Notes on Moscovici & Doise’s “Conflict and Consensus”

Conflict and Consensus A General Theory of Collective Decision


  • Serge Moscovici – Ecole des Hautes Etudes en Sciences Sociales, Paris, France
  • Willem Doise – University of Provence – (Aix-Marseille I)

My Takeaway:

  • Group cognition is a function of heading, velocity, and dimension reduction in belief/value space. I believe that this is because we use structures in our brain that originally evolved to coordinate physical group interaction, such as herding, flocking and schooling.
  • Individual cognition (when we’re alone) is different, but the boundaries are very fuzzy, since reading, architecture, and many other activities are inherently a form of group interaction. M&D describe group interaction as a form of hypnosis.
  • Groups in free discussion reduce dimensions as a mechanism to achieve agreement and polarization. Physical and procedural rules can reduce dimension reduction, which leads to agreement and compromise. This implies that there may be a form of ‘human-centered’ dimension reduction that is based variance in sentiment about topics. Meaningful self-organizing maps can probably be built using this intuition.
  • Norms are the area that the group points to. It is a function of alignment and velocity, so it has a distribution that is related to the group’s coherence. Closed and open societies emerge from this relationship
  • Social identity theory plays a role, in that there is some kind of repulsion effect between groups that are pointing (and moving?) away from each other.
  • Structured diversity equals resilience. Think of the difference between a mob and and organized soldiers. Or the difference between a herd and a stampede.


  • Thus they bring us closer to a different conception of the role of the group. This is, that it mobilizes the intellectual and affective potentialities of each one of its members by making them participate in a collective action, not in order to increase cohesion, but to allow them to breach together the barrier of norms from which, if faced alone, they would recoil. (Page 41): 
  • This does not warrant classing the group with the crowd, which is prey to over-enthusiasm and violence [p40]
  • If we wish to understand the nature of groups, it seems advisable to concentrate on the way they change , and in the way that they change individuals, rather than on their ability to aggregate individuals as part of a whole [p42]
  • …the danger lies less in anomie or disorder than in routine and apathy [p 42]
  • Acts of decision, as well as acts of consenting, are above all acts of participation. For various reasons their value springs from the bond that they create between individuals and from the impression each one receives that he counts in the eyes of everybody as soon as he begins to participate. [p47]
  • Consequently much effort is expended to become a member of an association, to be elected to a committee, to have the right to meet together and communicate with certain people, and so on.
    • But what if that effort becomes low or frictionless as we find online? And what about being an anonymous part of a group?
  • For the collectivity it is imperative to overcome its consuming tendency to impose a uniformity upon individuals and encourage their inclination to follow the law of least effort and obey. It is true that by causing them to abandon their personal arguments and interests, the collectivity ensures, for its own benefit, that decisions are made easy. But this is at the price of a passivity that deprives it of the energy and active initiative of individuals. They have to struggle against themselves in order to form a living entity, and the entity has to struggle against itself in order to be made up of individuals. This is in fact the necessity noted by Pascal in his time: ‘The multitude that is not reduced to a unity is confusion; the unity that does not depend upon the multitude is tyranny.’ [p 50]
  • Depth psychology
  • How and why this occurs emerges from a fine study by Freedman and Fraser (1966), the American psychologists, which deals with a familiar situation. We see volunteers going from door to door to get householders to sign a petition whose purpose was ‘to preserve the beauty of California’. Naturally, almost everyone signed it, since the beauty of the countryside, like child health or world peace, is a theme that strikes a chord. A fortnight later, these same people were asked to put up a board on their lawn: ‘Drive carefully’. Almost half agreed to do so, whereas the figure would have been much lower if they had not signed the petition. In fact, they had made the first step and then took part in an action. The participants deemed themselves infused with civic spirit, and loyal to their principles [p 52]
    • I think this is a way to reduce dimensions and as such reduce distance to make it easier to follow.
    • I’m wondering if there is some kind of sentiment analysis that can tell how much mutual support is going on in a community, and if it’s reactionary or progressive. This would be in addition to the amplitude and variance measures for beliefs in the community.
  • This tension arises less from the content of the argument or the difference that exists between them than because the disagreement manifests itself through someone else who has to be faced up to [p 55]
    • So what are the implications of CMC, where the ‘distance’ can be moderated? The spectrum can run from video chat to text chat to forum, to search results. What’s the sweet, frictionless spot that creates stapedes?
  • Thus, throughout controversies and counter-arguments, which resemble body-blows, the members of the group covertly exert upon one another an influence that emphasizes what can draw them closer. Between them can be observed a synchronized, imitative process which transforms every word into a signal, every gesture into a model, and every piece of information into an argument. All the forms of the rhetoric of mind and body become maneuvers through which the distances between the participants grow smaller and the frictions between them are deadened. [p 55]
  • But most frequently, by the very fact of being called upon to discuss, each individual feels himself to be an actor in the ritual and a member of the group instituting it. In this way, group cohesion is reinforced at regular intervals. [p57]
  • Numerous studies justify the assertion that people are more disposed to start out on that painful intellectual and affective path when they have to deal with opposing arguments coming from several sources rather than from one source alone. It is as if a group speaking with several voices were more conspicuous and offered greater room for maneuver than a group with only one voice.
    • Higher dimensions == less constraint? And yet, later in the book (p 180 or so), M&D show that these extra dimensions collapse in open discussion and are maintained only in structured environments.
  • In contrast to the consensual form, we can understand that the normalized form, which gives only a subordinate role to some members of the group, creates a certain distance, causing the group not to loom so large in the life and consciousness of individuals, so that in the end it appears strange and abstract. Immediately the participants become detached from one another, and instead of being actors become mere spectators in the discussions. [p 62]
  • Since controversy is in proportion to the participation of members, few conflicts are observed, unless it be in the ranks of the leaders. It is as if individuals tended to minimize their ‘investment’ and their attachment to the collectivity, remaining aloof from intrigues, and, so far as possible, conforming to the opinions and actions that were suggested to them. [p 62]
    • Is this what happens on forums and low-participation social systems like comments?
  • Although the one satisfies the need to participate in a more intense way, and one of which people cannot be deprived for long, the other at least provides a substitute for it. [p 62]
    • This could be another affordance of the system. Some way to grade participation and discussion as a threshold of entering?
  • There can scarcely be any doubt that, by meeting and talking together, a group’s members bring out the values predominant among them, ones to which they are attached. In some way their substance is given shape, so that what we hold in common, but is concealed, becomes manifest. [p 65]
  • …consensual participation probably has the effect of raising the level of collective involvement, whereas normative participation lowers it. One may conclude that the former polarizes the decisions leading to consensus, whereas the latter modifies them. The former causes the members of the group to converge on the pole of values already shared by them before they took part in the decision, and the latter towards the just mean. [p 65]
  • Thus, as a hypothesis concerning the polarization of groups, it may be concluded that the consensus reached will be the more extreme:
    (a) when individuals participate more directly in the discussions;
    (b) when the differences between them, their knowledge and their opinions are more marked;
    (c) when what is at stake in the discussions is perceived by them as valuable. [p 67]

