large groups of antelopes grazing in the savannah sustain waves of vigilance by following a simple rule: look up when my neighbor looks up, lower my head to munch on some grass when my neighbor lowers their head to munch grass.  This simple imitation algorithm–one amongst a broader set of ‘imitation’ behaviors–serves its evolutionary function well: the group sustains collective vigilance and all benefit by increasing their odds of survival. Of course, collective vigilance isn’t enough for the antelopes and gazelles and other large groups of herbivores, they also need to be able to run if a predator attacks.  Indeed, the vigilance algorithm is rapidly replaced by another algorithm that each member of the group applies when a threat is imminent: the protean algorithm–run in random and unpredictable directions when predators attack.

At the same time, predators may use different collective behavior algorithms in response to the vigilance and random movement of their prey, often by coordinating a more varied set of behaviors into a collective strategy when hunting together.  For example, a group of lions can bring down larger and faster prey by circling and herding and trapping prey in a confined space and then attacking simultaneously from both the rear and sides.  The collective behavior algorithms controlling these hunting sequences are more varied (i.e., complex) than the simple, sequential rules followed by antelopes [(1) vigilance -> (2) random run].  Indeed, their complexity makes them seem more ‘creative’ and, as such, less like ‘algorithms’. Nonetheless, these collective behaviors are repeatable and predictable, and different lion prides will use the same collective behaviors to produce similar outcomes.  Each new generation of lions learns some version of these same collective behaviours or risks the death of the pride.

The observation of collective behaviors often provokes awe and wonder in Homo sapiens, for example, bird flocks murmurations and the dynamic circling, splitting, and reformation of fish schools–and we might be surprised to learn that the highly organized schooling of fish can be explained by reference to three simple rules: if my neighbor swims too close, move away; if I’m too far away from the group, move closer; and whichever direction my neighbor goes, I go too (Sumpter, 2006). Understanding collective behaviour algorithms might detract from the experience of awe and wonder for some people, but hopefully not everyone. Collective behaviour algorithms are deeply important and should provoke our deepest feelings of wonder, as group living is incredibly significant for Homo sapiens.  From the Mexican wave at football matches to the iterative decision making of innovation design teams in high tech companies, the collective behavior algorithms we use vary from simple to complex and can operate in small or large group dynamics.  The group size that is optimized for different collective behavior algorithms varies as a function of the goal the group is pursuing in a particular ecological context.

In the broader ecological context, researchers studying a variety of species have identified many factors that influence group size, including foraging, migration, predation risk, intra-specific competition, and the amount of information available to the group. Recently, Vicente-Page and colleagues (2017) identified another factor influencing group size–the pursuit of collective decision accuracy. Using a series of mathematical models where the goal is to optimize collective decision accuracy in dynamic situations (i.e., where groups make multiple decisions across a series of rounds of decision making), Vicente-Page and colleagues help us to understand why high functioning teams that seek to maximize their collective intelligence and decision-making accuracy are often relatively small in size (Hackman & Vidmar, 1970).

Homo sapiens are deeply fascinating as a group living species, perhaps even more so in recent centuries, as population growth, globalization, urbanization, and new forms and scales of physical and virtual groups have emerged in tandem with the industrial and technological revolutions. In simple terms, unlike any other species, Homo sapiens can cluster in groups that vary in size from very small to very large.  From a historical perspective, prior to the agricultural revolution, before farming supported the emergence of larger human groups and settlements, human group sizes were relatively small.  Anthropologists and primatologists estimate that human group sizes (i.e., for bands and tribes), although relatively small, were generally larger than chimpanzee group sizes (i.e., troops).  One collective behavior algorithm that constrains group size amongst chimpanzees is their use of very time-consuming grooming rituals, which serve to maintain group cohesion through physical contact. And because there is a limit to the amount of time that each group member can devote to grooming other group members, this limits the size of the group where good social relations can be sustained.

Dunbar (1993) suggests that the evolution of conversational ability in Homo sapiens supported cohesion in slightly larger groups. But even with their new verbal collective behavior algorithms designed to sustain social contact (“Good morning, nice to see you, you’re looking well!”), hunter-gatherer groups rarely exceeded 150 people.  At the same time, any hunter-gatherer group working to sustain a broad coalition is actually comprised of smaller high functioning sub-groups that perform a range of complex collective behaviors (e.g., there is a hunting team, a foraging team, a home maintenance team, a team of next generation hunters and gatherers at play, developing friendships and life skills). Ideally, these smaller sub-groupings collectively optimize the distributed material and social functions needed to sustain the larger band or tribe. If they don’t pursue these functions well, the band or tribe will soon find itself in trouble.

