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Cited by 407Opinion Dynamics and Social InfluenceComplex Network Analysis TechniquesDistributed Control Multi-Agent Systems

Social Influence and the Collective Dynamics of Opinion Formation

Open access
Moussaïd, Mehdi, Kämmer, Juliane E., Analytis, Pantelis P., Neth, Hansjörg·2013·PLoS ONE
DOI 10.1371/journal.pone.0078433PMC PMC3818331
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Abstract

Social influence is the process by which individuals adapt their opinion, revise their beliefs, or change their behavior as a result of social interactions with other people. In our strongly interconnected society, social influence plays a prominent role in many self-organized phenomena such as herding in cultural markets, the spread of ideas and innovations, and the amplification of fears during epidemics. Yet, the mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation. Here, we report two controlled experiments showing how participants answering factual questions revise their initial judgments after being exposed to the opinion and confidence level of others. Based on the observation of 59 experimental subjects exposed to peer-opinion for 15 different items, we draw an influence map that describes the strength of peer influence during interactions. A simple process model derived from our observations demonstrates how opinions in a group of interacting people can converge or split over repeated interactions. In particular, we identify two major attractors of opinion: (i) the expert effect, induced by the presence of a highly confident individual in the group, and (ii) the majority effect, caused by the presence of a critical mass of laypeople sharing similar opinions. Additional simulations reveal the existence of a tipping point at which one attractor will dominate over the other, driving collective opinion in a given direction. These findings have implications for understanding the mechanisms of public opinion formation and managing conflicting situations in which self-confident and better informed minorities challenge the views of a large uninformed majority.

AI snapshot

Written from the paper’s full text.

TL;DR

Two controlled experiments show how people revise factual judgments after seeing another person’s opinion and confidence, yielding an empirical “influence map” of opinion adaptation. A model derived from these data reveals that collective opinion is driven by two attractors—the expert effect and the majority effect—with a tipping point around 15% experts.

Key findings

  • Initial opinions followed a lognormal distribution: Kolmogorov-Smirnov tests on log opinions yielded p-values above .05 for 84% of the 32 items.
  • Confidence was a weak cue for accuracy: the correlation between confidence and error was –.03; only maximum confidence (Ci = 6) was a good indicator, corresponding to a good or very good estimate 80% of the time, while Ci = 5 had a 39% chance of a bad or very bad estimate and Ci = 4 was more likely to accompany a bad or very bad estimate (53%) than a good or very good one (47%).
  • In 885 binary interactions, most people kept their initial opinion (53%), 43% made a compromise, and 4% adopted the other’s opinion; social influence was strongest at intermediate opinion distances.
  • Simulations identified two major attractors: the expert effect from highly confident individuals and the majority effect from a critical mass of low-confidence individuals sharing an opinion; the majority effect overcame the expert effect below about 10% experts, with a transition around 15% experts that remained stable even with neutral individuals until noise dominated above 70% neutral individuals.

Methods

  • Experiment 1: 52 participants answered 32 general knowledge questions and rated confidence on a 6-point scale, producing 1,664 data points used to characterize initial opinions and confidence-accuracy.
  • Experiment 2: 59 participants answered 15 questions, then saw another randomly selected Experiment 1 participant’s estimate and confidence and gave revised estimate and confidence, yielding 885 binary interactions used to build the influence map.
  • The authors derived a decision-tree/individual-based model from the influence map and ran numerical simulations with the 52 initial agents paired randomly over N = 300 rounds, plus additional simulations varying proportions of experts, majority, and neutral individuals.

Limitations

  • The paper states that neutral factual questions were used to control emotional impact, and that future work should test how the influence map changes with emotions and subjective beliefs.
  • The paper states that the assumption that the decision tree remains identical over repeated interactions needs verification, and that simulation outcomes require empirical validation.
  • The paper notes that edge zones of the influence map are uncertain due to scarce data, and that very remote opinions rarely occurred, so conclusions there are not reliable; it also makes evident that model parameters were extracted from the same experimental data used to build the model.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1371/journal.pone.0078433

Cites

52 of 52 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 34 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    There is no significant correlation between an individual's confidence level and the quality of their answer (correlation coefficient -.03).

