Collective decision-making: Definition and scope
Does a water molecule make a choice when the river reaches a fork? It, obviously, does not. But if all you can observe is the trajectory of that water molecule, how would you know? You could pick it up, drop it somewhere upstream, and observe its behavior again as it reaches the same fork. And repeat this a few dozen times at least. If the water molecule ends up on one side of the fork more often—statistically speaking—than on the other one, then maybe, after all, it has made a choice.
“Not so fast!”, an astute physics student interjects. “We have to account for asymmetries in the bed of the river and the size and relative orientation of the distributaries.” Very well then. You spend time and money equalizing the bed of the river and reshaping the fork so that it is perfectly symmetrical. And lo and behold, the water molecule does not anymore end up more often on one side of the fork than on the other. The water molecule does not make a choice.
“Not so fast!”, a cognitive scientist yells standing on the riverbank across from you, “By removing all asymmetries from the environment, you have also removed all sources of information available to the water molecule. Even if the water molecule could choose, it would not have any ground to do so.” And just like this, we are back at square one: how can one know if a water molecule can choose if all one can observe is its behavior?
This admittedly silly story is meant to illustrate that studying decision-making is no easy task. The process is often internal and, therefore, almost impossible to observe directly. It is also dependent on external inputs and, thus, cannot truly be studied in isolation. In that context, determining what constitutes a decision in a behavioral experiment is often arbitrary (
Gigerenzer et al., 2000). It cannot be otherwise.
This issue is, of course, present as well in the study of collective decision-making: does the water stream as a whole make a decision at each embranchment of the river? If anything, it is made even worse by the fact that “collective” is another concept that can be difficult to pinpoint scientifically. In some cases, it is easy to delimit the group of individuals participating in a collective choice. This is, for instance, the case in democratic elections where the pools of eligible and participating voters are clearly defined, and the weight of each individual in the outcome is fixed and established.
However, in more “natural” collectives, establishing group membership and the weight of each individual in the outcome can be very difficult, even impossible. Indeed, except in very rare cases, a collective is rarely made of units that interact with all others at all times. Fish in a school, birds in a flock, or pedestrians in a crowd only interact with a few others at a given moment (e.g., their closest neighbors) and do not continuously do so (
Camazine, 2001;
Garnier et al., 2007;
Moussaid et al., 2009;
Sumpter, 2010). In many cases, they may not even interact directly with each other at all, such as when an individual is influenced by the stigmergic traces (
Theraulaz and Bonabeau, 1999) others have left in the environment (e.g., an ant following a pheromone trail (
Goss et al., 1990;
Hölldobler and Wilson, 1990), or a pedestrian following in someone else’s footsteps in the snow (
Helbing et al., 2001)). In these conditions, it can be particularly challenging to determine who belongs to a group, when they join or leave it, and what their impact on the collective outcome is. In behavioral experiments, group membership is often based on simple habitat sharing (e.g., all the fish in a tank) or on more sophisticated proxies for connectivity such as distances between individuals (
Ballerini et al., 2008) or their presence in each other’s perceptual field (
Gallup et al., 2012;
Moussaïd et al., 2011;
Rosenthal et al., 2015;
Strandburg-Peshkin et al., 2013). But here again, arbitrary cutoffs must be set (e.g., maximum distance of perception) to construct a network of presumptive interactions between individuals.
In this context, how could one attempt to write a review on collective decision-making, given that neither the term “collective” nor “decision-making” can be unequivocally defined in the first place? We address this challenge by reducing the realm of possibilities, accepting that some important questions will be left out but hoping that what remains will be insightful enough. Choosing is eliminating, after all.
First, we choose to restrict the discussion on collective decision-making to the context of consensus-building amongst the members of a group (
Conradt and Roper, 2005). Here, we define consensus-building as the process of selecting among multiple available options one by which all the members of a group will abide (the
consensus), even if not all individuals are equally satisfied by the outcome. By doing so, we assume that a coherent collective response is more often than not beneficial to the members of the group. Therefore, we will not discuss much of the “whys” of collective decision-making, leaving the question of social evolution to others more qualified than us (
Conradt and Roper, 2007;
Conradt and Roper, 2009;
Torney et al., 2015;
Wenseleers et al., 2010). Rather, we will focus here more specifically on the “hows” and their consequences on group performance and group stability. In particular, we will concentrate our discussion on what Conradt and Roper called “shared consensus,” which is a consensus reached by a process involving all (or at least most) of the group members (
Conradt and Roper, 2005).