    • What interests me here is (b). I think that there are several measures of difference that matter
      1. The information distance, as determined by amplitude and variance. There is a difference between agreement about two extreme positions that are broadly based and two narrow positions.
      2. The heading alignment. It is possible to arrive at a position from different directions. Is it easier if the headings are similar?
      3. Velocity. Is there a situation where one piece of information is held fixed and everything else is allowed to change? (e.g. The Leader is always right, though the position is in constant flux [Trump supporters know Trump lies. They just don’t care.])
      4. Exogenous visibility. What does the information horizon look like to the discussants? Do they feel as though they are relatively close or far apart? The VI/Emacs disagreements seem both vast and trivial, depending on framing, for example.
  • Plainly, there is no halo effect on questions that are not included in it (the discussion)[p 69]
    • So in emergent groups, what is the discussion? Or do we look for polarizing behavior and infer the point of discussion from that? I think that this implies axis on a dimension-reduced map that might make sense. 
  • we assumed that where discussion had created tension, shifts in the direction of a consensus should be more frequent. To verify this, the distance was measured between the two individuals whose opinions diverged most before the beginning of the discussion. A distance of 1 meant that these two opinions were separated by one point on a seven-point attitude scale. The opinions of the others, whether identical or not among themselves, were located between those of the two individuals who differed most. In the same way a distance of 6 meant that one of the individuals in the group was located at the favourable pole and another at the unfavourable pole. Thus they were opposites; the opinions of the rest were distributed between these poles. It is here, where conflict was greatest, that the maximum polarization should be recorded. In fact, the shifts towards an extreme consensus turned out to be more frequent in the groups when the gap was more than three points than when it was below that figure. [p 69]
  • The finding was simple: the common choices were much more extreme in the groups of five than in those of four, which themselves were more extreme than those in the groups of three. Moreover, they polarized more when they engaged in discussion among themselves than when they proceeded to a silent exchange of notes [p 70]
  • The authors of this study therefore varied the degree of cohesion in the groups formed in their laboratory, whose task was to reach an agreement on the risks to be recommended to the fictitious persons of the questionnaire with which we are now very familiar. The results obtained were in conformity with expectations. It turned out that groups having less cohesion recommended daring options, and groups having more cohesion prudent ones. According to the former groups, the fictitious persons would jump at the chance of changing their job and lifestyle; according to the latter groups, they would be content with their present lot. At the same time it was discovered that groups conscious of their cohesion were little subject to tensions and contradictions; this means that their members showed more esteem for their group and desired more strongly to be together than did members of groups possessing less cohesion. They also declared that agreement was reached with their fellows in greater personal intimacy and in a more favourable atmosphere. These are indications that they have done everything to maintain harmony and minimize the differences between them by avoiding factors leading to discord. In short, as the long-standing theory of Festinger (1950) had predicted, cohesion increases the pressure to conform and leads to the search for a compromise in the group[p 73]
    • In reading this, I think that there may be a pattern where large, diverse groups split into progressively smaller, more cohesive groups, each on their own trajectory. An example of this could be the pattern of schism (and to a lesser degree union) in Christianity
  • Clearly, by favouring divergence, and then debate, through the heterogeneous nature of individuals, through their belonging to different professions, through the distance between individual positions, through a lesser cohesiveness in groups or increased trust among their members, consensus is polarized. Moreover, is it not characteristic of such a consensus for common choices not to be decided in advance by a majority rule or compromise, but discovered during adequate discussion? With this as a basis they are rooted in the collectivity as much as in individuals. This is why those who meet together have an interest in not resembling one another. And yet it is true that birds of a feather flock together. All our collective relationships hinge on this paradox. [p 76]
    • Is this a manifestation of explore/exploit? I think so.
  • Thus it is knowledge gleaned from several sources that fuels discussion among them. They are the cornerstones of a well-informed society, a collective organism that is endowed with the power of thought. But the organism shares out among individuals the task of selecting and exploiting the various kinds of knowledge, as well as the job of imparting meaning to words (Putnam, 1979). [p 76]
    • Looks like the authors may think this too
  • In half the groups all their members listened to the proofs in the same order; in the other half, each member listened to them set out in a special order that differed for each member. The first set of information was homogeneous, the second heterogeneous. Moreover, twelve juries listened to proofs that inculpated the accused, and the twelve others to proofs that exculpated him. According to the usual procedure, after listening in court to the facts presented, the jurors assessed separately the degree of guilt of the accused. Then, meeting together as a jury, they discussed the case before evaluating once more separately the degree of guilt. Here we are very close to a real life situation; hence the great significance of the findings.The following is what emerged: consultation together, yet again, led to more decisive verdicts. The difference was even more marked in the groups where each juror heard the proofs in a different order than in those which listened to them in the same order. In other words, when the task of cognition is divided up, the groups polarize more than when the task is uniform. One consequence among others is the following. It is often recommended that jurors should be selected from people whose social origins and intellectual training are as diverse as possible, that is, based on reality, in order to ensure fairer verdicts. The suspicion is that in this way they may be either more clement or more severe. In any case, the analysis of the discussions themselves showed that those jurors who had listened to the proofs presented in a different order mentioned a wider variety of facts than did the others, particularly towards the end of their discussion. [p 77]
    • This is near the core of the Precision and Recall Considered Harmful argument.
  • Showing the relationship that exists between , on the one hand, the conflict of opinion and differences in information and, on the other , the eyeball confrontations that lead to consensus. [p 79]
    • There was a presentation at Collective Intelligence 2017 that talked about how the ordering of results would affect the ‘quality’ of downloaded  (vs ‘liked’) items. Random ordering (with no visible rating) of results with no rating provided the most consistent results. Ordering based on visible ratings led to first-mover cascades, regardless of ‘quality’. Ratings and order do seem to behave in some ways for proxies for ‘eyeball confrontations’?
  • The mere presence of other people already produces a movement in this direction. It is hardly surprising that, through looking at and listening to them, one becomes a participant in the dialogue, engaging within oneself in one of those imaginary conversations with which we are all familiar. This is sufficient to spark off a ‘fictitious polemic’ with our friends or superiors, in which we argue with them, and which on occasion leads us to modify our attitudes or choices. [p 80]
    • I think forum lurking is an example of this, though we may seek forums where our imaginary conversations are in line with the crowd.
  • Hannah Arendt’s take: The power of judgment rests on a potential agreement with others, and the thinking process which is active in judging something is not, like the thought process of our reasoning, a dialogue between me and myself, but finds itself, always and primarily, even if I am quite alone in making up my mind, in an anticipated communication with others with whom I know I must finally come to some agreement [ p 80]
  • The conflicts or differences between members of the group are normally resolved by convergence towards an extreme position. Yet, depending on whether the discussion is public or private, or the dialogue exterior or interior, the convergence will be more, or less, close to that position. In other words, discussion, in its current meaning, depending on whether the individuals involved are active or passive, determines the extent to which the decision will become polarized. [p 81]
    • The book doesn’t cover CMC discussion, but the following two papers appear to perform similar experiments to the Moscovici work
  • Group and computer-mediated discussion effects in risk decision making
    • Managers individually and in 3-person groups made multiattribute risk choices (two investment alternatives, each with multiple outcomes). Two group decisions were reached during face-to-face discussion, and two were reached during (real-time) computer-mediated discussion. In comparison with prediscussion individual preferences, groups’ multiattribute risk choices and attitudes after face-to-face discussion were risk averse for gains and risk seeking for losses, a tendency predicted by prospect theory and consistent with choice shift and other group extremitization research. By contrast, group decisions during computer-mediated discussion did not shift in the direction of prospect theory predictions. The results are consistent with persuasive-arguments theory, in that computer-mediated discussion contained less argumentation than face-to-face discussion. Social decision schemes were used to evaluate alternative assumptions about the group process. A “(prospect-theory) norm-wins” decision scheme described group choice well in the face-to-face discussion condition, but not in the computer-mediated discussion condition. Another decision scheme, first-advocate wins, which described choices well in both face-to-face and computer-mediated discussions, was explored in a discussion of the role of communication in group decision making.
  • Group Polarization and Computer-Mediated Communication