    “First, we found no significant correlation between an individual i’s confidence level Ci and the quality of his or her answer (a correlation test between Ci and the error where T is the true value yielded a coefficient of –.03).”
    Quote in the paperNot a substantial claim
  • Findingcitation

    The majority of people systematically keep their opinion when their own confidence exceeds their partner's.

    “In particular, the majority of people systematically keep their opinion when the value of is positive, that is, when their own confidence exceeds their partner’s [30].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [30] J Soll, 2009, Strategies for revising judgment: How (and how well) people use others’ opinions, Journal of Experimental Psychology: Learning, Memory, and Cognition

      Not checked in the free run.

  • Findingown data

    The confidence level is not a reliable cue for accuracy.

    “Interestingly, the confidence level is not such a reliable cue for accuracy [34].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [34] G Gigerenzer, 1991, Probabilistic mental models: a Brunswikian theory of confidence, Psychological Review source

      Not checked in the free run.

  • Findingown data

    After social influence, the distribution of errors for very confident individuals (Ci = 5 or 6) becomes more noisy, widespread and clustered around certain values, thus becoming less informative about accuracy.

    “As shown in Fig. 2B, the distribution of errors for very confident individuals (Ci = 5 or 6) becomes more noisy, widespread and clustered around certain values thus becoming less informative about accuracy after social influence.”
    Quote in the paperSubstantial claim
  • Findingown data

    A critical amount of approximately 15% of experts is necessary to counteract the attractive effect of a large majority of lay individuals.

    “In particular, we show that a critical amount of approximately 15% of experts is necessary to counteract the attractive effect of a large majority of lay individuals.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree extracted from the experiment remains the same over repeated interactions.
    • Rests on an assumption: The experimental sample and the derived decision tree are representative of large groups of interacting people.
  • May combine two claims. 29
  • The quote only partly states this claim. 1
  • Classified as probably not a substantial claim. 12

  • May combine two claims.

    Findingown data

    Lower confidence levels are less informative about accuracy; for example, Ci = 5 has a 39% chance to correspond to a bad or very bad estimate, and Ci = 4 is more likely to accompany a bad or very bad estimate (53%) than a good or very good one (47%).

    “For instance, the second highest confidence value of Ci = 5 has a 39% chance to correspond to a bad or very bad estimate. Similarly, a value of Ci = 4 is more likely to accompany a bad or very bad estimate (53%) than a good or very good one (47%).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Initial opinions follow a lognormal distribution, with a long tail indicating the significant presence of outliers.

    “As shown in the example in Fig. 1A, the initial distribution of opinions has a lognormal shape, with a typical long tail indicating the significant presence of outliers.”
    • Also stated in: § Experimental results · hedged
      “The test yielded p-values above.05 for 84% of the items, indicating that the null hypothesis cannot be rejected at the 5% significance level for these items. The remaining 16% still had reasonably high p-values (always >10−3), suggesting that the initial opinions Oi indeed follow a lognormal distribution.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In the intermediate disagreement zone, the 'compromise' heuristic is selected by most people when [condition], and the 'adoption' heuristic appears for lower values of [condition].

    “In this zone, the “compromise” heuristic is selected by most people when , and the “adoption” heuristic appears for lower values of .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    When both individuals have a similar opinion (distance <0.3), individuals tend to keep their initial judgment, irrespective of their partner's confidence, and have a strong tendency to increase their confidence level.

    “First, when both individuals have a similar opinion (<0.3), individuals tend to keep their initial judgment, irrespective of their partner’s confidence. Moreover, they also have a strong tendency to increase their confidence level”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation

    In the compromise strategy, the average weight value measured from the data was less than 0.5, indicating that people exhibited a bias toward their own initial opinion.

    “When the individual chooses the “compromise” strategy, that is when , the average weight value as measured from our data equals to (SD = 0.24), indicating that people did not move exactly between their initial estimate and the feedback (which would correspond to a weight value of 0.5), but exhibited a bias toward their own initial opinion [30].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [30] J Soll, 2009, Strategies for revising judgment: How (and how well) people use others’ opinions, Journal of Experimental Psychology: Learning, Memory, and Cognition

      Not checked in the free run.

