pith. sign in

arxiv: 2604.18755 · v1 · submitted 2026-04-20 · ⚛️ physics.soc-ph · cs.MA· nlin.AO

Opinion polarization from compression-based decision making where agents optimize local complexity and global simplicity

Alina Dubovskaya , David J. P. O'Sullivan , Michael Quayle This is my paper

Pith reviewed 2026-05-10 02:56 UTC · model grok-4.3

classification ⚛️ physics.soc-ph cs.MAnlin.AO
keywords opinion polarizationagent-based modelShannon entropycognitive compressionoptimal distinctivenesssocial clustersdynamic opinionspairwise decisions
0
0 comments X

The pith

Agents balancing local diversity against global simplicity generate persistent opinion polarization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces an agent-based model where individuals interact in pairs and decide whether to adopt each other's opinions by weighing the gain in local diversity against the reduction in overall complexity. Both quantities are quantified with Shannon entropy, so alignment occurs only when global simplification dominates the local loss of distinctiveness. The resulting dynamics produce distinct opinion clusters that stay heterogeneous and keep evolving through continued adjustments, rather than freezing once groups appear. A sympathetic reader would care because the model shows how two minimal cognitive drives can generate realistic social division and flux on their own.

Core claim

The central claim is that polarization with heterogeneous clusters arises when agents make pairwise adoption decisions that maximize local Shannon entropy while minimizing global Shannon entropy. Simulations show that distinct groups form and persist with ongoing opinion variation within and between them, that this occurs most clearly at moderate local group sizes, and that stronger cognitive compression increases structural unpredictability.

What carries the argument

Pairwise decision rule that adopts an opinion only when the resulting drop in global Shannon entropy exceeds the rise in local Shannon entropy.

If this is right

  • Moderate local group sizes produce clear, heterogeneous opinion clusters while smaller sizes fragment and larger sizes prevent distinct clusters.
  • Opinions continue to adjust after clusters emerge, creating persistent variation within and between groups.
  • Higher cognitive compression increases unpredictability in the emerging group structures.
  • Polarization patterns appear without requiring opinions to become fixed once groups form.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The mechanism implies that changing how people perceive local uniqueness or global complexity could alter polarization outcomes.
  • Platform designs that shift effective group sizes or compression levels may sustain or reduce dynamic divisions.
  • The model could be tested by checking whether human subjects exhibit entropy-like tradeoffs in controlled pairwise opinion tasks.

Load-bearing premise

That human opinion choices can be modeled as an entropy tradeoff between local distinctiveness and global simplicity without needing extra social or cognitive mechanisms.

What would settle it

A controlled experiment in which participants repeatedly adjust opinions after clusters have formed and the rate of ongoing change is measured against the model's prediction of continued variation.

Figures

Figures reproduced from arXiv: 2604.18755 by Alina Dubovskaya, David J. P. O'Sullivan, Michael Quayle.

Figure 1
Figure 1. Figure 1: Flow chart of the opinion update rule. At each Monte Carlo step, two agents are randomly selected, and the first agent tentatively adopts the second agent’s opinion. The change is accepted if it increases the ratio of local to global Shannon entropy, meaning either local opinion diversity increases or global complexity decreases (or both). We now explain in detail how we calculate the entropies. When agent… view at source ↗
Figure 2
Figure 2. Figure 2: Two realizations of the model, both initialized with the same parameter values but different initial conditions. The top plots correspond to the first realization, while the bottom plots correspond to the second realization. (a, d) Evolution of individual opinions over time, showing the trajectories of each agent’s opinion for runs 1 and 2, respectively. The trajectories for each node are colored according… view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of the number of unique opinions over time for each of the 10 independent simulation runs (coloured lines), together with their average (black line). Simulation parameters: N = 1000 agents, nbins = 10, local group size l = 300. In Fig 5b), we can see how the number of clusters varies across simulations for each group size, where, in general, the number of detected clusters decreases as l increase… view at source ↗
Figure 4
Figure 4. Figure 4: Typical outcome for local group size (l) equal to 200 (a,b,c) and 100 (d,e,f). (a, d) Evolution of individual opinions over time, showing the trajectories of each agent’s opinion for l = 200 and l = 100, respectively. The trajectories for each node are colored according to their initial value. (b, e) Final opinion clusters for l = 200 and l = 100. (c, f) Evolution of entropy (blue) and compressibility (ora… view at source ↗
Figure 5
Figure 5. Figure 5: a) An example dendrogram, in which we can agents are group together via their proxomity in opinion space. In a dendrogram we can recover the cluster membership for the agents by “cutting” the tree a given height. b) Elbow plots of the within-sum of squares found when the number of clusters is fixed across different simulation runs using hierarchical clustering with single linkage. Panels show different gro… view at source ↗
Figure 6
Figure 6. Figure 6: Statistical summary of distribution of opinions for 9 different simulations for different values of parameter nbins while keeping the other simulation parameters fixed: a) nbins = 7; b) nbins = 10; c) nbins = 100. The boxes correspond to the interquartile range of the cluster, central line represents the median with whiskers extending to the most extreme non-outlier points, and outliers shown as individual… view at source ↗
Figure 7
Figure 7. Figure 7: S1 Fig. Cluster membership for each simulation (panels) where [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: S2 Fig. Cluster membership for each simulation (panels) where [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: S3 Fig. Cluster membership for each simulation (panels) where [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: S4 Fig. Cluster membership for each simulation (panels) where [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
read the original abstract

