The the detection of echo chambers and information bubbles is becoming increasingly relevant in this new era of personalized information and ‘fake news’. However, the behavior of groups of individuals has been researched since Le Bon’s 1896 book ‘The Crowd’ Of crowds, he states that ‘one of their general characteristics was an excessive suggestibility, and we have shown to what an extent suggestions are contagious in every human agglomeration; a fact which explains the rapid turning of the sentiments of a crowd in a definite direction’ (Le Bon, 2009, p. 28). The existence of this phenomenon was demonstrated in studies by Moscovici and Doise who showed that the consensus reached will be most extreme with less cohesive, homogeneous groups [Moscovici, Doise, & Halls, 1994].
Cass Sunstein described these tendencies as The Law of Group Polarization, which states that members of a deliberating group predictably move toward a more extreme point in the direction indicated by the members’ predeliberation tendencies. (Sunstein, 2002, p 176). Sunstein further states that:
- A deliberating group, asked to make a group decision, will shift toward a more extreme point in the direction indicated by the median predeliberation judgment.
- the tendency of individuals who compose a deliberating group, if polled anonymously after discussion, will be to shift toward a more extreme point in the direction indicated by the median predeliberation judgment
- The effect of deliberation is both to decrease variance among group members, as individual differences diminish, and also to produce convergence on a relatively more extreme point among predeliberation judgments
- people are less likely to shift if the direction advocated is being pushed by unfriendly group members; the likelihood of a shift, and its likely size, are increased when people perceive fellow members as friendly, likeable, and similar to them
- there will be depolarization if and when new persuasive arguments are offered that are opposite to the direction initially favored by group members. There is evidence for this phenomenon.
- Excluded by choice or coercion from discussion with others, such groups may become polarized in quite extreme directions, often in part because of group polarization.
Similar social interactions have been modeled in the agent-based simulation community using opinion dynamics, voter and flocking models. In this paper, I attempt to model Sunstein’s statements using agents navigating within a multidimensional information space where the amount of social influence is controlled. The results of these experiments are a set of identifiable behaviors that range from random walks to tight clusters that resemble the polarized groups described by Sunstein and others.
The intuition behind this research is that group polarization appears to reproduce certain aspects of flocking behavior, but in information space, where individuals can hold overlapping opinions across a large numbers of dimensions. In other words, individuals within a certain ‘Social Horizon’ (SH) of each other should be capable of influencing each other’s orientation and speed in that space. The closer the heading and speed, the easier to align completely to a nearby neighbor. If the speed and particular the orientation is not closely aligned, there will not be as much on an opportunity to ‘join the flock’. These three factors – proximity, speed and heading appear sufficient to address Sunstein’s statements from the introduction.
Animal flocking has been shown to represent a form of group cognition [Deneubourg & Goss. 1989] [Petit et. al. 2010]. We chose the Reynolds boids flocking model [Reynolds 1987] as the basis for our model, which was developed to work in any number of dimensions greater than one. We further modified the boids algorithm to have each agent only calculate its next position with respect to the other visible agent’s heading and speed without a collision avoidance term.
N-dimensional position was handled as a set of named variables that could vary continuously on an arbitrary interval similarly to the Opinion Dynamics models of Krause [Hegselmann & Krause, 2002], but extended to multiple dimensions. For this initial work, each ‘social dimension’ was considered equivalent. This allowed the straightforward implementation of distance-based cluster detection using DBSCAN [Ester, et al 1996]. Social distance interactions across dissimilar spaces have been discussed by Bogunia  and Schwammle  and show that this approach can be extended to more sophisticated environments. Since agents in this simulation also have an orientation, n-dimensional heading was handled in a similar way. We developed a platform for interactively exploring the simulation space or performing repeatable experiments in batch mode
Initial experiments were done in 2 dimensions for ease of visualization and understanding. Very rapidly, we were able to see that agent behavior manifested in three phases by varying only the parameter that controlled the ‘social horizon radius’, which is the distance that one agent can ‘see’ another agent. The influence of neighboring agents falls off linearly as a function of distance until the horizon radius is reached. This follows Sunstein’s statement that ‘the likelihood of a shift, and its likely size, are increased when people perceive fellow members as friendly, likeable, and similar to them‘ [pp 181].