  • May combine two claims.

    Findingreasoning

    Judgments of high confidence are good indicators of accuracy before social influence occurs, but no longer after people have been exposed to the opinion of others.

    “Interestingly, judgments of high confidence are good indicators of accuracy before social influence occurs, but no longer after people have been exposed to the opinion of others.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Contradictory feedback is typically underestimated or ignored, while opinions corroborating one's initial opinion trigger an increase in confidence.

    “Therefore, contradictory feedback is typically underestimated—if not completely ignored—but opinions corroborating one’s initial opinion trigger an increase in confidence.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    When the distance is intermediate, the confidence level is changed only if [condition]; in this case, Ci increases with probability p = 0.5, and remains the same otherwise.

    “The data shows that the confidence level is changed only if (Fig. 4B). In this case, Ci increases with probability p = 0.5, and remains the same otherwise.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Over all data points, 53% correspond to the first strategy (keep own opinion), 43% to the second (compromise), and 4% to the third (adopt other opinion).

    “Over all our data points, 53% correspond to the first strategy (), 43% to the second (), and 4% to the third ().”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In the simulations, although some opinion fragmentation remains, a majority of individuals converge toward a similar opinion.

    “Although a certain level of opinion fragmentation still remains, a majority of individuals converge toward a similar opinion.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • May combine two claims.

    Findingcitation

    Unconfident people tend to increase their own confidence after interacting with a very confident person, creating a basin of attraction around that person's opinion.

    “Second, unconfident people tend to increase their own confidence after interacting with a very confident person, creating a basin of attraction around that person’s opinion [38], [39].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [38] I Couzin, 2005, Effective leadership and decision-making in animal groups on the move, Nature source

      Not checked in the free run.

    • cites [39] J Dyer, 2008, Leadership, consensus decision making and collective behaviour in humans, Philosophical Transactions of the Royal Society B: Biological Sciences source

      Not checked in the free run.

    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • May combine two claims.

    Findingown data

    As pExp increases from 10% to 20%, a transition occurs and the convergence point shifts from the majority to the experts' opinion.

    “However, as pExp increases from 10%, to 20% a transition occurs and the convergence point shifts from the majority to the experts’ opinion.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • May combine two claims.

    Findingown data

    When the distance is small, the confidence level Ci is increased by one point if [condition], and is also increased by one point with probability p = 0.5 when [condition], and remains the same otherwise.

    “Additionally, the confidence level Ci is increased by one point if . As indicated by Fig. 4A, Ci is also increased by one point with a probability p = 0.5 when , and remains the same otherwise.”
    Quote in the paperSubstantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data

    When the distance is large, the confidence level decreases by one point when [condition], and remains the same otherwise.

    “This time, the confidence level decreases by one point when , and remains the same otherwise.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Findingreasoning

    People who are initially very confident exhibit a high likelihood (almost 70%) of reducing their confidence level when the distance between opinions is very large.

    “Moreover, people who are initially very confident (i.e. ) presumably begin to doubt the accuracy of their judgment and exhibit a high likelihood (of almost 70%) of reducing their confidence level.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductreasoning

    Exposing participants to another participant's estimate and confidence and asking them to revise renders opinion changes traceable and the effects of social influence measurable at the individual level.

    “This procedure renders opinion changes traceable, and the effects of social influence measureable at the individual level.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    The mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation.

    “Yet, the mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation.”
    • Also stated in: § Introduction · plain
      “these simulation-based contributions share a common drawback: the absence of empirical verification of the models’ assumptions [28].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [28] P Sobkowicz, 2009, Modelling opinion formation with physics tools: Call for closer link with reality, Journal of Artificial Societies and Social Simulation

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The findings of local rules of opinion adaptation have not yet been used to study the collective dynamics of the system, and it remains unclear how social influence plays out in larger scale social contexts over time.