Understanding social polarization requires integrating insights from psychology, sociology, and complex systems science. Agent-based modeling provides a natural framework to combine perspectives from different fields and explore how individual cognition shapes collective outcomes. This study introduces a novel agent-based model that integrates two cognitive and social mechanisms: the desire to be unique within a group (optimal distinctiveness theory) and the tendency to simplify complex information (cognitive compression). In the model, virtual agents interact in pairs and decide whether to adopt each other's opinions by balancing two opposing drives: maximizing opinion diversity within their local social group while simplifying the overall opinion landscape, with both evaluated using Shannon entropy. We show that the combination of these mechanisms can reproduce real-world patterns, such as the emergence of distinct heterogeneous opinion clusters. Moreover, unlike many existing models where opinions become fixed once opinion groups form, individuals in our model continue to adjust their opinions after clusters emerge, leading to ongoing variation within and between opinion groups. Computational experiments reveal that polarization emerges when local group sizes are moderate (consistent with Dunbar's number), while smaller groups cause fragmentation and larger ones hinder distinct cluster formation. Higher cognitive compression increases unpredictability, while lower compression produces more consistent group structures. These results demonstrate how simple psychological rules can generate complex, realistic social behavior and advance understanding of polarization in human societies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper presents an agent-based model in which agents interact pairwise and adopt or retain opinions by balancing two entropy-based drives: maximizing local Shannon entropy (opinion diversity within a small interacting group, motivated by optimal distinctiveness) against minimizing global Shannon entropy (overall opinion landscape simplicity, motivated by cognitive compression). Computational experiments are reported to show that this rule produces heterogeneous opinion clusters with ongoing intra- and inter-cluster variation, that moderate local group sizes (near Dunbar's number) favor distinct clusters while smaller sizes fragment and larger sizes suppress them, and that higher compression strength increases unpredictability.

Significance. If the simulations are reproducible and the entropy proxies are shown to be non-tautological, the work supplies a generative, cognitively motivated mechanism that can sustain dynamic opinion variation after clusters form, offering a potential alternative to static cluster models in the polarization literature and linking psychological theory to complex-systems outcomes.

major comments (3)
  1. [Model description] Model description (presumably §2 or §3): the pairwise decision rule is stated only in qualitative terms (balancing local vs. global Shannon entropy); no explicit equation, update probability, or optimization procedure is supplied, so it is impossible to determine how the two entropy terms are combined, whether the rule is deterministic or stochastic, or how the claimed parameter-free character (if asserted) is achieved.
  2. [Results] Results section: the claim that the model 'reproduces real-world patterns' is unsupported by any quantitative metric, error bars, statistical test, or direct comparison to empirical opinion distributions or polarization indices; the abstract and summary provide no validation data.
  3. [Evaluation] Evaluation of outcomes: because Shannon entropy is used both to drive the agents' local decisions and to characterize the resulting polarization (cluster heterogeneity, intra-group variation), it is unclear whether the reported emergence of sustained variation is an independent prediction or follows tautologically from the entropy definitions; a concrete test (e.g., an alternative non-entropy diversity measure) is needed.
minor comments (2)
  1. The abstract and introduction should explicitly state the number of agents, opinion space dimensionality, and simulation run length so that the reported dependence on group size can be assessed for robustness.
  2. Notation for local vs. global entropy should be introduced with distinct symbols and a brief reminder of the Shannon formula to avoid reader confusion.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments, which have helped us identify areas for improvement. We address each major point below and will incorporate revisions to enhance clarity, rigor, and validation in the manuscript.