For the simulation runs, agents were initialized on a range of (-1.0, 1.0) on each dimension. A reflective barrier was placed at (-2.0, 2.0). This reflects the intuition that many concepts have inherent limits. For example in fashion, a skirt can only be so low or so high [Curran 1999]. The three phases can be seen in figures 1 – 3 below. In each figure, a screenshot of the mature state is shown on the left. On the right are traces of the distance of each agent from the center of the n-dimensional space. These particular simulations took place in 2D for easier visualization in the screenshots.
Figure 1: Zero SH – No social interaction and no emergent behaviors
Figure 2 : Limited SH Radius (0.2) with emergent flocks and rich interaction.
Figure 3: ‘Infinite’ SH (10.0) with strong group polarization
The first phase is determined entirely by the random generation of the agents. They continue along their paths until they encounter the containing barrier and are reflected back in . The resulting chart shows this random behavior and no emergent pattern. The second phase is the richest, characterised by the emergence of ‘flocks’ that can be discriminated using DBSCAN (each color is a cluster, while white is unaffiliated). Interestingly, the flocks tend to orbit near the center of the space. This makes sense, as any agent offering attraction is on average spending most of its time nearer the center of the stage than the edges. The third phase represents a good example of Sunstein’s definitions. All agents become aligned and each agent as well as the average belief become more extreme over time. The only thing that interferes with the polarized group heading off into infinity is the reflective boundary.
To verify that these patterns emerge involving higher dimensions, simulation runs were performed for up to 10 dimensions. The only adjustment that needed to be incorporated is that the social horizon distance is influenced by the number of dimensions. Since distance is the sum of the squares in each dimension, we found that the ‘social radius’ had to be multiplied by the square root of the number of dimensions used to produce the same effect. once appropriately adjusted, the same three phases emerged.
We also examined the effects of having populations with different social horizons. Multiple studies across different disciplines ranging from neurology [Cohen et. al. 2007] to computer-human interaction [Munson & Resnick 2010] have shown that populations often have explorer and exploiter subgroups. In game theory, this is known as the multi-armed bandit problem, which explores how to make decisions using incomplete information [Burnetas & Katehakis 1997]. Does the gambler stay with a particular machine (exploit) or go find a different one (explore). The most effective strategies revolve around a majority exploit/minority explore pattern. In the case of the simulation, 10% of the population were given zero SH, which let them explore the environment unhindered, while the other 90% were given the highest SH, which in prior runs had resulted in the group polarization of figure 3. These values reflect the numbers found in the above studies as well as the percentage of diverse news consumers found by Flaxman, Goel and Rao in their study of weblogs [Flaxman et. al. 2016]
The results of mixing these populations was startling. Although still tightly clustered, the ‘exploit’ group would rarely interact with the simulation boundary and would instead be pulled back towards the center by the presence of the ‘explorers’
Figure 4: Two populations interacting (10% Zero SH and 90% Infinite SH)
DISCUSSION [designing interfaces for populations]
This study shows that it is possible to implement many of the claims of Cass Sunstein’s Law of Group Polarization using a simple flocking agent-based model. By manipulating only the ‘social horizon radius’, behaviors ranging from random to flocking to polarizing group were produced. Surprisingly, the introduction of even a small number of ‘explorers’ with diverse positions in the information space were capable of sufficiently influencing the behavior of the polarized ‘exploiters’ that they would bend back towards the central areas of the information space.
This work also refines the idea of Group Polarization in that polarization need not be linear – it can curve and meander under the influence of other individuals. Indeed, one need only look at the recent switch in regard to Vladimir Putin by American right wing politics to see that this can manifest in reality as well. If influence from diverse sources can change extremely polarized behavior and keep it more ‘centered’, then perhaps the design of our search interfaces should reflect the ability to explore by some users and then in turn use that exploration as a means of influencing more polarized groups. Currently, most work in information retrieval from Search to Social Networks is to provide the most relevant information to the user. This research implies that it may be even more important to provide diverse information.