    “However, the findings of local rules of opinion adaptation have not yet been used to study the collective dynamics of the system, and it remains unclear how social influence plays out in larger scale social contexts over time [31].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [31] W Mason, 2007, Situating social influence processes: Dynamic, multidirectional flows of influence within social networks, Personality and Social Psychology Review source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    The area of agreement (similar opinions) can be interpreted as a confirmation zone, where feedback tends to simultaneously reinforce initial opinions and increase an individual's confidence.

    “Therefore, we interpret this area of agreement as being a confirmation zone, where feedback tends to simultaneously reinforce initial opinions and increase an individual’s confidence.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductcitation

    Asking neutral, general knowledge questions allows capturing the mechanisms of opinion adaptation while controlling its emotional impact.

    “Following the methods of existing experiments, we deliberately asked neutral, general knowledge questions, which allows capturing the mechanisms of opinion adaptation while controlling its emotional impact [6], [30].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [6] I Yaniv, 2004, Receiving other people’s advice: Influence and benefit, Organizational Behavior and Human Decision Processes source

      Not checked in the free run.

    • cites [30] J Soll, 2009, Strategies for revising judgment: How (and how well) people use others’ opinions, Journal of Experimental Psychology: Learning, Memory, and Cognition

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    People sharing similar extreme opinions, such as racial prejudices, tend to strengthen their judgment and confidence after interacting with one another.

    “it has been shown that people sharing similar extreme opinions, such as racial prejudices, tend to strengthen their judgment and confidence after interacting with one another [12].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [12] D Myers, 1970, Discussion effects on racial attitudes, Science source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    The collective dynamics of opinion formation in large groups of people are driven by two major attractors of opinion: the presence of a highly confident individual and the presence of clusters of low-confidence individuals sharing a similar opinion.

    “By exploring a simple model derived from our observations, we demonstrate that the collective dynamics of opinion formation in large groups of people are driven by two major “attractors of opinion”: (i) the presence of a highly confident individual and (ii) the presence of clusters of low-confidence individuals sharing a similar opinion.”
    • Also stated in: § Abstract · plain
      “In particular, we identify two major attractors of opinion: (i) the expert effect, induced by the presence of a highly confident individual in the group, and (ii) the majority effect, caused by the presence of a critical mass of laypeople sharing similar opinions.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree extracted from the experiment remains the same over repeated interactions.
    • Rests on an assumption: The experimental sample and the derived decision tree are representative of large groups of interacting people.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given

    The study was approved by the Ethics Committee of the Max Planck Institute for Human Development.

    “The present study has been approved by the Ethics Committee of the Max Planck Institute for Human Development.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Early experiments showed that opinions tend to get reinforced by group discussions involving people who initially share a similar judgment.

    “This result is also in line with early experiments showing that opinions tend to get reinforced by group discussions that involve people who initially share a similar judgment [12].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [12] D Myers, 1970, Discussion effects on racial attitudes, Science source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given

    The order of the questions was randomized for each participant.

    “The order of the questions was randomized for each participant.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Premisenone given

    The macroscopic features of the system are only visible when a large number of people interact many times, making it extremely difficult to investigate under laboratory conditions.

    “Because the macroscopic features of the system are only visible when a large number of people interact many times, it would be extremely difficult to investigate this under laboratory conditions.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Recent studies on animal groups have shown that the presence of uninformed individuals in fish schools acts in favor of the numerical majority, at the expense of very opinionated individuals.

    “By contrast, recent studies on animal groups have shown that the presence of uninformed individuals in fish schools acts in favor of the numerical majority, at the expense of very opinionated individuals [1].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [1] I Couzin, 2011, Uninformed individuals promote democratic consensus in animal groups, Science source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    Confidence serves as a system memory: over simulation rounds, individuals are less easily influenced because their confidence level gradually increases as they receive new feedback.

    “First, confidence serves as a sort of system memory. In fact, over simulation rounds, individuals are less easily influenced by others because their confidence level gradually increases as they receive new feedback.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • May combine two claims.

    Study design and conductown data

    A correlation test of accuracy of answers and question order yielded non-significant p-values for 90% of participants with p>0.05, confirming the absence of any learning process over experimental rounds.

