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arxiv: 1906.08772 · v1 · pith:GIE227QSnew · submitted 2019-06-20 · 💻 cs.SI · physics.soc-ph

Understanding Filter Bubbles and Polarization in Social Networks

Uthsav Chitra , Christopher Musco This is my paper

Pith reviewed 2026-05-25 18:53 UTC · model grok-4.3

classification 💻 cs.SI physics.soc-ph
keywords filter bubblespolarizationopinion dynamicsecho chamberssocial networksFriedkin-Johnsen modelnetwork administrator
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The pith

Small changes by a network administrator to reduce disagreement can create echo chambers and increase polarization.

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

The paper adds a network administrator to the Friedkin-Johnsen opinion dynamics model who makes small changes to edge weights to filter content for users. Experiments on Reddit and Twitter networks show that incentives to minimize disagreement lead to echo chambers and higher polarization even with minor adjustments. Theoretical analysis on stochastic block model graphs backs the observed sensitivity, and a slight shift in the administrator's objective can reduce the echo chamber effect while still lowering disagreement.

Core claim

Adding a network administrator who adjusts edge weights to minimize disagreement in the Friedkin-Johnsen model leads to the formation of echo chambers and increased user polarization on real Reddit and Twitter networks; the same sensitivity appears in stochastic block model graphs, and a modified objective for the administrator can mitigate the polarization increase while preserving most of the disagreement reduction.

What carries the argument

The Friedkin-Johnsen opinion dynamics model extended by a network administrator actor that adjusts edge weights to optimize an objective such as minimizing user disagreement.

If this is right

  • Echo chambers form in the network from relatively small edge changes.
  • User polarization increases as a result of the administrator's intervention.
  • The effect appears in both real networks and synthetic graphs generated from the stochastic block model.
  • A slight modification to the administrator's incentives mitigates the filter bubble effect while keeping disagreement low.

Where Pith is reading between the lines

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

  • Recommendation systems may need multiple objectives beyond disagreement reduction to avoid unintended increases in polarization.
  • The sensitivity result could be checked by applying the same edge-adjustment process to other opinion dynamics models.
  • Tracking real platform changes before and after algorithm updates would provide a direct test of the model's predictions.

Load-bearing premise

The extended Friedkin-Johnsen model with the administrator actor accurately represents how real recommendation algorithms shape opinion evolution on platforms such as Reddit and Twitter.

What would settle it

Empirical observation that small edge-weight adjustments aimed at lowering disagreement produce no increase in polarization or echo chambers in actual user interaction data.

Figures

Figures reproduced from arXiv: 1906.08772 by Christopher Musco, Uthsav Chitra.

Figure 1
Figure 1. Figure 1: Social network graphs after converging to equilibrium in the Friedkin-Johnsen opinion dynamics model. Node [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Applying network administrator dynamics to real-world social networks. Details in Section 3. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The equilibirum polarization of a SBM social network plotted as a function of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Applying regularized network administrator dynamics to real-world social networks, γ = 0.2. Details in Section 5. 5.1 Regularized Dynamics We modify the role of the network administrator by adding an L 2 regularization term to its objective function. Regularized Network Administrator Dynamics. Given initial graph G (0) = G and initial opinions z (0) = s, in each round r = 1, 2, 3, . . . • First, the users … view at source ↗
read the original abstract

Recent studies suggest that social media usage -- while linked to an increased diversity of information and perspectives for users -- has exacerbated user polarization on many issues. A popular theory for this phenomenon centers on the concept of "filter bubbles": by automatically recommending content that a user is likely to agree with, social network algorithms create echo chambers of similarly-minded users that would not have arisen otherwise. However, while echo chambers have been observed in real-world networks, the evidence for filter bubbles is largely post-hoc. In this work, we develop a mathematical framework to study the filter bubble theory. We modify the classic Friedkin-Johnsen opinion dynamics model by introducing another actor, the network administrator, who filters content for users by making small changes to the edge weights of a social network (for example, adjusting a news feed algorithm to change the level of interaction between users). On real-world networks from Reddit and Twitter, we show that when the network administrator is incentivized to reduce disagreement among users, even relatively small edge changes can result in the formation of echo chambers in the network and increase user polarization. We theoretically support this observed sensitivity of social networks to outside intervention by analyzing synthetic graphs generated from the stochastic block model. Finally, we show that a slight modification to the incentives of the network administrator can mitigate the filter bubble effect while minimally affecting the administrator's target objective, user disagreement.