The same is true in modern societies, as large groups, upon close analysis, are seen to cluster into smaller groups (Forsyth, 2014). These smaller groups pursue a variety of different functions, and it is clear that the variety of functions Homo sapiens have sought to pursue has increased across the agricultural, industrial, and technological revolutions (Pettersson, 1996). In recent times, we often refer to highly cohesive, high performing groups as teams, be they military teams, executive teams, investigative teams, scientific teams, design teams, etc., and these teams are most often characterized by group sizes in the range of 3 – 15 people.  High functioning teams may develop a preference, amongst themselves, for relatively small group sizes, often in the region of 4 – 7 people (Hackman & Vidmar, 1970).  One reason for this is that beyond this size it becomes difficult to sustain highly coordinated exchanges within the group, given the exponential increase in the number of possible social interactions (i.e., the sum of all possible combinations of group members taken two at a time or higher).

Sometimes, in the context of our excited, globalized, technology-supported information exchanges–and what we intuit as potential wisdom of the crowd –we lose sight of the significance of smaller groups and teams. While large group dynamics are hugely influential, when it comes to the dynamic social exchanges that optimize collective intelligence and decision making accurate in knowledge-rich domains, and the critical steering of societies across local and global networks, the decisions and actions taken by small groups and teams are very important.  Naturally, decision accuracy is critical for our adaptive success and, therefore, optimizing group size to support decision making accuracy becomes a target for natural and cultural selection.

However, as noted by Vicente-Page and colleagues (2017) our understanding of how decision accuracy depends on group size is surprisingly limited.  Historically, influential work on the Condorcet jury theorem (Condorcet, 1785) and group estimation experiments by Galton (1907) reinforced the idea that large groups make more accurate decisions than smaller groups. For example, when individuals are independently asked to estimate the weight of an ox or the number of marbles in a jar, each individual is likely to be inaccurate, to a greater or lesser extent, and thus the group members are ‘noisy estimators’.  However, within the noise of estimations, the errors that group members make often cancel each other out and, collectively, the group will often produce an average estimate that is reasonably accurate.  This idea was taken up with particular zeal during the early days of Web 2.0 and, perhaps in part because Galton’s basic observation was given a new label, specifically, the wisdom of crowds(Surowiecki, 2004).  The idea that there is some ‘wisdom’ in the average of our group estimates reinforced a certain faith that people were cultivating at the time in relation to large group dynamics on the social web.

However, the use of large group average estimates will only get us so far in efforts to resolve complex societal problems. The average estimates generated by large groups can certainly be informative and useful at times, but the varied and distributed and iterative set of decisions and actions that smaller cohesive groups can implement when working together as a team is critical to our adaptive success. Variety and complexity and iterative movement toward enhanced decision accuracy are important in human systems, given the variety and complexity and changeable nature of the environment we seek to control. Consistent with Ashby’s Law of Requisite Variety, for a system to be stable in its pursuit of complex adaptive functions, the number of states that its control mechanism is capable of attaining (i.e., its variety) must be greater than or equal to the number of states in the system being controlled. In essence, adapting to our current human and environmental systems cannot be sustained via any simple collective behavior algorithm (e.g., one that grounds all group decisions and actions in a large group average estimator algorithm)–the varied and iteratively optimized set of functions that multiple, smaller groups can deliver is critical.

As noted by Vicente-Page and colleagues (2017), while the models of group decision making derived from the work of Galton and Condorcet hinge on the idea that individuals decide independently of one another, the reality of group living means that (a) individuals interact and share information with one another, and (b) they make sequential decisions across repeated rounds of interaction using both their private information and information in relation to past decisions of group members. Models that focus on these social and sequential decision-making scenarios indicate that initial errors made by a small number of individuals early in the first round of decision making can propagate and cascade through the group, and correcting for these decision errors in future rounds is thus important – but it’s not always easy for a group to self-correct. Optimizing group decision making accuracy in this context implies optimizing group size, and it appears that small groups can do this better than large groups, and thus avoid catastrophic error cascades that derail the group.