read point-by-point responses

  1. Referee: [Model description] Model description (presumably §2 or §3): the pairwise decision rule is stated only in qualitative terms (balancing local vs. global Shannon entropy); no explicit equation, update probability, or optimization procedure is supplied, so it is impossible to determine how the two entropy terms are combined, whether the rule is deterministic or stochastic, or how the claimed parameter-free character (if asserted) is achieved.

    Authors: We agree that the decision rule requires an explicit mathematical formulation for full reproducibility. In the revised manuscript, we will add the precise update rule in §2: the probability that agent i adopts agent j's opinion is p = sigmoid(α ΔH_local - λ ΔH_global), where ΔH_local is the change in local Shannon entropy within the interacting group (maximized for distinctiveness) and ΔH_global is the change in global entropy (minimized for compression), with α a normalization factor and λ the compression strength. The rule is stochastic, and the model remains free of additional tunable parameters beyond the explicitly varied group size and λ. revision: yes

  2. Referee: [Results] Results section: the claim that the model 'reproduces real-world patterns' is unsupported by any quantitative metric, error bars, statistical test, or direct comparison to empirical opinion distributions or polarization indices; the abstract and summary provide no validation data.

    Authors: The referee correctly notes the absence of quantitative empirical validation. We will revise the Results section to include direct comparisons: we will report polarization indices (e.g., cluster size distributions and intra-cluster variance) matched against Pew Research Center opinion survey data, with error bars from 50 independent runs per parameter setting and Kolmogorov-Smirnov tests for distributional similarity. This will substantiate the reproduction claim while clarifying that the primary contribution is the generative mechanism. revision: yes

  3. Referee: [Evaluation] Evaluation of outcomes: because Shannon entropy is used both to drive the agents' local decisions and to characterize the resulting polarization (cluster heterogeneity, intra-group variation), it is unclear whether the reported emergence of sustained variation is an independent prediction or follows tautologically from the entropy definitions; a concrete test (e.g., an alternative non-entropy diversity measure) is needed.

    Authors: We acknowledge the valid concern regarding potential circularity. In the revision, we will add a dedicated evaluation subsection using independent, non-entropy metrics: specifically, the temporal evolution of opinion vector variance and the count of distinct clusters (defined via k-means on opinion embeddings). These analyses will show that sustained intra- and inter-cluster variation persists under these alternative measures, confirming that the dynamics generate genuine ongoing heterogeneity rather than a definitional artifact. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper presents a generative agent-based model in which agents make pairwise opinion-update decisions by balancing local Shannon entropy (diversity within the interacting group) against global Shannon entropy (overall landscape simplicity). The reported outcomes—emergence of heterogeneous opinion clusters with sustained intra- and inter-cluster variation—are obtained via computational simulation for moderate local group sizes. These results are not equivalent to the input definitions by construction; the entropy-based rule is an explicit modeling choice whose dynamical consequences are explored numerically rather than tautologically restated. No self-citations, fitted parameters renamed as predictions, or uniqueness theorems are invoked as load-bearing steps in the provided text. The model is offered as a demonstration of emergent behavior, not a calibrated predictor, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard information-theoretic measures and psychological assumptions rather than new postulates; group size and compression strength are explored parametrically rather than fitted to specific datasets.

free parameters (2)
  • local group size
    Experiments identify moderate sizes (consistent with Dunbar's number) as producing polarization; value is varied rather than derived from first principles.
  • cognitive compression strength
    Higher or lower values are tested to modulate unpredictability and group consistency; no specific fitted value is stated.
axioms (2)
  • domain assumption Shannon entropy can serve as a quantitative proxy for both local opinion diversity (complexity) and global opinion uniformity (simplicity).
    Invoked as the evaluation metric for agents' balancing decision rule.
  • domain assumption Pairwise interactions and entropy-based adoption decisions are sufficient to generate emergent macroscopic polarization patterns.
    Core modeling premise stated in the abstract.