    • Group polarization is the tendency of people to become more extreme in their thinking following group discussion. It may be beneficial to some, but detrimental to other, organizational decisions. This study examines how computer-mediated communication (CMC) may be associated with group polarization. Two laboratory experiments were carried out. The first experiment, conducted in an identified setting, demonstrated that removal of verbal cues might not have reduced social presence sufficiently to impact group polarization, but removal of visual cues might have reduced social presence sufficiently to raise group polarization. Besides confirming the results of the first experiment, the second experiment showed that the provision of anonymity might also have reduced social presence sufficiently to raise group polarization. Analyses of process data from both experiments indicated that the reduction in social presence might have increased group polarization by causing people to generate more novel arguments and engage in more one-upmanship behavior. Collectively, process and outcome data from both experiments reveal how group polarization might be affected by level of social presence. Specifically, group discussion carried out in an unsupported setting or an identified face-to-face CMC setting tends to result in weaker group polarization. Conversely, group discussion conducted in an anonymous face-to-face CMC setting or a dispersed CMC setting (with or without anonymity) tends to lead to stronger group polarization. Implications of these results for further research and practice are provided
  • We would have, on the one hand, a mimetic sociability, and, on the other, a catharticsociability. But once more this is an antimony that depends upon circumstances and upon human nature. If we mention here both lines of thinking it is not in order to plead for one rather than the other, but to put both in perspective. [p 92]
  • Ratio decidendi [p 95]
  • At the same time, the more precise the information, the less the field is left free for differences and individual positions. Gradually these are supplanted by collective positions in the consciousness of group members. If the members continue for long enough, the consensus approximates to these values, just as a house under construction does to the architect’s plan. [p 97]
    • I think that I see this as a dimension reduction issue. Too many dimensions, and the distances are too great to come to a consensus, average or extreme. But some dimensions have very little variability, and can be discarded. Some dimensions can be placed outside of the scope of the discussion while others are included by mutual consent. The process of interactive dimension reduction continues until there is enough range of opinion across a sufficiently small set of dimensions that it is possible for a group opinion to emerge. The qualities would be different for different groups – humans, AI, or genes.
  • It justifies our emphasizing how obsolete are the distinctions between factual and value judgments, the one exercising an informative influence, and the other a normative influence. Yet others continue to adhere to these distinctions. [p 97]
  • Each time the assessment is arrived at by ordering the terms on a scale, one of whose poles has in our eyes greater importance than the other. It is in relation to this pole that we place persons, things or ideas. [p 98]
    • This is what I was discussing above. It should be possible to determine what these poles are, and create maps using them. These maps will have utility, because they reflect what is important in the discussion.
    • A second issue is to be able to show the pattern where what is important changes. A timeline of pole eigenvectors might be helpful.
  • In a social environment, as soon as this hierarchy becomes explicit, individuals and groups clearly move towards the dominant pole. They seek to become more than they were, and this more so than others: more loyal, more courageous, more tolerant, more patriotic, more modern, and so on. This occurs particularly in novel circumstances, where experience does not relativize values or the image individuals wish to have of themselves. [p 98]
    • So, what does explicit mean here?
  • This is most certainly very apparent nowadays, where the value assigned to novelty, to being avant-garde, to the fact of being different, is very high. [p 98]
    • I think this is the motion part that leads to flocking and other dynamic behavior (e.g. fashion trends). Novelty is always attractive, because as animals that had to hunt and gather, we understand at a genetic level that stasis means that we starve.
  • the normative hypothesis of the theory: the tendency defined by the dominant values and attitudes is accentuated during the discussions, meetings, etc., and determines the directional shift of the decisions that lead to group consensus. [p 98]
  • To sum up: it may seem strange that groups spontaneously swing away from the just mean and the conformity they should adhere to. But they do not do so regardless of the direction, which is towards the norm to which they all adhere. This is why one can scarcely ask whether a consensus is going in the right or the wrong direction, without asking on what basis it has been established and by whom. Stated in statistical terms, this hypothesis predicts that the mean of the choices on which the group members reach agreement is closer to the dominant pole of its scale of values than the mean of the initial choices made by each one of them separately. [p 99]
  • In many respects this hypothesis is the most important one. It indicates how greatly the direction taken by collective opinions and judgements is predetermined, no matter what one does. Thus they are predetermined by the store of previous knowledge and values, and up to a certain point by the collective memory that all share before they meet, and which are all ingrained in them. [p 99]
    • This is the inertia of the group moving across belief (value????) space. And this is why the flocking algorithm, based only on heading and velocity is appropriate.
  • risky shift
  • they demonstrated this in a very simple way. On the one hand, they devised a questionnaire with choice dilemmas analogous to that used by the American social psychologists. Four dilemmas brought into play risk values; four others called for prudence values. But they changed the method of answering by using – as we did – a graduated seven-point scale. This read as follows: 1: strongly recommend x, the risky solution; up to 7: strongly recommend the prudent solution; with 4 as the neutral point at which both solutions appear of equal value.
  • The scale provides a measure of the tendency of the group, indicating unambiguously whether the average of the attitudes of its members at the beginning was located on the side of prudence or of risk. In order to verify the hypothesis, consensuses must be polarized in the direction of the initial values prevailing before the discussion, that is, they should not go beyond the neutral point, crossing the invisible Rubicon of risk towards prudence, or vice versa. The answer can therefore easily be given, since this neutral point expresses indecision or psychological indifference. It is clear that in most cases the groups have polarized, if one makes the comparison between the consensuses or final decisions and the initial decisions. Very rarely did they go beyond this neutral point in the opposite direction to that which their members had tended at the outset. If these members were bold, the shift took place in the direction of risk, and if they were prudent at the beginning, they became even more so. [p 101 -102]
  • Gouge and Fraser (1972) instead of choice dilemmas, proposed to the groups that they debate a great variety of problems ranging from drugs to sexuality, and including racism, suicide, etc. With one single exception, consensus accentuated the initial tendency of attitudes and judgements. Those propositions about which participants were already in agreement separately secured even greater agreement after discussion. Those that met with moderate agreement from individuals separately produced a more extreme agreement when they assembled in a group. [p 102]
    • There is a selection of the dimension(s) that the discussion will take place over.
    • There has to be a level of agreement along those dimensions
    • Closely aligned dimensions are therefore more likely to be in agreement, while further ones are less likely, since the ‘motion’ has less (implicit?) correlation.
    • Collapsing dimensions makes for easier discussion. If everything could be collapsed to one dimension, then it’s trivial (Arednt suggests that this is what totalitarianism is)
    • In the absence of external influence, with a sufficiently small number of dimensions, direction stays fixed, though I’m not sure about velocity. But this is echo chamber/stampede space
    • Diversity can be the presence of different headings, opposing velocity or additional dimensions (enlarging the information horizon)
  • depending on whether individuals are nearer or further away from the dominant pole of the scale, things proceed differently. When nearer to it, the extremists maintain their position, shifting less than do the moderates. This arises because the extremists can move only in a direction running counter to the norms, which is an eventuality ruled out, whereas the moderates can shift closer to this pole. As regards the other pole, it is the extremists who change more than do the moderates (p <-.001). They are comparatively more numerous than the latter (70 per cent as against 59 per cent) in linking up with the predominant norm in the population. Moreover, their greater distance from the norm has the result that after the discussion not only do they change in greater proportion, but also this change occurs to a significant degree. [p 104]
    • This implies that there is a physics model with respect to normative poles, though it may not fall off with distance.
  • … to establish, on the one hand, the existence of a positive correlation between the average of individual positions and the shift towards the mean of positions around which a consensus is formed, and, on the other hand, the reduction in variance between the different positions after discussion in groups. [p 106]
    • echochambertest My model, All Exploit, stampede settings
  • polarization depended not upon the inclination of individuals to take risks or to remain prudent, but indeed on the form in which dilemmas are couched and debated, which causes the balance to swing one way or another. [p 106]
    • This is an example of the presentation affecting the outcome. If this were a gatekeeperissue, the information presented would have been different
  • Cvetkovitch and Baumgardner show that “group interaction will increase the participants’ involvement with the discussed topic and eventuate in individual opinion and group consensus that is more extreme than pre-discussion attitude. Additionally, the direction of polarization will be towards the naturally occurring majority opinion of the salient reference group and not toward the average attitude within the discussion groups. (1973: 161)” [p 107]
  • Main and Walker (1973) noted that in this respect the decisions were more liberal when the judges decided as a body (55 per cent as against 45 per cent). Knowing that only a minority of decisions taken by a judge presiding alone were of a liberal kind, the authors hypothesized that judges nevertheless had a liberal code of values. When they decided alone, the pressure of anti-liberal public opinion led them to a compromise. On the other hand, when they judged collegially their personal values came out and became more radical during discussion with their colleagues, who were of the same persuasion. [p 111]