    “A correlation test of the accuracy of answers and the order of the questions yielded non-significant p-values for 90% of participants with a probability p>0.05, confirming the absence of any learning process over experimental rounds.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    High confidence is an indicator of accuracy when judgments are independent but becomes an indicator of consensus when social influence takes place.

    “Therefore, high confidence is an indicator of accuracy when judgments are independent but becomes an indicator of consensus when social influence takes place [43], [44].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [43] A Koriat, 2012, When are two heads better than one and why?, Science source

      Not checked in the free run.

    • cites [44] R Hertwig, 2012, Tapping into the wisdom of the crowd—with confidence, Science source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    The process often turns out to be detrimental to the group because local confidence may grow artificially, providing false cues and triggering a snowball effect that may drive the group in an erroneous direction.

    “This process often turns out to be detrimental to the group, because the local amount of confidence may grow artificially in a given region of the opinion space, which provides false cues to others and triggers a snowball effect that may drive the group in an erroneous direction.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • May combine two claims.

    Interpretationcitation

    The presence of these elements confirms that the experimental design captured the fundamental mechanisms of social influence, and factual questions can be used to some extent to study fundamental features of opinion dynamics.

    “The presence of these elements confirms that our experimental design has indeed captured the fundamental mechanisms of social influence, and that factual questions can be used, to some extent, to study the fundamental features of opinion dynamics [29].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [29] J Lorenz, 2011, How social influence can undermine the wisdom of crowd effect, Proceedings of the National Academy of Sciences source

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation

    The collective outcome appears poorly predictable and strongly dependent on initial conditions.

    “In agreement with previous works [15], the collective outcome appears to be poorly predictable and strongly dependent on the initial conditions [36].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [15] M Salganik, 2006, Experimental study of inequality and unpredictability in an artificial cultural market, Science source

      Not checked in the free run.

    • cites [36] L Valori, 2012, Reconciling long-term cultural diversity and short-term collective social behavior, Proceedings of the National Academy of Sciences source

      Not checked in the free run.

    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given

    All participants gave written and informed consent to the experimental procedure.

    “All participants gave written and informed consent to the experimental procedure.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The majority effect and the expert effect are not systematically beneficial to the group, as both attractors could drive the group away from the truth.

    “Our simulations show that the majority effect and the expert effect are not systematically beneficial to the group, as both attractors could possibly drive the group away from the truth (Fig. 5-Example 2).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • May combine two claims.

    Interpretationreasoning

    Neutral individuals make the crowd less vulnerable to the influence of opinion attractors, and thus less predictable.

    “Therefore, neutral individuals make the crowd less vulnerable to the influence of opinion attractors, and thus less predictable.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The decision tree observed at the first round of interaction remains identical over repeated interactions.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Study design and conductnone given

    N = 300 rounds of simulated interactions were performed, chosen large enough to ensure that the system reached a stationary state.

    “We performed N = 300 rounds of simulated interactions, where N has been chosen large enough to ensure that the system has reached a stationary state.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationcitation

    The sharp transition of the system's global confidence level is a typical signature of phase transitions in complex systems.

    “This amplification process is also marked by a sharp transition of the system’s global confidence level (Fig. S2), which is a typical signature of phase transitions in complex systems [2].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [2] Camazine S, Deneubourg J-L, Franks N, Sneyd J, Theraulaz G, <etal>et al</etal>.. (2001) Self-organization in biological systems. Princeton University Press. source

      Not checked in the free run.

38 of 38

  • The authors state this as an assumption.

    The decision tree extracted from the experiment remains the same over repeated interactions.

    “Here, we make the assumption that the decision tree that has been extracted from our experiment remains the same over repeated interactions.”

  • The paper relies on this without support.

    The experimental sample and the derived decision tree are representative of large groups of interacting people.

    “Having characterized the effects of social influence at the individual level, we now scale up to the collective level and study how repeated influences among many people play out at the population scale.”
    “By exploring a simple model derived from our observations, we demonstrate that the collective dynamics of opinion formation in large groups of people are driven by two major “attractors of opinion””

  • The authors state this as an assumption.