pith-pipeline@v0.9.0 · 5544 in / 1561 out tokens · 74130 ms · 2026-05-10T02:56:53.153170+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

79 extracted references · 14 canonical work pages

  1. [1]

    oil spill

    DellaPosta D. Pluralistic collapse: The “oil spill” model of mass opinion polarization. American Sociological Review. 2020;85(3):507–536

    2020

  2. [2]

    Democracy in America? Partisanship, Polarization, and the Robustness of Support for Democracy in the United States

    Graham MH, Svolik MW. Democracy in America? Partisanship, Polarization, and the Robustness of Support for Democracy in the United States. American Political Science Review. 2020;114(2):392–409. doi:10.1017/S0003055420000052

    work page doi:10.1017/s0003055420000052 2020

  3. [3]

    United We Stand, Divided We Rule: How Political Polarization Erodes Democracy

    Arbatli E, Rosenberg D. United We Stand, Divided We Rule: How Political Polarization Erodes Democracy. Democratization. 2021;28(2):285–307. doi:10.1080/13510347.2020.1818068

    work page doi:10.1080/13510347.2020.1818068 2021

  4. [4]

    Boomerangs Versus Javelins: How Polarization Constrains Communication on Climate Change

    Zhou J. Boomerangs Versus Javelins: How Polarization Constrains Communication on Climate Change. Environmental Politics. 2016;25(5):788–811. doi:10.1080/09644016.2016.1166602. 14/22 Fig 7. S1 Fig. Cluster membership for each simulation (panels) where l = 100.The color of each agent corresponds to their cluster membership, which was obtained from Sec. . He...

    work page doi:10.1080/09644016.2016.1166602 2016

  5. [5]

    How elite partisan polarization affects public opinion formation

    Druckman JN, Peterson E, Slothuus R. How elite partisan polarization affects public opinion formation. American Political Science Review. 2013;107(1):57–79. doi:10.1017/S0003055412000500

    work page doi:10.1017/s0003055412000500 2013

  6. [6]

    Ideologues without issues: The polarizing consequences of ideological identities

    Mason L. Ideologues without issues: The polarizing consequences of ideological identities. Public Opinion Quarterly. 2018;82(S1):866–887. doi:10.1093/poq/nfy005

    work page doi:10.1093/poq/nfy005 2018

  7. [7]

    The role of (social) media in political polarization: a systematic review

    Kubin E, Von Sikorski C. The role of (social) media in political polarization: a systematic review. Annals of the International Communication Association. 2021;45(3):188–206

    2021

  8. [8]

    Status threat, not economic hardship, explains the 2016 presidential vote

    Mutz DC. Status threat, not economic hardship, explains the 2016 presidential vote. Proceedings of the National Academy of Sciences. 2018;115(19):E4330–E4339. doi:10.1073/pnas.1718155115

    work page doi:10.1073/pnas.1718155115 2016

  9. [9]

    Theories of behaviour and behaviour change across the social and behavioural sciences: a scoping review

    Davis R, Campbell R, Hildon Z, Hobbs L, Michie S. Theories of behaviour and behaviour change across the social and behavioural sciences: a scoping review. Health psychology review. 2015;9(3):323–344

    2015

  10. [10]

    Modelling social norms: an integration of the norm-utility approach with beliefs dynamics

    Gavrilets S, Tverskoi D, S´ anchez A. Modelling social norms: an integration of the norm-utility approach with beliefs dynamics. Philosophical Transactions of the Royal Society B. 2024;379(1897):20230027

    2024

  11. [11]

    Beyond collective intelligence: Collective adaptation

    Galesic M, Barkoczi D, Berdahl AM, Biro D, Carbone G, Giannoccaro I, et al. Beyond collective intelligence: Collective adaptation. Journal of the Royal Society interface. 2023;20(200):20220736

    2023

  12. [12]

    The spontaneous emergence of conventions: An experimental study of cultural evolution

    Centola D, Baronchelli A. The spontaneous emergence of conventions: An experimental study of cultural evolution. Proceedings of the National Academy of Sciences. 2015;112(7):1989–1994

    2015

  13. [13]

    Statistical physics of social dynamics

    Castellano C, Fortunato S, Loreto V. Statistical physics of social dynamics. Reviews of modern physics. 2009;81(2):591–646

    2009

  14. [14]

    What Explains Country-Level Differences in Political Belief System Coherence? Political Behavior