    • A thought about how interacting with different groups with different norms might help reduce polarization. The flip side of this is that social media allows us to continually be present in a group online. We don’t visit in the same way as going to a meeting, social hour, gathering of friends, etc.
  • This is tantamount to stating that the social universe resembles the organic universe of Aristotle, in which there can be distinguished a centre and a periphery, a top and a bottom, and a high and a low, rather than the mechanical universe of Newton, homogeneous and lacking any one favoured direction. Without wasting words, we may state that in decision making there is no tabula rasa, any more than there are many decisions that are disputed once they have been taken. [p 113]
  • …consensus polarized in the direction of emerging norms [p 114]
    • Are norms poles that have a position and velocity in belief space? Or are they a manifestation of the group behavior, sort of the position of the average future center (position and variance?) of the group. In other words, do norms have an attraction or are they an implicitly agreed on, emergent, set of beliefs that exist at a certain time? And along these lines, are there patterns that persist over different time spans? I would bet that a circling flock has a centroid of (persistent beliefs), while a stampede doesn’t. This ties back to Arednt’s description of totalitarianism and terror where change is the only constant.
  • On the whole here we are looking at, broadly sketched out, the picture of what must occur when a problem evokes a large-scale movement of opinion. People participate in the debate frequently and with intensity. The series of decisions leading to consensus polarizes towards the norm that is emerging and, by this very fact, emphasizes it. Thus these decisions cause the norm to crystallize and facilitate its being embraced fully by each individual, who feels himself a little its creator. Therefore no coercion or forced consensus should enter into it. [p 117]
    • Support for the idea that the norms are not a pole, but a projection of the future?
  • Attitude polarization, familiarization and group process
  • What happened where a feminist or anti-feminist confederate was present? Of course both were confronting an attitude that had crystallized, had become solidly fixed, and was almost a cultural cliche. The feminist confederate was no longer proposing anything new, but was defending what had become a norm and his or her influence was reinforcing conformity, whereas the anti-feminist confederate seemed to be utterly conservative, a reactionary deviant. Upon examining the data, it was found that their influence had little room in which to be exerted, and that it was weak. Thus the feminist confederates succeeded in polarizing somewhat during the discussion, but to a significant degree (F = 6.56;p < .01), the consensus. On the other hand, the confederate defending an anti-feminist position brought about no reaction, as if this was already ruled out (see Table 5.4). This is why one can no longer observe the former bi-polarization, when the discussions on the status of women set pro-feminists against their adversaries. At any rate the heated atmosphere had cooled down. The researchers noted that there were fewer arguments, and that the discussions were flat and unenthusiastic. An air of nostalgia hung over the groups, who seemed to be asking themselves, ‘But where are the debates of yesteryear?’, just as the poet Villon had once asked, ‘Where are the snows of yesteryear?’ They knew they were waging a fight that had been won by others quite a time ago. [p 120]
    • This would be the old study, where norms are emerging (beliefs in collision): UnstableFlockFormation This would be stable, evolving norms: StableFlock And this would be something like a fixed ideology FixedIdeologyStampede
    • Here’s some charts of ideology in Congress. Picture links to article. The variance is interesting – it implies in the chart on the left that democrats are becoming less diverse, while republicans seem to be breaking into sub-populations(?). polarization
  • Inevitably we will end up by acknowledging the place of values in a world of information. Indeed the problem is to know which items of information to use ‘and which to discard, in order to arrive at a particular agreement. [p 122]
    • To restate, how to perform manifold reduction from a high dimensional, incomprehensible problem to something that is a more manageable size. This can include combining dimensions, deleting dimensions and synthesizing new dimensions that may or may not have a direct connection to the problem but seem relevant (Blindly following a leader, for example).
  • We may say that values are their vertical and horizontal coordinates: Even if they are not rational, they make reason possible, reason which for us has – and we must not forget it- the meaning of a value or norm, the highest norm to which our society pays homage. Hence the requirement that is emphasized by two specialists in decision-making; it is ‘a theory of rational consensus and commitment when, in fact there is a dissensus (Lehrer and Wagner, 1982: 4). To fulfil this need, such a theory, as we have demonstrated, must establish a relationship between these ideas.[p 122]
    • Self-organizing value maps, with axis based on dissensus measures. I think this is what I’m aiming for. And I think that dissensus could be measured by looking for the broadest range of sentiment applied to words, phrases or entities. These axis may be organizable using betweenness centrality measures that keep like axis together.
  • …certain aspects of a situation that bear no relationship to one another, such as the dimensions of a room and the decisions taken in it, that is, aspects deemed to be ancillary and which apparently should not be significant, may in reality be determining factors. In other words, what one considers to be a factor of the world external to social relationships has indeed an action within them. [p 130]
    • Design matters in all kinds of ways, and can affect the outcome and quality of the result. Consider polling – focus group, personal home interview, phone, online. What kind of bias do these modalities introduce? There was more detail on p 131 as well
  • In the case where different opinions can be freely expressed, discussion allows each individual better to defend his own viewpoint and to become more involved in the activity of the group. Thus we expected that the consensus would stress the dominant tendency among its members – in short, be polarized. On the other hand, when the participants placed a distance between one another and paid attention to the manner in which they arrived at a decision, their attention was concentrated upon positional differences. The discussion of the latter could not involve them greatly. Moreover, they had no means of justifying or forcibly making their position prevail, and thus were thrown back on resolving their differences by a compromise. This is indeed what we observed. Consequently attention to rules of procedure, which direct discussion towards information regarding the responses, leads towards a decision of ‘the just mean’. Discussion directed towards content produces the opposite effect. [ p 136]
    • This makes me a little nervous about using Pro Publica congressional data, since the law is very process oriented. Still, the body does seem to be polarizing, and potentially in different ways. Republicans are moving to the right and also disrupting process. Democrats appear to be moving less and have been more focused on ‘standard procedure’. Something to consider is if this is a function of being the opposition party of the party in power. The incentive when in power is to do things, which may require more compromise, as opposed to being the opposition party, which is almost by definition, uncompromising.
  • Imposing time limits on discussions also leads to compromise, while having open-ended discussions tend to polarize. The time constraint acts as a limiter of possible options? [p 136-137]
  • …groups that had to deal with information according to a set method, following directions, took compromise decisions. By contrast, with groups who could deal with the information without being subject to any constraints, the decisions were more extreme than the individual decisions. In principle we have here a confirmation of what we had always supposed to be the case: a normalized form of participation, which involves individuals less, leads to a moderate decision[p 138]
  • [ p 143], M&D discuss how charismatic leaders can pull a group towards more extreme decisions while a more constrained process of interaction leads to compromise. This can be mapped to gatekeeper (the information presented) and UI, the charisma of the person, and the lack of constraint on the discussion. UIs can be charismatic or dull, wide ranging or limiting. In the same way that the shape and texture of the room are subconscious contributors to the discussion, the UI and IR systems shape and frame the human interaction. To look into this, we need to build (or find) a study that supports some kind of chat interaction that follows not only the discussants interactions with each other, but their interaction with the IR system as they look for facts that support their points. Does constraining the available information affect the outcome of the decision? Does it still polarize in the same way? I could expect, for example, in a discussion about risk, that being able to find different information about the likelihood of a small business to succeed were changed from 10% to 50% or 1%, that the group and individual consensus would be different. Similarly, a more constrained UI could result in the user interaction resulting in more compromise or polarization independently of the search activities of the users during the discussion.
  • It’s important to understand what it means when a computer is mediating a discussion. In many respects it is acting as the leader of the discussion, based on ruled that it has been programmed to follow. For example, ranking comments by karma has a dramatic effect on the content of the discussion, since it insures that only the popular posts are given priority.. So even if a forum is moderated by a human, in reality it is co-moderated by the human and the mechanism.
    • Something like the plane landing problem [p 143-144] might be a good model Though instead the problem could be updated, with specific sets of information made available to the searchers.  A Google CSE pointing at one of a set of corpora could do this, plus a chat UI. A single page app that supported both would be nice for monitoring all actions.
    • In their discussion of open and closed groups, I am struck by how much this also looks like explore/exploit. A closed group exploits its current conformation and its relationships against other groups. There are elements that can anchor such groups such as location and race, since these are visible to all and not easy to change. Social identity says that opposition is a very unifying characteristic. But that only works when there is something to oppose. The ideal explore configuration is an even distribution across the belief space, which makes for an amorphous target. Is the anti-intellectual, anti-elite stance a way of finding a frame to oppose explorers? And once that sets up on one side, is it reflected by the explorers as individuals (stay away, we don’t want your kind here) Or, like Chris Arnade, do they seek it out?