As noted by Vicente-Page and colleagues (2017), when groups have an opportunity to re-evaluate decisions in a second, third, and fourth round, and so on, having access to social information is particularly valuable for those that chose early in the first round (i.e., those who had limited access to social information first time around). However, large groups cannot improve in re-evaluation in later rounds because of error propagation–the wrong choices made by early adopters of the wrong choice influence the remaining agents in the group, who are more likely to make the same wrong choices. If the group is small, when early adopters make their decision in the second round, they will find a relatively small number of individuals in error and, based on the distribution of errors in the group and the probability that they possess private information in relation to the correct decision, there is a reasonable probability they will move away from inaccurate to accurate responding in subsequent rounds, and soon the group will self-correct. In contrast, when the group is large, by the time the early adopters make a decision in the second round, the number of individuals making a wrong decision is large, and therefore, the early adopters are unlikely to correct their choice in the next round–the social information dominating the group decision making profile is false. Because there is a high prevalence rate of false information across a large group, the group is slow to self-correct based on new information coming either from outside the social group or from within the group itself.

As such, smaller groups are more agile and flexible in the sense that they can more readily self-correct across multiple rounds of decision making, whereas larger groups are slower to do so, and are more likely to propagate and cascade ‘errors’ across the group. Extreme examples of these cascade effects in large groups are increasingly prevalent with the arrival of large group social web dynamics. For instance, although the positive feedback and propagation dynamics driving the sale of fidget spinners played out in a very large group, driving massive global sales, the second round deciders no doubt identified the limited play value of fidget spinners, and, after the truly massive cascade effects observed in the system, analysts were noting that “Fidget Spinners Are Over” Interestingly, the key social information driving the ‘first round’ of decision making of consumers from February to June, 2017, when fidget spinner interest and sales were peaking, included a number of hugely popular YouTube videos that ramped up excitement and reinforced the idea that fidget spinners provide a non-technology play option for highly distractible ‘attention deficit’ youth. For example, one YouTube video published on June 19, 2017, by Dude Perfect has more than 121 million views as of June 30, 2019. Prior to the rise of YouTube, it is unlikely that interest and associated sales of fidget spinners would have peaked so high so quickly. Unlike some hugely popular toys that achieved massive (and more sustained) market share in the days before YouTube (e.g., the Rubik’s Cube), the fidget spinner has limited play value.

As noted by Sumpter (2006), it is important to analyze the collective behavior algorithms that are operating across different groups and contexts, and the principles that undergird collective animal behavior (e.g., variation, positive feedback, negative feedback, response thresholds, redundancy, inhibition, etc.). Understanding human systems requires an understanding of how these collective behavior principles and algorithms play out across small groups and large groups in different ecosystems. If Homo sapiens wish to evolve new structures (e.g., optimizing a team of teams and associated collective intelligence assemblies) that help us to behave in intelligent ways that are consistent with Ashby’s Law of Requisite Variety, then, broadly speaking, we can either work to reduce the complexity of the environment or process we are seeking to manage, or increase our behavioural variety to match the variety in the environment. Both pathways of adaptation are likely to play out, but the broader dynamic, if we follow current trends, is likely to be dominated by a need to increase our behavioral variety.

It’s important to understand some of the challenges that teams face in this regard when they seek to address complex societal problems, and we’ll look at a particular subset of these challenges in the next blog post. More generally, it’s important to keep in mind that Ashby’s principle or ‘law’ of requisite variety runs all the way down every level of human systems – it applies as much to small groups as it does to large groups, and it applies also to individuals, who must themselves manage the requisite variety needed to adapt to their own unique environment, whatever that environment might demand of them as individuals. It’s at this level, in the broader science of systems and human systems in particular, that the science of large and small groups meets with the science of psychology. For psychologists, and for psychology as a discipline, it’s good to know: you never stand alone.

© Michael Hogan


Featured Paper:

Vicente-Page, J., et al. (2018). Dynamic choices are most accurate in small groups. Theoretical Ecology, 11(1): 71-81.

Other references:

Dunbar, R. I. M. (1993). Coevolution of neocortical size, group size and language in humans.Behavioral and Brain Sciences16 (4): 681-735.

Forsyth, D. R. (2014). Group dynamics (6th ed.). Belmont, CA: Wadsworth Cengage Learning

Hackman, J. R., & Vidmar, N. (1970). Effects of size and task type on group performance and member reactions. Sociometry, 33(1), 37-54.

Humphries, D.A. & Driver, P.M. Oecologia (1970) 5: 285.

Pettersson, M. (1996). Complexity and evolution. New York: Cambridge University Press.

Sumpter, D. (2006). The Principles of Collective Animal Behaviour. Philosophical Transactions: Biological Sciences, 361(1465), 5-22.

Surowiecki, J. (2004). The wisdom of crowds: Why the many are smarter than the few and how collective wisdom shapes business, economies, societies, and nations. New York, NY, US: Doubleday & Co.