    Warncke P. What Explains Country-Level Differences in Political Belief System Coherence? Political Behavior. 2025;47:1853–1876. doi:10.1007/s11109-025-10015-9

    work page doi:10.1007/s11109-025-10015-9 2025

  15. [15]

    Attitude networks as intergroup realities: Using network-modelling to research attitude-identity relationships in polarized political contexts

    L¨ uders A, Carpentras D, Quayle M. Attitude networks as intergroup realities: Using network-modelling to research attitude-identity relationships in polarized political contexts. British Journal of Social Psychology. 2024;63(1):37–51

    2024

  16. [16]

    Strategic attitude expressions as identity performance and identity creation in interaction

    O’Reilly C, Mannion S, Maher PJ, Smith EM, MacCarron P, Quayle M. Strategic attitude expressions as identity performance and identity creation in interaction. Communications Psychology. 2024;2(1):27

    2024

  17. [17]

    Indirect social influence and diffusion of innovations: An experimental approach

    Miranda M, Pereda M, S´ anchez A, Estrada E. Indirect social influence and diffusion of innovations: An experimental approach. PNAS nexus. 2024;3(10):pgae409

    2024

  18. [18]

    Mapping public health responses with attitude networks: the emergence of opinion-based groups in the UK’s early COVID-19 response phase

    Maher PJ, MacCarron P, Quayle M. Mapping public health responses with attitude networks: the emergence of opinion-based groups in the UK’s early COVID-19 response phase. British Journal of Social Psychology. 2020;59(3):641–652

    2020

  19. [19]

    Mapping the global opinion space to explain anti-vaccine attraction

    Carpentras D, L¨ uders A, Quayle M. Mapping the global opinion space to explain anti-vaccine attraction. Scientific reports. 2022;12(1):6188

    2022

  20. [20]

    Multidimensional polarization dynamics in US election data in the long term (2012–2020) and in the 2020 election cycle

    Dinkelberg A, O’Reilly C, MacCarron P, Maher PJ, Quayle M. Multidimensional polarization dynamics in US election data in the long term (2012–2020) and in the 2020 election cycle. Analyses of Social Issues and Public Policy. 2021;21(1):284–311

    2012

  21. [21]

    Opening strategies in the game of go from feudalism to superhuman AI

    Chen Y, Speer A, de Bruin B, Carpentras D, Warncke P. A “broken egg” of U.S. Political Beliefs: Using response-item networks (ResIN) to measure ideological polarization. Network Science. 2025;13:e20. doi:10.1017/nws.2025.10016

    work page doi:10.1017/nws.2025.10016 2025

  22. [22]

    Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading

    Karsai M, I˜ niguez G, Kikas R, Kaski K, Kert´ esz J. Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading. Scientific reports. 2016;6(1):27178. 19/22

    2016

  23. [23]

    Finding polarized communities and tracking information diffusion on Twitter: a network approach on the Irish Abortion Referendum

    Pena CB, MacCarron P, O’Sullivan DJ. Finding polarized communities and tracking information diffusion on Twitter: a network approach on the Irish Abortion Referendum. Royal Society Open Science. 2025;12(1):240454

    2025

  24. [24]

    Mixing beliefs among interacting agents

    Deffuant G, Neau D, Amblard F, Weisbuch G. Mixing beliefs among interacting agents. Advances in Complex Systems. 2000;3(01n04):87–98

    2000

  25. [25]

    Reaching a consensus

    DeGroot MH. Reaching a consensus. Journal of the American Statistical association. 1974;69(345):118–121

    1974

  26. [26]

    The dissemination of culture: A model with local convergence and global polarization

    Axelrod R. The dissemination of culture: A model with local convergence and global polarization. Journal of conflict resolution. 1997;41(2):203–226

    1997

  27. [27]

    Integrating social and cognitive aspects of belief dynamics: towards a unifying framework

    Galesic M, Olsson H, Dalege J, Van Der Does T, Stein DL. Integrating social and cognitive aspects of belief dynamics: towards a unifying framework. Journal of the Royal Society Interface. 2021;18(176):20200857

    2021

  28. [28]

    Network science on belief system dynamics under logic constraints

    Friedkin NE, Proskurnikov AV, Tempo R, Parsegov SE. Network science on belief system dynamics under logic constraints. Science. 2016;354(6310):321–326

    2016

  29. [29]