    • But because of System Trust, the relationship that we have with our computer mediated channels of indirect communication (Search/IR) is different. If the search returns results that are subjectively true, then there is no reason to believe that there is information outside of the ‘closed community beliefs’
    • There is a difference between the decision making of crowds of individuals (Wisdom of Crowds) and groups. It is possible to make an individual behave like the member of a group though, by providing visibility to upvotes and downvotes via a UI. Can a member of a group be convinced to act like an individual? Is PageRank an example of this?
  • By causing the majority to converge towards a social representation, the multiplicity of decisions that lead to a consensus do more than draw viewpoints closer: they initiate or reinforce social ties. Beyond the specific dilemmas that each decision resolves, they correspond to this general aim. They produce a mass effect in the network of groups that choose and discuss, creating and re-creating the bonds in our society by a common action, just as at one time public opinion originated in the market-places and cafes, and from drawing-room conversations. It is the surplus value that we extract from this task of collective decision-making, the diversity and multiplicity of which have reached so high a level that it has become a profession -we speak of decision-makers – and a significant factor in our social and moral world. [p 174]
    • Is community building inherently an act of dimension reduction? We find commonalities and focus on those, while excluding other areas. It’s not necessarily about agree/disagree, but more like areas that we can create norms of behavior in. It’s easier to create norms in homogeneous, closed cultures, and harder in heterogeneous cultures. But though homogeneous cultures may be faster to respond, they are also less resilient. I’m thinking in particular of the Aspen, or any plant that reproduces asexually. The there is an initial advantage, but if conditions change, the plant goes extinct quickly.
  • The socio-cognitive conflict inherent in any decision taken in common combines together two permanent tendencies. The one aims at maintaining existing uniformity and agreement, the other at changing them by imparting an original form to things and ideas. The choices that are made usually express a balance of forces between the two because, without any element of novelty, they are mere stereotypes or ritual, and, without a dose of conformity, they become fancies and fluctuations that lead to disorder. It is of real theoretical interest to recognize at work in the socio-cognitive conflict a dual process of social thought. It can only be dual, in.view of the opposing functions that it fulfils and of the simultaneous use it makes of divergent and convergent thinking, the one the badge of innovation and the other of uniformity [p 174]
    • This is a very good example of the explore/exploit condition as it relates to social cognition. The same for sea turtles and people
  • To resolve the conflict by eliminating convergent thinking would be to abandon discussion and any choice made in common. To resolve the conflict by censoring divergent thinking would condemn participants to routine, to stereotyping, to what is termed ‘groupthink’. On the other hand, to negotiate this conflict, which is both social and cognitive, is an arduous task. [p 175]
  • The effects of a normative intervention on group decision-making performance
    • A space ship having crashed on the moon, a team of astronauts has to cover a distance of some 300 kilometres in order to reach the spot where they have a rendezvous with another team. Before embarking on this perilous undertaking, the members of the team have to decide which of the fifteen objects necessary for survival – oxygen reserves, concentrated food, signalling equipment, heating requisites, etc. – they will take with them. Those participating in the study were asked to draw up a list of priorities for these objects, first separately as individuals, and then in groups, by arriving at a consensus. Half of the groups received no special instructions for this common task of decision-taking. The other half were instructed to confront other members of the group and resolve the differences between them. They were informed that they had to set out their arguments lucidly and were not to change their opinion with the sole aim of avoiding conflict, nor to seek agreement using procedures such as a majority vote, the establishment of a mean position, bargaining, tossing a coin, or in other ways. Moreover, the instructions emphasized the need to look upon differences of opinion as both natural and useful, so that any precipitous agreement would be suspect, so long as the reasons for it had not been gone into thoroughly. The main thing was to resist group pressures that tempted one to yield to others without sound reasons, just in order to attain a consensus, which would lack any guarantee of success. [p 176]
      • Good game for study design?
    • Hall and Watson were persuaded that by weakening such pressures they would encourage divergent thinking to be displayed. This would lead groups first to produce solutions of a superior quality, and then to make better use of the resources of each member, so that overall performance would exceed even that of the group’s cleverest members, and finally to discover novel solutions. Most of these hypotheses were verified.
  • The other means of encouraging divergent thinking is by the presence of a minority participating actively in the group’s discussions. This is a comparatively natural means for use in decisions leading to a consensus, since it arises solely from the obligation to respect one of the essential conditions. These assume in fact a state of equality between the members of the group. This means the majority recognizes the right of the minority to express itself, and will set very great store by its opinions; otherwise the agreement arrived at would be worthless. [p 177]
  • (Moscovici and Zavalloni, 1969) looked for indications of this cognitive transformation of individuals in a group. It is no exaggeration to state that the decisions, in the broadest sense, prepare the way for it and make it their prime target. The students who participated, it will be recalled, had to adopt a common attitude towards de Gaulle and the Americans. In order to arrive at this, particularly if the attitude were unfavourable, they had to acknowledge a common set of values and a common code. This most possibly assumed , among the categories available to each individual, the use solely of those that corresponded to that code. These were the ones that were retained, that were used frequently, and towards which individuals would converge. In order to verify this we calculated an entropy index (H) of the distribution of categories, borrowed from information theory. [p180]
    • This looks like dimension reduction to me. It also implies a way of testing for it. The description for how they calculated entropy isn’t that clear from the book, but I’m guessing that it has something to do in the variability of the terms used. Combined with an awareness of sentiment, this might be a reasonable way to determine relevant axis of discussion
  • Moreover, the existence of a common representation is marked by the emergence of a series of categories of opinions and judgments most frequently used, and one might say, more general. Stripped of any singularity, and in a way simplified, they assume a prominence, and in so doing make explicit the alternatives that are at stake and orient the decision to be taken.In addition, and this must not be forgotten, they offer focal points around which personal representations of group members can be organized and articulated more easily. [C&C p 180]
  • This again can be interpreted as an argument for self-organizing axis that can be used in our belief maps. The trick will be to develop software that can recognize the salient features of these discussions. It may be possible o base this on the ‘Cognitive Tuning’ work of Robert Zajonc (1955/1960). Later, (Feeling and thinking: Preferences need no inferences – 1980), he argues that affect is precognitive. Not sure what to do with that or if it relates directly. Can group discussion be precognitive?
  • …groups discussing freely ended up using less categories than those that did so following a set procedure.””What in this manner they lose in information, they gain in comprehension and mental sociability” “there are reasons to think that categories used by groups take on prominence. They give a special contour to one dimension of the problem and to the angle from which one should look at and judge it
    , so that it can be discussed in optimum terms [C&C p 182].
  • However, it was clear that this stock of information and arguments was the expression of a system of representations and beliefs common to the group, rather than the sum of ideas or propositions” “Something else is needed, a representation or belief shared in common (as the saying goes, ‘one only preaches to the converted’), or indeed involvement in a common purpose. [C&C p 185]
  • Just as it is preferable to have a hypothesis to observe facts, so the sketchy outlines of a representation must be shared in order to assimilate information and arguments and move in a direction towards which they point [C&C p 186]
    • As good an argument for belief maps as I have come up with…
  • It is no exaggeration to state that the way in which individuals occupy themselves with a problem, seek information about it and discuss it, gives a rough measure of the knowledge they possess of it and the interest they take in it. When it fixes their attention occupies their thoughts, leads them to read books or articles, and to talk about it among themselves, they become ever more involved and are better informed as to what one may think about it [C&C p 189]
    • I think this may be incomplete or even potentially backwards. If this is an explore/exploit pattern, then there are going to be individuals who are driven to explore a belief space more thoroughly, while others sit back and exploit. I still think that this is more contextual, but there are also individual aspects that may matter as well. The important thing is to provide tools that afford the exploration as well as the exploitation. It would also be worth seeing how these explorations become socialized. I like the metaphor for startups. There is the blue sky research that few care about (though even here, funding is prone to swings in fashion, and what kind of research *should* be pursued). There is the bleeding edge technologies where a few adventurous investors will take a chance, then there is leading edge, as early adopters step in, then mainstream, etc. The initial stages in this process depend much more on the individual, while the later stages are crowd behaviors and more prone to fashion.