We also choose the consensus framework for practical reasons. Indeed, a consensus is a convenient benchmark for a researcher: it is either achieved or it is not, and one can easily measure by how much it was missed. As such, it is a natural performance target for comparing groups or decision mechanisms against each other. Consensus also allows for treating the group as a unit, making it possible to interpret experimental observations against the background of optimality and rationality theories. Optimality theory provides a well-established economic framework for linking decision mechanisms to their respective costs and benefits, allowing for the comparison of decision outcomes to their expected optimal value (
Marshall et al., 2009). It allows for establishing global benchmarks or theoretical upper bounds to the performance of a system given the conditions it is placed in and independently from its internal mechanics. This is particularly useful, for instance, to understand whether the optimization of a system is restricted by the external conditions or by the composition of the system itself. Rationality theory, on the other hand, provides a convenient framework to reverse engineer the computations performed by the deciding system and to identify its (logical) limitations (
Sasaki and Pratt, 2011,
2017). It focuses on determining the choices that maximize a system’s utility, given the information available to the system when making a decision. Any deviation from the utility maximization principle will indicate the existence of constraints during the decision-making process that can be used to infer the information processing pipeline of the system. In both cases (optimality and rationality theories), this opens up the possibility to draw up parallels between the processing capabilities of social systems and of, for instance, neuronal networks and computerized applications. Moreover, considering the group as a functional unit embedded in an environment allows for asking questions about the intricate relationship between individual and collective phenotypes, both in a proximate and an evolutionary context (
Dalziel et al., 2021;
Guttal and Couzin, 2010).
We will also restrict our discussion to situations in which the deciding collective system is presented with discrete options (
Figure 1). The options may differ from each other on one or more variables, and members of the group may perceive and even interact with all the available options at once, but no individual member of the group should be able to benefit or suffer the consequences from more than one option at any given time. If that condition is not respected, then it is not possible anymore to unambiguously determine the quality of the consensus. This is not to say that this condition is always respected in natural situations—it is not, obviously—but it is desirable in experimental settings to disambiguate the interpretation of the results.
Furthermore, if not respected, it can be difficult to distinguish between opinion averaging and collective decision-making. The latter implies the existence of a mechanism to break the symmetry between the available options, while the former simply calculates the central tendency of the group. When the available options are discretized, opinion averaging will result in the group sitting somewhere between them depending on the balance between the different opinions in the group; collective decision-making, on the other hand, will result in the group sitting at one of the options only or split between them if a consensus is not reached. If the options are not discretized, however, the outputs of opinion averaging and collective decision-making will resemble each other. Note that opinion averaging is often the first step of many collective decision-making processes, but it is then followed by a mechanism to break the symmetry. For instance, the ballot collection during a democratic election is a form of opinion averaging; the majority rule turns it into a consensus by selecting the winning option.
Finally, we will in this manuscript purposely conflate preferences and personal information into the word “opinion” (i.e., the expression of an individual’s choice). Preferences correspond to an individual’s ranking of the available options based on their relative utility. Personal information is the knowledge that has been integrated by an individual. Studies of human systems typically make a distinction between collective decision-making processes that aggregate personal information and those that aggregate preferences. In the first case, the options have similar relative utilities and the opinions are expressed based on the knowledge that each individual has about, for instance, the availability of the options in the environment or their ease of access. In the second case, the relative utilities of the options differ from one individual to another and the opinions reflect that conflict of preferences. In practice, however, individual opinions are rarely purely information- or preference-based. In fact, personal information and preferences are not independent of each other: personal information is interpreted through the prism of preferences (e.g., a piece of information may be disregarded because it conflicts with an individual’s preferences), whereas utility is a function of the information that the individual can collect and integrate (e.g., incomplete information about a product may reduce its perceived utility when compared to an identical product with more accessible information). Therefore, except for extremely controlled experimental conditions, it is difficult to separate practically the effect of personal information from that of preferences (especially in non-human systems), and we will, instead, refer to their combination as the individual’s opinion.
From Condorcet to swarm intelligence: A brief historical perspective
Even with all our self-imposed restrictions, the scientific study of collective decision-making has a long and rich history (
Figure 2). The first studies, which may date back to the Middle Ages, were primarily interested in the statistical properties of various opinion pooling mechanisms and, in particular, their ability to lead to a fair and/or accurate choice (
McLean, 1990). Some of the best examples of these early works are by Marie Jean Antoine Nicolas de Caritat, better known as Marquis of Condorcet. For instance, in his “Essay on the Application of Analysis to the Probability of Majority Decisions” (
de Caritat (Marquis de Condorcet), 1785) published just a few years before the French Revolution, Condorcet showed that the probability of a majority decision to be correct increases with the group size, provided that the voters are individually more often right than wrong. This result—often referred to as Condorcet’s Jury Theorem—helped kickstart the field of
social choice theory which is primarily concerned with understanding how collective decisions in human societies result from combining individual opinions, self-interests, and/or personal well-being (
Arrow, 1963;
Kerr and Tindale, 2004). It has also inspired a large number of studies extending it to special case scenarios (e.g., more than two options) or relaxing some of the unrealistic assumptions of the original theorem (e.g., independence of the votes) (
Kerr and Tindale, 2004).