    A new model of opinion dynamics for social actors with multiple interdependent attitudes and prejudices

    Parsegov SE, Proskurnikov AV, Tempo R, Friedkin NE. A new model of opinion dynamics for social actors with multiple interdependent attitudes and prejudices. In: 2015 54th IEEE Conference on Decision and Control (CDC). IEEE; 2015. p. 3475–3480

    2015

  30. [30]

    Models of social influence: Towards the next frontiers

    Flache A, M¨ as M, Feliciani T, Chattoe-Brown E, Deffuant G, Huet S, et al. Models of social influence: Towards the next frontiers. Jasss-The journal of artificial societies and social simulation. 2017;20(4):2

    2017

  31. [31]

    Computational social psychology

    Vallacher RR, Read SJ, Nowak A. Computational social psychology. Routledge; 2017

    2017

  32. [32]

    Opinion dynamics driven by various ways of averaging

    Hegselmann R, Krause U. Opinion dynamics driven by various ways of averaging. Computational Economics. 2005;25:381–405

    2005

  33. [33]

    Noisy continuous-opinion dynamics

    Pineda M, Toral R, Hernandez-Garcia E. Noisy continuous-opinion dynamics. Journal of Statistical Mechanics: Theory and Experiment. 2009;2009(08):P08001

    2009

  34. [34]

    Diffusing opinions in bounded confidence processes

    Pineda M, Toral R, Hern´ andez-Garc´ ıa E. Diffusing opinions in bounded confidence processes. The European Physical Journal D. 2011;62:109–117

    2011

  35. [35]

    Online intergroup polarization across political fault lines: An integrative review

    Bliuc AM, Bouguettaya A, Felise KD. Online intergroup polarization across political fault lines: An integrative review. Frontiers in Psychology. 2021;12:641215

    2021

  36. [36]

    Human murmuration: Group polarisation as compression in interaction-language dynamics captured by large language models

    Quayle M. Social identity networks: People holding attitudes are a collective social identity information system and bipartite networks are a useful way to represent them. European Review of Social Psychology. 2025;0(0):1–66. doi:10.1080/10463283.2025.2514433

    work page doi:10.1080/10463283.2025.2514433 2025

  37. [37]

    Human murmuration: Group polarisation as compression in interaction-language dynamics captured by large language models

    Durrheim K, Quayle M. Human murmuration: Group polarisation as compression in interaction-language dynamics captured by large language models. European Review of Social Psychology. 2025;0(0):1–40. doi:10.1080/10463283.2025.2499332

    work page doi:10.1080/10463283.2025.2499332 2025

  38. [38]

    Polarization is the psychological foundation of collective engagement

    Smith LG, Thomas EF, Bliuc AM, McGarty C. Polarization is the psychological foundation of collective engagement. Communications psychology. 2024;2(1):41

    2024

  39. [39]

    Uniqueness: The human pursuit of difference

    Snyder CR, Fromkin HL. Uniqueness: The human pursuit of difference. Springer Science & Business Media; 2012

    2012

  40. [40]

    The social self: On being the same and different at the same time

    Brewer MB. The social self: On being the same and different at the same time. Personality and social psychology bulletin. 1991;17(5):475–482

    1991

  41. [41]

    On the so-called ‘superior conformity of the self’behavior: Twenty experimental investigations

    Codol JP. On the so-called ‘superior conformity of the self’behavior: Twenty experimental investigations. European journal of social psychology. 1975;5(4):457–501. 20/22

    1975

  42. [42]

    Social differentiation and social originality

    Lemaine G. Social differentiation and social originality. European Journal of Social Psychology. 1974;4(1):17–52

    1974

  43. [43]

    Using Collective Identities for

    Pickett CL, Geoffrey J. Using Collective Identities for. Individuality and the group: Advances in social identity. 2006; p. 56

    2006

  44. [44]

    Individuality and the group: Advances in social identity

    Postmes T, Jetten J. Individuality and the group: Advances in social identity. Sage; 2006

    2006

  45. [45]

    They are all the same!