The Gamergate model of press relations








Filter bubbles, echo chambers, and online news consumption

Filter bubbles, echo chambers, and online news consumption

  • Spearman’s Rank-Order Correlation
    rarely read substantive news articles from conservative sites, and vice versa

  • Interestingly, exposure to opposing perspectives is higher for the
    counterintuitively, we find evidence that recent technological changes both
    increase and decrease various aspects of the partisan divide.

    • This fits nicely with my notion of belief space
  • ideological-segregation-across-channels
  • opposingpartisanexposure
    • So left leaning is more diverse across ideology

Modeling The Law of Group Polarization


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:

  1. 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.
  2. 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
  3. 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
  4. 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
  5. 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.
  6. 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 [2004] and Schwammle [2007] 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.






The Law of Group Polarization


Relevant flocking and collective decision making papers:

Relevant Sociophysics papers:

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]


  • 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 [20]. 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 [8]. 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.

Notes on “Sociophysics, an Introduction”

Sociophysics (Parongama Sen, Bikas K. Chakrabarti – 2013)

These are my notes as I was reading the book, which I found to be a very good overview with good detail that didn’t get in the way of the narrative. The references are stellar. When I found an appropriate paper mentioned in the text, I’ve included it as a link, usually with an accompanying abstract.

I read the book to support the model I’m working on for my PhD on trustworthy news. I’ve been doing agent-based simulations since the ’90s when I was working on my Master’s thesis on the The Coevolution of Weapons and Aggression. I certainly feel as though it has helped update my awareness of progress in the field since that effort, back when the term sociophysics didn’t even exist.

  • Chapter 2: Basic features of social systems and modelling
    • Minority Opinion Spreading in Random Geometry
      • Abstract: The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry shaped by social life (offices, houses, bars, and restaurants). A perfect world is considered with no advantage to the minority. A one person-one argument principle is applied to determine locally individual mind changes. In case of equality, a collective doubt is evoked which in turn favors the Status Quo. Starting from a large in favor of the proposal initial majority, repeated random size local discussions are found to drive the majority reversal along the minority hostile view. Total opinion refusal is completed within few days. Recent national collective issues are revisited. The model may apply to rumor and fear propagation.
      • Clustering coefficient (video)
        CC = 0
        numNodes = 0
        for(i = 0 to max)
        	for(j = 0 to max)
        		n = node(i,j)
        		k = n.numNeighbors()
        		a = n.numLinksBetweenNeighbors()
        		CC += n.getNodeCC()
        CC = CC/numNodes
      • Clustering coefficient ordering: random -> small world -> regular
      • To build a scale-free network, AL Barabási, R Albert in Emergence of scaling in random networks start with a small random network and incrementally add nodes where the probability of connecting a new node with existing nodes is proportional to how many connections the current nodes have.
        for(i = 0 to desired)
        	n = createNewNode()
        	totalLinks = countAllLinks()
        	for(j = 0 to network.numNodes)
        		curNode = getNode(j)
        		links = curNode.getLinks
        		probability = links/totalLinks
        		curNode.addNeighbor(n, probability)
      • Does node aging matter in this model?
      • Null Models For Social Networks (for comparison and testing)
      • Downloaded the following from the references section to my Group Polarization folder
      • A bubble could be an example of a strong community [pg 17] would need to figure out a way of establishing in and out links in knowledge space
      • Benchmark networks to test community detection algorithms [pg 17]. Artificially generated and the Zachary Karate club
      • I appear to be working with (maybe?) class ‘C’ social networks, where links connect people indirectly [pg 19].Covered in chapter 7 – Of Flocks, Flows and Transports
      • Page 25 discusses Marian Boguña et al Models of Social Networks based on Social Distance Attachment which uses the concept of social distance. A set of quantities (e.g. profession, religion, location) are used and the social distance between two individuals is the difference in the quantities.
      • More state-space simulation from page 28: Spin-glass-like Dynamics of Social Networks. Digging around uncovered her thesis: Information and Entropy in Neural Networks and Interacting Systems. From the abstract:
        • Like neural networks, large ensembles of similar units that interact also need a generalization of classical information-theoretic concepts. We extend the concept of Shannon entropy in a novel way, which may be relevant when we have such interacting systems, and show how it differs from Shannon entropy and other generalizations, such as Tsallis entropy.
    • Chapter 3: Opinion formation in a society
    • Chapter 4: Social choices and popularity – skimmed, not appropriate
    • Chapter 5: Crowd-avoiding dynamical phenomena – skimmed, not appropriate
    • Chapter 6: Social phenomena on complex networks
      • Claudio Castellano (Google Scholar)
      • Loops of nodes behave differently from trees. what to do about that? I think loops drive the echo chamber process? It is, after all, feedback..
      • There is also a ‘freezing’ issue, where a stable state is reached where two cliques containing different states are lightly connected, but not enough that the neighbors in one clique can be convinced to change their opinion [Fig. 6.2, pg 135]
      • Residual Energy: The difference between the actual energy and the known energy of the perfectly-ordered ground state (full consensus).
      • Dynamical Processes on Complex Networks. Got the Kindle edition so now I can search! Interesting section: 10.6 Coevolution of opinions and network
      • Similar chapter in this book – Social Phenomena on coevolutionary networks [pg 166]. One of the interesting things here is the use of the iterated prisoner’s dilemma. On a network, the agents typically calculate and aggregate payoff and imitate the strategy of the neighbor with the best payoff. In the coevolutionary model, an agent can cut off the link to a defector with a probability. This seems a bit like polarization, where the group severs ties with entities with sufficiently divergent views (and individuals leave when the group becomes too extreme)
      • Coevolution of agents and networks: Opinion spreading and community disconnection Abstract: We study a stochastic model for the coevolution of a process of opinion formation in a population of agents and the network which underlies their interaction. Interaction links can break when agents fail to reach an opinion agreement. The structure of the network and the distribution of opinions over the population evolve towards a state where the population is divided into disconnected communities whose agents share the same opinion. The statistical properties of this final state vary considerably as the model parameters are changed. Community sizes and their internal connectivity are the quantities used to characterize such variations.
      • Opinion and community formation in coevolving networks (Gerardo Iñiguez González)
        • Abstract: In human societies opinion formation is mediated by social interactions, consequently taking place on a network of relationships and at the same time influencing the structure of the network and its evolution. To investigate this coevolution of opinions and social interaction structure we develop a dynamic agent-based network model, by taking into account short range interactions like discussions between individuals, long range interactions like a sense for overall mood modulated by the attitudes of individuals, and external field corresponding to outside influence. Moreover, individual biases can be naturally taken into account. In addition the model includes the opinion dependent link-rewiring scheme to describe network topology coevolution with a slower time scale than that of the opinion formation. With this model comprehensive numerical simulations and mean field calculations have been carried out and they show the importance of the separation between fast and slow time scales resulting in the network to organize as well-connected small communities of agents with the same opinion.
        • Citing paper: Effects of deception in social networks (Gerardo Iñiguez González)<— Important???
          • Abstract: Honesty plays a crucial role in any situation where organisms exchange information or resources. Dishonesty can thus be expected to have damaging effects on social coherence if agents cannot trust the information or goods they receive. However, a distinction is often drawn between prosocial lies (‘white’ lies) and antisocial lying (i.e. deception for personal gain), with the former being considered much less destructive than the latter. We use an agent-based model to show that antisocial lying causes social networks to become increasingly fragmented. Antisocial dishonesty thus places strong constraints on the size and cohesion of social communities, providing a major hurdle that organisms have to overcome (e.g. by evolving counter-deception strategies) in order to evolve large, socially cohesive communities. In contrast, white lies can prove to be beneficial in smoothing the flow of interactions and facilitating a larger, more integrated network. Our results demonstrate that these group-level effects can arise as emergent properties of interactions at the dyadic level. The balance between prosocial and antisocial lies may set constraints on the structure of social networks, and hence the shape of society as a whole.
      • Section 6.5: Is it really a small world? Searching post Milgram
        • In the introduction to this section [page 168], the authors say a very interesting thing: “Although the network may have the small world property, searches are usually done locally: the individual may not know the global structure of the network that would help them find the shortest path to the target node“. I think that they are talking about social networks explicitly here, but the same concept applies to an information network. This is a network description of the information horizon problem. You can’t find what you can’t see, at least in a broad outline.
        • Also this: “Searching can regarded as a learning process; repeating the search several times can avoid infinite loops and lead to better solutions
        • 6.5.8 Funneling properties.
            • The funneling capability of a node can be defined as the fraction of successful dynamic paths through it when the target is fixed and the source is varied. Two thoughts: First, this seems to be a measurement of centrality. Second, Large, vague nodes are needed for ‘laundering’ information into misinformation or conspiracy theory.
            • Consider four agents. Who have characteristics that can vary between (0, 1).
              • Agent 1 has two color intensities: R=0.1, G= 0.7
              • Agent 2 has one color and two note volumes R=0.3, A=0.2, F=0.6
              • Agent 3 also has one color and two note volumes B=0.4, D=1, E=0.2
              • Agent 4 has three notes A=0.3, D=0.4, E=0.5
            • Let’s assume that funneling is not required if agents share a color or note. This means that A4 can get to A1 through A2, but A3 has to get to A1 via A4 and then A2. In a matrix this looks like
          R G B A D E F
          Agent1 0.1 0.7
          Agent2 0.3 0.2 0.6
          Agent3 0.4 1.0 0.2
          Agent4 0.3 0.4 0.5
            • But if we add the hypernyms Color and Notes, we can get funneling. I am summing the color and notes to give a sense of the agent’s ‘projection’ into the larger, more general space. I think the ‘size’ of the funnels are the number of items that go in them times the range of each item. So Color would have a range of (0, 3) and Notes would have a range of (0, 4), since I’m not including B, C, and G here:
          R G B A D E F Color Notes
          Agent1 0.1 0.7 0.8
          Agent2 0.3 0.2 0.6 0.3 0.8
          Agent3 0.4 1.0 0.2 0.4 1.2
          Agent4 0.3 0.4 0.5 1.2
            • Now agents 2 and 3 can get to each other through either Color or note in two hops, and the Agents 1 and 4 can reach each other by going through each of the funnels.
            • There should be a cost in using a funnel though. You loose the information about which color or which note. Intuitively, a series of steps with non-funnel links should be somehow more specific than the same number of steps through a funnel.
            • Practical uses would be a way to detect poorly reasoned conclusions, as long as the beginning and end of the train of thought could be identified.
      • Knowing a network by walking on it: emergence of scaling (Alexei Vázquez) Looks like an interesting guy with a wide range of publications.
    • Chapter 7:  of flocks, flows and transports [page 179]
      • Boids (Flocks, herds and schools: A distributed behavioral modelCraig Reynolds):
        • Try to avoid collisions with other boids (repulsion)
        • Attempt to match velocity with neighboring boids
        • attempt to stay close to nearby boids
      • If the collision avoidance is taken out and the number of dimensions increased, then this could be the model. Rather than the flock converging around a position, look at the distances between the individuals using DBSCAN and cluster.
      • Density and noise need to be independent variables and saved on runs. This would also be true in information space. You can have high organization in high density, low noise states. Thinking about that, this also implies one of the emergent properties of an information bubble is the low noise. Even though the environment may be very noisy, the bubble isn’t.
      • As with the other social models, individuals can have weight. That way the flock can have leaders and followers. (See Misinformed leaders lose influence over pigeon flocks to inform the model)
      • Also, I like the idea of a social network being built from belief proximity, which raises the cost for switching to another flock, even if they are nearby. It could be that once a social network forms that anti-belief repulsion starts to play a role.
      • Another component to include would be a Levy Flight (truncated?). That could account for cases where a leader makes a big jump and then the crowd follows with some ejection for those who can’t/won’t keep up.
      • Power law distribution of weight and max step size in the creation of the population
      • Thomas Schelling (Another Herbert Simon type) Segregation Model
      • Phase diagram of a Schelling segregation model (L Gauvin, J Vannimenus, JP Nadal – The European Physical Journal B, 2009). I’m beginning to think that the model could be a combination of a flocking and segregation model. That could be really interesting. I also seem to get nothing when I do a Scholar search on “flocking and segregation agent simulation
        • Satisfaction criteria – when the number of unlike agents is less than a fixed proportion F. As F gets larger there is an abrupt transition to a segregated state.
        • Definition of segregation coefficient – the weighted average (normalized) of all cluster sizes averaged over all configurations. When only two clusters survive, n(c) = N/2
      • Migration in a small world: A network approach to modeling immigration processes (B Fotouhi, MG Rabbat – Communication, Control, and Computing, 2012 –
    • Chapter 8: Endnote [page 202]
      • Frustration in Complexity (2008 – Philippe Binder)- The common thread between all complex systems may not be cooperation but rather the irresolvable coexistence of opposing tendencies.
      • Definition of consensus in an opinion model – the emergence of long-range order.
      • Looking for phase changes from heterogeneous to homogeneous or clustered states is important. Finding what parameters are causal and the values is considered a publishable result. Canonical types of transitions, such as the percolation threshold are discussed in the appendices.