Deneubourg, Jean-Louis, and Simon Goss. “Collective patterns and decision-making.” Ethology Ecology & Evolution 1.4 (1989): 295-311.
Petit, Odile, and Richard Bon. “Decision-making processes: the case of collective movements.” Behavioural Processes 84.3 (2010): 635-647.
Reynolds, Craig W. “Flocks, herds and schools: A distributed behavioral model.” ACM SIGGRAPH computer graphics 21.4 (1987): 25-34.
Hegselmann, Rainer, and Ulrich Krause. “Opinion dynamics and bounded confidence models, analysis, and simulation.” Journal of Artificial Societies and Social Simulation 5.3 (2002).
Ester, Martin, et al. “A density-based algorithm for discovering clusters in large spatial databases with noise.” Kdd. Vol. 96. No. 34. 1996.
Curran, Louise. “An analysis of cycles in skirt lengths and widths in the UK and Germany, 1954-1990.” Clothing and Textiles Research Journal 17.2 (1999): 65-72.
Cohen, Jonathan D., Samuel M. McClure, and J. Yu Angela. “Should I stay or should I go? How the human brain manages the trade-off between exploitation and exploration.” Philosophical Transactions of the Royal Society of London B: Biological Sciences 362.1481 (2007): 933-942.
Munson, Sean A., and Paul Resnick. “Presenting diverse political opinions: how and how much.” Proceedings of the SIGCHI conference on human factors in computing systems. ACM, 2010.
Burnetas, Apostolos N., and Michael N. Katehakis. “Optimal adaptive policies for Markov decision processes.” Mathematics of Operations Research 22.1 (1997): 222-255.
Flaxman, Seth, Sharad Goel, and Justin Rao. “Filter bubbles, echo chambers, and online news consumption.” Public Opinion Quarterly (2016): nfw006.
Cass R. Sunstein is currently the Robert Walmsley University Professor at Harvard. From 2009 to 2012, he was Administrator of the White House Office of Information and Regulatory Affairs. He is the founder and director of the Program on Behavioral Economics and Public Policy at Harvard Law School.
Relevant flocking and collective decision making papers:
- Collective patterns and decision-making
- Decision-making processes: The case of collective movements
Relevant Sociophysics papers:
- Class A network – all agents have (constrained) visibility to all other agents
- ‘Belief Distance’ is an implementation of Bogunia et al Social Distance from Models of Social Networks based on Social Distance Attachment and Schwammle et al Different topologies for a herding model of opinion. In this model, noise is injected to obtain phase transition, in mine, distance is used)
- Rather than the stable opinion dynamics outcomes from models such as Krause’s ( e.g. Opinion dynamics and bounded confidence models, analysis, and simulation), the value of the opinion may change, but the convergence to a tight cluster does not. So rather than static consensus, we have a dynamic consensus.