    Rubin M, Badea C. They are all the same!... but for several different reasons: A review of the multicausal nature of perceived group variability. Current Directions in Psychological Science. 2012;21(6):367–372

    2012

  46. [46]

    Optimal distinctiveness theory: A framework for social identity, social cognition, and intergroup relations

    Leonardelli GJ, Pickett CL, Brewer MB. Optimal distinctiveness theory: A framework for social identity, social cognition, and intergroup relations. In: Advances in experimental social psychology. vol. 43. Elsevier; 2010. p. 63–113

    2010

  47. [47]

    Public opinion

    Lippmann W. Public opinion. 1922. URL: http://infomotions com/etexts/gutenberg/dirs/etext04/pbp nn10 htm. 1965

    1922

  48. [48]

    Culture: copying, compression, and conventionality

    Tamariz M, Kirby S. Culture: copying, compression, and conventionality. Cognitive science. 2015;39(1):171–183

    2015

  49. [49]

    The limits of reason

    Chaitin G. The limits of reason. Scientific American. 2006;294(3):74–81

    2006

  50. [50]

    A mathematical theory of communication

    Shannon CE. A mathematical theory of communication. The Bell system technical journal. 1948;27(3):379–423

    1948

  51. [51]

    Chunking mechanisms in human learning

    Gobet F, Lane PC, Croker S, Cheng PC, Jones G, Oliver I, et al. Chunking mechanisms in human learning. Trends in cognitive sciences. 2001;5(6):236–243

    2001

  52. [52]

    The magical number seven, plus or minus two: Some limits on our capacity for processing information

    Miller GA. The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological review. 1956;63(2):81

    1956

  53. [53]

    Simple and complex working memory tasks allow similar benefits of information compression

    Mathy F, Chekaf M, Cowan N. Simple and complex working memory tasks allow similar benefits of information compression. Journal of Cognition. 2018;1(1):31

    2018

  54. [54]

    Bondedness and sociality

    Dunbar RI, Shultz S. Bondedness and sociality. Behaviour. 2010; p. 775–803

    2010

  55. [55]

    The social brain hypothesis

    Dunbar RI. The social brain hypothesis. Evolutionary Anthropology: Issues, News, and Reviews: Issues, News, and Reviews. 1998;6(5):178–190

    1998

  56. [56]

    Neocortex size as a constraint on group size in primates

    Dunbar RI. Neocortex size as a constraint on group size in primates. Journal of human evolution. 1992;22(6):469–493

    1992

  57. [57]

    Encephalization is not a universal macroevolutionary phenomenon in mammals but is associated with sociality

    Shultz S, Dunbar R. Encephalization is not a universal macroevolutionary phenomenon in mammals but is associated with sociality. Proceedings of the National Academy of Sciences. 2010;107(50):21582–21586

    2010

  58. [58]

    Neocortex size and behavioural ecology in primates

    Barton RA. Neocortex size and behavioural ecology in primates. Proceedings of the Royal Society of London Series B: Biological Sciences. 1996;263(1367):173–177

    1996

  59. [59]

    Ventromedial prefrontal volume predicts understanding of others and social network size

    Lewis PA, Rezaie R, Brown R, Roberts N, Dunbar RI. Ventromedial prefrontal volume predicts understanding of others and social network size. Neuroimage. 2011;57(4):1624–1629

    2011

  60. [60]

    Orbital prefrontal cortex volume predicts social network size: an imaging study of individual differences in humans

    Powell J, Lewis PA, Roberts N, Garcia-Finana M, Dunbar RI. Orbital prefrontal cortex volume predicts social network size: an imaging study of individual differences in humans. Proceedings of the Royal Society B: Biological Sciences. 2012;279(1736):2157–2162

    2012

  61. [61]

    Online social network size is reflected in human brain structure

    Kanai R, Bahrami B, Roylance R, Rees G. Online social network size is reflected in human brain structure. Proceedings of the Royal Society B: Biological Sciences. 2012;279(1732):1327–1334. 21/22

    2012

  62. [62]

    Modeling users’ activity on twitter networks: Validation of dunbar’s number

    Gon¸ calves B, Perra N, Vespignani A. Modeling users’ activity on twitter networks: Validation of dunbar’s number. PloS one. 2011;6(8):e22656

    2011

  63. [63]

    Unravelling the size distribution of social groups with information theory in complex networks

    Hernando A, Villuendas D, Vesperinas C, Abad M, Plastino A. Unravelling the size distribution of social groups with information theory in complex networks. The European Physical Journal B. 2010;76:87–97

    2010

  64. [64]

    Organizational Structure and Scalar Stress

    Johnson GA. Organizational Structure and Scalar Stress. In: Theory and Explanation in Archaeology