Condorcet was also amongst the first to formally demonstrate that the implementation of a vote can have significant consequences on its final output. Most famously, the voting paradox that bears his name illustrates a situation where transitive preferences at the individual level can translate into non-transitive preferences at the population level, making it impossible to designate a winning option (
de Caritat (Marquis de Condorcet), 1785). Down’s paradox of voting stated that, as the number of voters increases, the relative influence of each voter on the outcome decreases, possibly leading to a loss of interest in participating in the democratic process (
Downs and Others, 1957). Later, Feddersen and Pesendorfer identified the “swing voter’s curse”—a situation in which indifferent or uninformed individuals are less likely to vote because of their higher likelihood of impacting the election by being the swing vote (
Feddersen and Pesendorfer, 1996). Likewise, strategic voting—a vote that is made in response to the vote of others—can change the properties of judgment aggregation (T.
Feddersen and Pesendorfer, 1999). In other words, voting is a free-rider problem.
That general line of inquiries—looking into opinion pooling mechanisms better adapted to given decision-making scenarios—has had a very successful descent (see, e.g., Christian List’s theory of aggregating judgments (
List, 2012)), with important repercussions in modern political sciences, obviously, but also more generally in the fields of decision science and computer science. Recent research has focused on elaborating new pooling mechanisms—beyond a crude majority—that could yield better collective decisions (
Dietrich and List, 2007;
Hastie and Kameda, 2005;
Hertwig et al., 2019;
Kerr and Tindale, 2004) or guarantee convergence to the truth in networks of influences (
Degroot, 1974;
Golub and Jackson, 2010). This, unsurprisingly, turned out to be a rich and complex challenge in which numerous factors played equally important roles: the statistical structure of the environment (
Herzog et al., 2019), the group composition (
Davis-Stober et al., 2015), the initial diversity of judgments (
Ladha, 1992,
1995;
Shi et al., 2019), the structure of the interaction network (
Becker et al., 2017), or the degree of social influence within the group (
Lorenz et al., 2011)—to name a few. Pooling mechanisms often involve weighing the judgments of the individuals before combining them using external cues such as the individuals’ confidence or their past performance. This resulted in real-world applications in a variety of domains, including medical diagnostics (
Kämmer et al., 2017;
Kurvers et al., 2016), and geopolitical and economic forecasts (
Batchelor and Dua, 1995;
Clemen, 1989;
Hibon and Evgeniou, 2005).
Nearly 200 years after Marquis of Condorcet’s mysterious death in a revolutionary jail (
Crépel, 2001), the then-nascent field of
swarm intelligence started revisiting the question of collective decision-making from a different perspective (
Conradt and Roper, 2005;
Garnier et al., 2007). It put the focus on how collective choice can be achieved in
decentralized systems lacking an explicit mechanism for pooling opinions together (
Camazine, 2001). Until then, most studies considered the pooling mechanism (e.g., democratic voting) as independent of the opinion formation process: first, individuals would form an opinion; and then a centralized process would aggregate these opinions to determine the winning option. However, evidence of collective choices in non-human societies such as ant colonies (
Beckers et al., 1990;
Deneubourg and Goss, 1989), honeybee hives (
Seeley, 2010;
Seeley et al., 1991), cockroach aggregates (
Jeanson and Deneubourg, 2006,
2007), fish schools (
Ward et al., 2008), and bird flocks (
Biro et al., 2006) pushed the development of new research on collective decision-making in decentralized systems.
The central paradigm of swarm intelligence is based on the theory of self-organization: consensus at the level of the group emerges from interactions between its members; interacting members locally align their opinions with each other, allowing for the progressive propagation of a consensus through the population; and when two or more opinions compete with each other in the population, the opinion with the fastest propagation properties (because of, for instance, a higher convincing rate or a larger initial share of supporters) is more likely to win (
Camazine, 2001;
Couzin, 2009;
Couzin et al., 2005;
Garnier et al., 2007). This general principle was identified in pretty much all animal societies, especially in situations where the cognitive abilities of individuals are overwhelmed by the sheer complexity of the information available to them. This is the case, for instance, in foraging ants that can collectively select the shortest path towards a food source out of many possible options, even though no individual ant ever compares them directly (
Garnier et al., 2009;
Goss et al., 1989;
Reid et al., 2011). Likewise, a similar amplification effect also exists during the process of opinion formation in humans (
Moussaïd, 2013).