- The proximity value can be changed to reflect the fact that “Although the network may have the small world property, searches are usually done locally” Sociophysics
- Funneling (Sociophysics sect 6.5.8, pus my write up) is a future work. It’s a form of dimension reduction, but also allows for things like conspiracy theories (wikipedia information distance paper – Computational fact checking from knowledge networks)
- The flocking model is derived from Reynold’s Boids (Flocks, herds and schools: A distributed behavioral model, using 2 of the three rules:
Try to avoid collisions with other boids (repulsion)
- Attempt to match velocity with neighboring boids
- attempt to stay close to nearby boids
Machine learning to classify agents:
The following are what I consider to be the most pertinent statements in the paper, and a discussion of modelling, measurements and potential implications
In brief, group polarization means that members of a deliberating group predictably move toward a more extreme point in the direction indicated by the members’ predeliberation tendencies. [pp 176]
Note that this statement has two different implications. First, a deliberating group, asked to make a group decision, will shift toward a more extreme point in the direction indicated by the median predeliberation judgment. Second, the tendency of individuals who compose a deliberating group, if polled anonymously after discussion, will be to shift toward a more extreme point in the direction indicated by the median predeliberation judgment. [pp 176]
Notably, groups consisting of individuals with extremist tendencies are more likely to shift, and likely to shift more (a point that bears on the wellsprings of violence and terrorism); the same is true for groups with some kind of salient shared identity (like Republicans, Democrats, and lawyers, but unlike jurors and experimental subjects). When like-minded people are participating in “iterated polarization games” -when they meet regularly, without sustained exposure to competing views- extreme movements are all the more likely. [pp 176]
One of my largest purposes is to cast light on enclave deliberation, a process that I understand to involve deliberation among like-minded people who talk or even live, much of the time, in isolated enclaves. I will urge that enclave deliberation is, simultaneously, a potential danger to social stability, a source of social fragmentation or even violence, and a safeguard against social injustice and unreasonableness [pp 177]
Without a place for enclave deliberation, citizens in the broader public sphere may move in certain directions, even extreme directions, precisely because opposing voices are not heard at all [pp 177]
Though standard, the term “group polarization” is somewhat misleading. It is not meant to suggest that group members will shift to the poles, nor does it refer to an increase in variance among groups, though this may be the ultimate result. Instead the term refers to a predictable shift within a group discussing a case or problem. As the shift occurs, groups, and group members, move and coalesce, not toward the middle of antecedent dispositions, but toward a more extreme position in the direction indicated by those dispositions. The effect of deliberation is both to decrease variance among group members, as individual differences diminish, and also to produce convergence on a relatively more extreme point among predeliberation judgments. [pp 178]
It is possible that when people are making judgments individually, they err on the side of caution, expressing a view in the direction that they really hold, but stating that view cautiously, for fear of seeming extreme. Once other people express supportive views, the relevant inhibition disappears, and people feel free to say what, in a sense, they really believe. There appears to be no direct test of this hypothesis, but it is reasonable to believe that the phenomenon plays a role in group polarization and choice shifts. [pp 180]
First, it matters a great deal whether people consider themselves part of the same social group as the other members; a sense of shared identity will heighten the shift, and a belief that identity is not shared will reduce and possibly eliminate it. Second, deliberating groups will tend to depolarize if they consist of equally opposed subgroups and if members have a degree of flexibility in their positions. [pp 180]
Hence people are less likely to shift if the direction advocated is being pushed by unfriendly group members; the likelihood of a shift, and its likely size, are increased when people perceive fellow members as friendly, likeable, and similar to them. [pp 181]
- This is handled in the model by having a position and heading in the n-dimensional belief space. Two agents may occupy the same space, but unless they are travelling in the same direction or the social influence horizon is very large, there will not be sufficient time to overcome the orientation of the agents (slew rate)
…it has been found to matter whether people think of themselves, antecedently or otherwise, as part of a group having a degree of solidarity. If they think of themselves in this way, group polarization is all the more likely, and it is likely too to be more extreme. Thus when the context emphasizes each person’s membership in the social group engaging in deliberation, polarization increases. [pp 181]
- The model shows this as the ‘tightness’ of the group, which can be described also as the variance of distance or angle measures.
Depolarization and deliberation without shifts. … In fact the persuasive arguments theory implies that there will be depolarization if and when new persuasive arguments are offered that are opposite to the direction initially favored by group members. There is evidence for this phenomenon. [pp 181]
- The model shows something slightly different. As long as there is a sufficient diversity of visible opinion, the polarized flock is influenced back towards the center of the (bounded) belief space
“familiar and long debated issues do not depolarize easily.” With respect to such issues, people are simply less likely to shift at all. And when one or more people in a group know the right answer to a factual question, the group is likely to shift in the direction of accuracy [pp 182]
- For future work. Agents that have associated over a period of time can be more attracted to each other, creating greater inertia and mimicking this effect.
- From Presenting Diverse Political Opinions: How and How Much: In interviews with users of several online political spaces, Stromer-Galley found that those participants sought out diverse opinions and enjoyed the range of opinions they encountered online . A study by the Pew Internet and American Life Project during the 2004 election season found that, overall, Americans were not using the Internet to access only supporting materials . Instead, Internet users were more aware than non-Internet users of a range of political arguments, including those that challenged their own positions and preferences.