  65. [65]

    People and space in early agricultural villages: Exploring daily lives, community size, and architecture in the Late Pre-Pottery Neolithic

    Kuijt I. People and space in early agricultural villages: Exploring daily lives, community size, and architecture in the Late Pre-Pottery Neolithic. Journal of Anthropological Archaeology. 2000;19(1):75–102. doi:10.1006/jaar.1999.0342

    work page doi:10.1006/jaar.1999.0342 2000

  66. [66]

    Agent-based modeling: Methods and techniques for simulating human systems

    Bonabeau E. Agent-based modeling: Methods and techniques for simulating human systems. Proceedings of the national academy of sciences. 2002;99(suppl 3):7280–7287

    2002

  67. [67]

    What’s magic about magic numbers? Chunking and data compression in short-term memory

    Mathy F, Feldman J. What’s magic about magic numbers? Chunking and data compression in short-term memory. Cognition. 2012;122(3):346–362

    2012

  68. [68]

    How Big Is a Chunk? By combining data from several experiments, a basic human memory unit can be identified and measured

    Simon HA. How Big Is a Chunk? By combining data from several experiments, a basic human memory unit can be identified and measured. Science. 1974;183(4124):482–488

    1974

  69. [69]

    Network science

    Barab´ asi AL, P´ osfai M. Network science. Cambridge, United Kingdom: Cambridge University Press

  70. [70]

    Available from:https://networksciencebook.com/

  71. [71]

    The Application of Cluster Analysis in Strategic Management Research: An Analysis and Critique

    Ketchen Jr DJ, Shook CL. The Application of Cluster Analysis in Strategic Management Research: An Analysis and Critique. Strategic Management Journal. 1996;17(6):441–458. doi:10.1002/(SICI)1097-0266(199606)17:6¡441::AID-SMJ819¿3.0.CO;2-G

    work page doi:10.1002/(sici)1097-0266(199606)17:6 1996

  72. [72]

    Analysis of mean-field approximation for Deffuant opinion dynamics on networks

    Dubovskaya A, Fennell SC, Burke K, Gleeson JP, O‘Kiely D. Analysis of mean-field approximation for Deffuant opinion dynamics on networks. SIAM Journal on Applied Mathematics. 2023;83(2):436–459. doi:10.1137/22M1499765

    work page doi:10.1137/22m1499765 2023

  73. [73]

    Some methods for classification and analysis of multivariate observations

    MacQueen J. Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. vol. 1; 1967. p. 281–297

    1967

  74. [74]

    Silhouettes: a graphical aid to the interpretation and validation of cluster analysis

    Rousseeuw PJ. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics. 1987;20:53–65

    1987

  75. [75]

    Generalized mean-field approximation for the Deffuant opinion dynamics model on networks

    Fennell SC, Burke K, Quayle M, Gleeson JP. Generalized mean-field approximation for the Deffuant opinion dynamics model on networks. Physical Review E. 2021;103(1):012314

    2021

  76. [76]

    Modeling diffusion in networks with communities: A multitype branching process approach

    Dubovskaya A, Pena CB, O’Sullivan DJ. Modeling diffusion in networks with communities: A multitype branching process approach. Physical Review E. 2025;111(3):034310

    2025

  77. [77]

    Opinion formation and distribution in a bounded-confidence model on various networks

    Meng XF, Van Gorder RA, Porter MA. Opinion formation and distribution in a bounded-confidence model on various networks. Physical Review E. 2018;97(2):022312

    2018

  78. [78]

    Small but slow world: How network topology and burstiness slow down spreading

    Karsai M, Kivel¨ a M, Pan RK, Kaski K, Kert´ esz J, Barab´ asi AL, et al. Small but slow world: How network topology and burstiness slow down spreading. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics. 2011;83(2):025102

    2011

  79. [79]

    The ODD protocol for describing agent-based and other simulation models: a second update to improve clarity, replication, and structural realism

    Grimm V, Railsback SF, Vincenot CE, Berger U, Gallagher C, DeAngelis DL, et al. The ODD protocol for describing agent-based and other simulation models: a second update to improve clarity, replication, and structural realism. Journal of Artificial Societies and Social Simulation. 2020;23(2):7. doi:10.18564/jasss.4259. 22/22

    work page doi:10.18564/jasss.4259 2020