    The decision tree observed at the first round of interaction remains identical over repeated interactions.

    “Besides, another important follow-up study that should be conducted in the near future is the verification of our assumption that the decision tree observed at the first round of interaction remains identical over repeated interactions.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The empirical Twitter data sets show a bimodal shape of expressed opinions across all three considered data sets.

    “The data on x i yield the distributions of expressed opinions, P ( x ), which show a bimodal shape across all three considered data sets (see Fig. S1(a) in Ref. [47]).”

    From Modeling echo chambers and polarization dynamics in social networks (2020) · cites this paper as [2]

  • For all three Twitter topics (guncontrol, Obamacare, abortion), user engagement rises towards the extremes of opinion space.

    “Fig. 3(a) shows the average engagement, or activity a , of users as a function of their opinions x . For all three topics under consideration, the engagement rises towards the extremes of opinion space.”

    From Modeling echo chambers and polarization dynamics in social networks (2020) · cites this paper as [2]

  • The model qualitatively reproduces opinion segregation in the interaction network (echo chambers) observed in empirical data.

    “Both our model (Fig. 4(a)) and empirical data (Figs. 4(b) - (d)) clearly show two bright areas characterized by a high density of users with likely-minded neighbors, identifying two echo chambers corresponding to opposite opinion groups.”

    From Modeling echo chambers and polarization dynamics in social networks (2020) · cites this paper as [2]

  • The model qualitatively reproduces the observed relation between users' engagement and opinions in polarized Twitter debates: more active users tend to show more extreme opinions.

    “Compared with empirical data of polarized debates on Twitter, the model qualitatively reproduces the observed relation between users' engagement and opinions”

    From Modeling echo chambers and polarization dynamics in social networks (2020) · cites this paper as [2]

  • Several empirical features of social networks characterized by echo chambers and their relations to opinion polarization have not been addressed within a unified modeling framework.

    “Although, echo chambers and modular network structures were previously also related to homophily [29, 30], several empirical features of social networks characterized by echo chambers [2, 16, 17, 30] and their relations to opinion polarization have not been addressed within a unified modeling framework.”

    From Modeling echo chambers and polarization dynamics in social networks (2020) · cites this paper as [2]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Intermediate and far opinion-distance ranges overlap

    Minor

    The stated intermediate range extends up to 1.1, while the far range starts above 1. Distances between 1 and 1.1 therefore fall into both zones.

1 of 1

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Authors
Moussaïd, M., Kämmer, J. E., Analytis, P. P., & Neth, H.
Affiliations
  • Max Planck Institute for Human Development (DE)
  • Max Planck Society (DE)
Corresponding author
Moussaïd, Mehdi
ORCID
Venue
PLoS ONE
Publisher
Public Library of Science (PLoS)
Published
2013-11-05
Volume
8
Issue
11
Pages
e78433
ISSN
1932-6203 (ISSN-L)
DOI
10.1371/journal.pone.0078433
PMC
PMC3818331
OpenAlex
W2019976298
Semantic Scholar
4fb20ba0e882ba9a92952c3e333407327a7f1d8f
Cited by
407
References
52
Citations by year
2026: 29 · 2025: 56 · 2024: 40 · 2023: 36 · 2022: 38 · 2021: 37 · 2020: 43 · 2019: 37 · 2018: 24 · 2017: 28 · 2016: 18 · 2015: 15 · 2014: 5 · 2013: 1
FWCI
9.17
Type
journal article
Language
en
Open access
Licence
Locations
  • PLoS ONE (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • Max Planck Digital Library (submittedVersion, other-oa)
  • Figshare (submittedVersion, cc-by)
  • MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
Max-Planck-Gesellschaft
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Opinion Dynamics and Social Influence
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
  • Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
Keywords
social influence, opinion formation, peer influence, influence maps, tipping points, attractors, collective dynamics, confidence, public opinion, herding behavior, diffusion of innovations
MeSH terms
Adolescent, Adult, Attitude, Conflict, Psychological, Culture, Expert Testimony, Female, Humans, Judgment, Male, Models, Psychological, Peer Group, Public Opinion

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-09.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-09.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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