- The model divides groups into explorers (diversity seekers) and exploiters (Confirmers and Avoiders). These behave differently with respect to how much they pay attention to their social influence horizons.
Group polarization has particular implications for insulated “outgroups” and (in the extreme case) for the treatment of conspiracies. Recall that polarization increases when group members identify themselves along some salient dimension, and especially when the group is able to define itself by contrast to another group. Outgroups are in this position-of self-contrast to others-by definition. Excluded by choice or coercion from discussion with others, such groups may become polarized in quite extreme directions, often in part because of group polarization. It is for this reason that outgroup members can sometimes be led, or lead themselves, to violent acts [pp 184]
- Note the “salient dimension”
- Anti-belief is designed in, but disabled at this point. Future work
- Exclusion from other groups can be modelled as only disabling intra-group communication “allow interaction” check
The central problem is that widespread error and social fragmentation are likely to result when like-minded people, insulated from others, move in extreme directions simply because of limited argument pools and parochial influences. As an extreme example, consider a system of one-party domination, which stifles dissent in part because it refuses to establish space for the emergence of divergent positions; in this way, it intensifies polarization within the party while also disabling external criticism. [pp 186]
- Domination is modeled here by increasing the radius of social interaction such that all agents are visible to all other agents. This does result in the maximization of polarization.
A certain measure of isolation will, in some cases, be crucial to the development of ideas and approaches that would not otherwise emerge and that deserve a social hearing. [pp 186]
- Limiting the radius of social interaction provides this capability in the model. Low, non-zero values provide conditions for the emergence of individual flocks, identifiable by DBSCAN clustering, which identifies clusters using density measures rather than an a priori determination of the number of clusters to find.
Answering Sunstein’s Questions
If people are shifting their position in order to maintain their reputation and self-conception, before groups that may or may not be representative of the public as a whole, is there any reason to think that deliberation is making things better rather than worse? [pp 187]
- The model implies that visibility between deliberating groups may providing a “restoring force” that brings all groups to a more moderate position that exists between destructive/reflective boundaries (not sure what would happen with “sticky” boundaries). As an aside here, the movement of the lethal boundaries should result in a movement of the average center of the population.
Implications for Design
By contrast, those who believe that “destabilization” is an intrinsic good, or that the status quo contains sufficient injustice that it is worthwhile to incur the risks of encouraging polarization on the part of diverse groups, will, or should, be drawn to a system that enthusiastically promotes insular deliberation within enclaves [pp 191]
- The internet seems in many ways to have evolved into a system that encourages destabilization (disruption) and the creation of many isolated groups. The level of this seems to have become dangerous to the cohesion of society as a whole, where the acceptance of “alternative facts” is now an accepted political reality. Changing that design so that there is more visibility to the wider range of points of view could bring back moderation.
The constraints of time and attention call for limits to heterogeneity; and-a separate point-for good deliberation to take place, some views are properly placed off the table, simply because time is limited and they are so invidious, implausible, or both. This point might seem to create a final conundrum: To know what points of view should be represented in any group deliberation, it is important to have a good sense of the substantive issues involved, indeed a sufficiently good sense as to generate judgments about what points of view must be included and excluded. But if we already know that, why should we not proceed directly to the merits? If we already know that, before deliberation occurs, does deliberation have any point at all? [pp 193]
- It’s not that heterogeneity needs to be limited per se. There does need to be a mechanism that provides sufficient visibility across individuals and groups so that as a whole, society stares reasonably centered. The model shows that flocking can occur across arbitrarily high dimensions, but that the information distance increases as a function of the number of dimensions. Computer-Mediated communication might be able to address this issue by projecting high-dimensional sets of concepts and projecting them into spaces (e.g. self-organizing maps) that can be navigated by individuals and groups of human users. The goal is to recognize and encourage particular types of flocking behaviors while providing enough credible visibility to counter information so that this interaction of flocks of flocks stays within the bounds that support a healthy society.