Trustworthy News Model Assumptions


  • 12.13.16: Initial post
  • 12:16:16: Added reference to proposal and explicitly discussed explorer and exploiter types.

A web version of my Google Docs dissertation proposal is here. Blame them for the formatting issues. The section this is building on is Section 5.3.1. A standalone description of this task is here.

The first part of my dissertation work is to develop an agent-based simulation that exhibits information bubble/antibubble behavior. Using Sen and Chakrabarti’s Sociophysics as my guide, I’m working up the specifics of the model. My framework is an application (JavaFX, because that’s what I’m using at work these days). It’s basically an empty framework with a trivial model that allows clustering based on similar attributes such as color: strawmanapp

Going forward, I need to clarify and defend the model, so I’m going to be listing the components here.

Agent assumptions

  • Agents get their information from global sources (news media). They have equal access, but visibility is restricted
    • Agents are Explorers or Exploiters (Which may be made up of Confirmers and Avoiders)
    • Agents have ‘budgets’ that they can allocate
    • Finding sources has a cost. Sources from the social network has a lower cost to access
    • Keeping a source is cheaper than getting a new one
    • For explorers, the cost of getting a new source is lower than an exploiter.
    • The ‘belief’ as a set of ‘statements’ appears to be valid
    • The collection of statements and the associated values create a position in an n-dimensional hilbert space of information. Position and velocity should be calculable.
    • Start at one dimension to reproduce prior opinion models

Network assumptions

  • There are two items that we are looking for.
    • The first is the network configuration over time. What nodes do agents connect to for their information.
    • The second is the content of that information. For that, we’ll probably need some dimensionality reduction, such as NMF (look for a post on implementing this later). This is where we look for echo chambers of information, as opposed to the agents participating in them
  • Adjustable to include scale-free, small world, and null configurations
  • What about loops? Feedback could be interesting, since a small group that is semi-isolated could form into a very loud bubble that could lower the cost of finding information. So a notion of volume might be needed that emerges from a set of agreeing agents. This could be attraction, though I think I like an economic approach more?


  • Deviation from null network.
  • Clustering as per community detection (Girard et. al)

Implementation details

  • Able to be run multiple times with the same configuration but different seed
  • Outputs to… something. MySql or Excel probably
  • Visualization using t-SNE? Description plus Java implementation is here:

More to come as the model fleshes out.