Over the past 40 years or so, that swarm intelligence perspective has evolved to include more complex scenarios. Originally, it considered that all members of a group were identical or drawn from the same unimodal distribution. This helped simplify the models and their predictions and facilitated the study of the general principles underlying self-organized collective decision-making. Later research, however, showed that diversity in individual behaviors (
Jolles et al., 2020) and sensitivity to social information (
Sasaki et al., 2018) can have dramatic effects on the outcome of the collective process. For instance, individuals with higher physiological needs or with personal knowledge of the locations of resources will be more likely to initiate a collective decision, making them apparent—but de facto—leaders of the group (
Conradt et al., 2009;
Couzin et al., 2011;
Couzin et al., 2005;
Guttal and Couzin, 2011;
Papageorgiou and Farine, 2020;
Sueur, 2012).
This complexification is also illustrated by the increasing use of interaction networks to represent social connections (
Croft et al., 2008;
Farine and Whitehead, 2015;
Proulx et al., 2005;
Sosa et al., 2021). As a first simplification, early models often considered that individuals were influenced by their “neighbors” (e.g., the N closest individuals, or all those located within a certain interaction radius, see for instance
Ballerini et al. (2008);
Couzin et al. (2002)). Recent approaches, in contrast, highlight the existence of privileged social pathways through which information flows between individuals. These ties could be defined by visual perception capabilities (i.e., one interacts with those it can see), or by specific social relationships (friends, peers, family members) (
Moussaïd et al., 2011;
Rosenthal et al., 2015;
Strandburg-Peshkin et al., 2013). Over time, new social ties often appear, and old ones die out, producing a complex and non-stationary network of interactions.
The two general lines of research—social choice theory and swarm intelligence—eventually met each other in the early 2000s to form a new research area that one—or maybe just we?—may call “swarm choice theory.” It was already apparent in Condorcet’s time that some of his original assumptions could not be realistically met. In particular, the assumption that agents form opinions independently of each other is virtually impossible to realize in a system that is, by nature, social. Moreover, the assumption that agents should not be—on average at least—biased toward unfavorable options is often difficult to meet when the information available to the agents is itself biased (for instance, by social or racial prejudice) or when the “better” option is a matter of taste and not of quantifiable outcomes (e.g., fashion choices, political views). In all these cases, Condorcet’s predictions fail more often than not, and new paradigms need to be invented to salvage the so-called “wisdom of the crowd” (
Surowiecki, 2004).
In this context, swarm intelligence provides tools and a theory to understand the dynamics of opinion emergence, spreading, and competition in networks of highly correlated individuals (
O’Bryan et al., 2020). Therefore, it can help explain how information entering such networks can eventually bias an entire population (
Lorenz et al., 2011;
Moussaïd et al., 2015), or how the interaction dynamics within a population can lead to the emergence of more accurate decisions in some cases (
Kao and Couzin, 2014;
Mann, 2018;
Marshall et al., 2019), but also of groupthink and opinion polarization in others (
Hegselmann and Krause, 2002;
Janis, 1982). Social choice theory then allows for evaluating the consequences of a crowd’s dynamics after a collective choice, by comparing its outcome to predictions from optimality and rationality theories. It also allows for determining which—if any—opinion pooling mechanism may help with correcting the negative consequences of crowd dynamics on the quality of the collective choice. For instance, common pooling mechanisms such as the majority or the confidence-weighted majority rules typically fail when most individuals are biased towards the wrong option (
Hastie and Kameda, 2005). Nevertheless, these situations can be detected and dealt with by using, for instance, the “surprisingly popular” pooling rule (
Prelec et al., 2017). This mechanism proposes that the option that is more popular than people predict is selected as the collective outcome (i.e., by asking group members what they think others will choose). Similarly, the “select-crowd strategy” proposes to average only the opinions of the individuals in a crowd who have previously demonstrated their judgment accuracy (
Mannes et al., 2014), thereby combating the decrease in accuracy that large crowds can experience when making difficult decisions with largely inexperienced members (
Galesic et al., 2016). In both cases, a bias in the statistical structure of the judgments can, therefore, be exploited to indicate the correct answer.