Opinion Dynamics With Decaying Confidence: Application to Community Detection in Graphs

Opinion Dynamics With Decaying Confidence: Application to Community Detection in Graphs

  • Irinel-Constantin Morarescu
  • Antoine Girard (some supporting slides from 2006. Very helpful!)
  • Really important reference: Community detection in graphs.
  • Handy chart of symbols, and a bigger chart
  • Data sources for the paper:
  • Italics indicate direct quotes
  • From the slides, a flock is an entity in a network where the members have agreed upon a direction and a velocity. In the paper, rather than movement vector, the value is an ‘opinion’
  • We consider a network of agents where each agent has an opinion. At each time step, the agents exchange their opinion with their neighbors and update it by taking into account only the opinions that differ from their own less than some confidence bound. This confidence bound is decaying: an agent gives repetitively confidence only to its neighbors that approach sufficiently fast its opinion.
    • This seems like a nice way to form bubbles. Agents only see their neighbors and have to accommodate with their neighbors within a narrowing range of acceptance. This means that other agents elsewhere in the network (and depending on the connectivity) would converge differently, and different opinions would be created.
  • Under that constraint, global consensus may not be achieved and only local agreements may be reached. The agents reaching a local agreement form communities inside the network.
    • If the decay rate is low enough, then global consensus can be reached. Faster, and the network starts to break apart.
  • Our model can be interpreted in terms of opinion dynamics. Each agent has an opinion. At each time step, the agent receives the opinions of its neighbors and then updates its opinion by taking a weighted average of its opinion and the opinions of its neighbors that are within some confidence range of its own. The confidence ranges are getting smaller at each time step: an agent gives repetitively confidence only to the neighbors that approach sufficiently fast its own opinion. This can be seen as a model for a negotiation process where an agent expects that its neighbors move significantly towards its opinion at each negotiation round in order to keep negotiating.
  • We assume that the relation is symmetric and anti-reflexive
    • Undirected graph where no nodes are connected to themselves
  • This model can be related to the one discussed in [17], [18] where agents harden their position by increasing over time the weight assigned to their own opinion. In our model, the agents implicitly increase also the weights assigned to their neighbors whose opinion converges sufficiently fast to their own opinion, by disregarding the opinions of the other agents. As noticed in [18], hardening the agents positions may hamper the agents to reach an asymptotic consensus. This will be observed in our model as well. However, the aim in this paper is not to exogenously increase the self-confidence of the agents, but to meet a prescribed convergence speed towards the final opinion profile.
    • This last line follows my thinking on bubbles somewhat. I think the hardening is a function of the information distance between the two positions. Convergence can only happen at a certain rate, so the farther apart the harder it is to converge. In this model, that’s done by arbitrarily reducing the confidence, but I think the math should be pretty similar. I do wonder if anti-agreement is useful here.
  • our model would coincide with Krause model of opinion dynamics with bounded confidence [9][10][11].
    • It looks like Krause is the fountainhead of this area of research. Lots of really interesting work. Everything seems to be from a perspective that agents will converge on one or more opinions, and then the simulation ends. So I know how to make bubbles (and possibly antibubbles, simply by not having agents ‘harden’). What seems to be missing is the notion in Group Polarization that the opinion becomes more extreme. When searching through the works that cite [9], there does seem to be work in this area, but I wasn’t able to find anything that actually has a model using agent-based simulation.
  • In this section, we explore the relation between communities and asymptotically connected components of the network. Let us remark that the set of edges can be classified into two subsets. Intuitively, an edge E(finite)is in if the agents and stop interacting with each other in finite time. E(infinite)consists of the interactions between agents that are infinitely recurrent.
    • So this works in the context that the final opinion is static. I think opinions need a random walk component. Given that there are multiple opinions, is the difference a hypotenuse or manhattan distance?
    • As discussed in the the end of the simulation, any connected agents must be in agreement. That means that you can just look at the connections and determine the group?
  • Asymptotic Agreement Implies Asymptotic Connectivity
    • They show that this holds for most but not all conditions. That’s an interesting finding, since it implies in almost any sufficiently connected network, a bubble will engulf most individuals that agree…
    • In this section, we showed that asymptotic connectivity of agents implies asymptotic agreement and that under additional reasonable assumptions these are actually equivalent except for a set of vectors of initial opinions of Lebesgue measure 0. In other words, we can consider almost surely that the communities of agents correspond to the connected components of the graph G(infinity). I think this agrees with my above point.
  • Community Detection: In the usual sense, communities in a graph are groups of vertices such that the concentration of edges inside one community is high and the concentration of edges between communities is comparatively low. Because of the increasing need of analysis tools for understanding complex networks in social sciences, biology, engineering or economics, the community detection problem has attracted a lot of attention in the recent years. The problem of community detection is however not rigorously defined mathematically. One reason is that community structures may appear at different scales in the graph: there can be communities inside communities. Another reason is that communities are not necessarily disjoint and can overlap. We refer the reader to the excellent survey [12] and the references therein for more details. Some formalizations of the community detection problem have been proposed in terms of optimization of quality functions such as modularity [13] or partition stability [14].
  • Essentially, the modularity Q(P)of the partition P is the proportion of edges within the classes of the partition minus the expected proportion of such edges, where the expected number of edges between vertex i and j is assumed to be (degree_i*degree_j)/(all edges)
  • The higher the modularity, the better the partition reflects the community structure of the graph. Thus, it is reasonable to formulate the community detection problem as modularity maximization. However, it has been shown that this optimization problem is NP-complete [21]. Therefore, approaches for community detection rely mostly on heuristic methods. In [15], a modularity optimization algorithm is proposed based on spectral relaxations. Using the eigenvectors of the modularity matrix, it is possible to determine a good initial guess of the community structure of the graph. Then, the obtained partition is refined using local combinatorial optimization. In [16], a hierarchical combinatorial approach for modularity optimization is presented. This algorithm which can be used for very large networks, is currently the one that obtains the partitions with highest modularity.
  • Bubbles at scales? “Stability measures the quality of a partition by giving a positive contribution to communities from which a random walker is unlikely to escape within the given time scale. For small values of t, this gives more weights to small communities whereas for larger values of t , larger communities are favored. Thus, by searching the partitions maximizing the stability for several values of , one can detect communities at several scales.
  • we want to find groups of vertices that are more densely connected than the global graph. This coincides with the notion of community. The larger δ, the more densely connected the communities. This makes it possible to search for communities at different scales of the graph.
  • For each combination of parameter value, the model was simulated for 1000 different vectors of initial opinions chosen randomly in [0,1]34. Simulations were performed as long as enabled by floating point arithmetics.
    • I think that this means that each agent was given a distinct random opinion for each of 1,000 runs. Then they looked for the most common clusterings
  • It is interesting to remark that for δ = 2 we almost obtained the communities that were reported in the original study [23]. Only one agent has been classified differently.
  • When δ increases, the communities become smaller but more densely connected.
    • It should be very interesting to look at belief velocity at different scales.
  • …for the same value of parameter δ, the modularity is very similar for all partitions. Actually, all the partitions obtained for the same value of δ are almost the same. As in the previous example, we can see that the choice of parameters R and α affects the probability of obtaining a given partition. The partition with maximal modularity is obtained for δ = 0.2, it is a partition in 4 communities with modularity 0.523
  • Let us remark that even though the information on the political alignment of the books is not used by the algorithm, our approach allows to uncover this information. Indeed, for δ = 0.1, we obtain 2 communities that are essentially liberal and conservative. For δ = 0.2, we then obtain 4 communities: liberal, conservative, centrist-liberal, centrist-conservative.
    • Note that this is information appears to be latent
  • The last example we consider consists of a significantly larger network of 1222 political blogs [24]. In this network, an edge between two vertices means that one of the corresponding blogs contained a hyperlink to the other on its front page. We also have the information about the political alignment of each blog based on content: 636 are conservative, 586 are liberal.
  • There are 2 main communities: one with 653 blogs, from which 94% are conservative, and one with 541 blogs, from which 98% are liberal. The 28 remaining blogs are distributed in 10 tiny communities. When we progressively increase δ, we can see that the size of the two large communities reduces moderately but progressively until δ = 0.65 where the conservative community splits into several smaller communities, the largest one containing 40 blogs. The liberal community remains until δ = 0.725 where it splits into smaller communities, the largest one containing 54 blogs.