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 introduces a modified Friedkin-Johnsen opinion dynamics model that includes a network administrator who adjusts edge weights to minimize a global disagreement objective. It reports that, on Reddit and Twitter networks, even small such interventions produce echo chambers and higher polarization; this sensitivity is analyzed theoretically via the stochastic block model, and a modified administrator objective is shown to reduce the effect while preserving most of the disagreement reduction.

Significance. If the central modeling and simulation results hold, the work supplies a clean mathematical framework for studying how an external actor optimizing disagreement can inadvertently amplify polarization, together with a constructive mitigation. The combination of real-network experiments and SBM analysis is a strength; the incentive-modification result is a concrete, potentially actionable contribution.

major comments (3)
  1. [§4 (real-network results)] The real-network experiments (abstract and §4) report that small edge changes produce echo chambers, yet provide no description of the optimization procedure used to solve for the administrator's edge weights, no error bars or statistical tests on the polarization outcomes, and no explicit data-selection or preprocessing rules for the Reddit/Twitter graphs. These omissions make it impossible to assess whether the reported sensitivity is robust or sensitive to post-hoc choices.
  2. [Introduction and model definition] The central claim equates the administrator's direct edge-weight interventions with the mechanism of real recommendation algorithms (content ranking or user-item scores). No mapping, equivalence argument, or validation is supplied showing that the polarization effect observed under edge modification would arise under the actual intervention types used on platforms; this assumption is load-bearing for the filter-bubble interpretation.
  3. [SBM theoretical analysis] In the SBM analysis, the quantitative measure of sensitivity (how small an intervention produces echo chambers) is not derived explicitly from the model equations; it is unclear whether the reported threshold depends on the particular choice of the administrator's objective or on the block-model parameters.
minor comments (2)
  1. [Model section] Notation for the modified Friedkin-Johnsen update rule and the administrator's objective should be collected in a single preliminary section for readability.
  2. [Figures in §4] Figure captions for the real-network polarization plots should state the number of independent runs and the precise definition of the polarization metric used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, indicating revisions where appropriate to improve clarity, reproducibility, and theoretical grounding.

read point-by-point responses

  1. Referee: [§4 (real-network results)] The real-network experiments (abstract and §4) report that small edge changes produce echo chambers, yet provide no description of the optimization procedure used to solve for the administrator's edge weights, no error bars or statistical tests on the polarization outcomes, and no explicit data-selection or preprocessing rules for the Reddit/Twitter graphs. These omissions make it impossible to assess whether the reported sensitivity is robust or sensitive to post-hoc choices.

    Authors: We agree that these details are essential for reproducibility. In the revised manuscript we will add: (i) a full description of the optimization procedure (including the solver, objective formulation, and any regularization or convergence criteria), (ii) error bars together with appropriate statistical tests on all polarization and echo-chamber metrics reported in §4, and (iii) explicit statements of the data-selection criteria, filtering steps, and preprocessing applied to the Reddit and Twitter graphs. revision: yes

  2. Referee: [Introduction and model definition] The central claim equates the administrator's direct edge-weight interventions with the mechanism of real recommendation algorithms (content ranking or user-item scores). No mapping, equivalence argument, or validation is supplied showing that the polarization effect observed under edge modification would arise under the actual intervention types used on platforms; this assumption is load-bearing for the filter-bubble interpretation.

    Authors: We acknowledge that the manuscript would benefit from a more explicit discussion of this modeling choice. We will expand the introduction to clarify that edge-weight adjustment is intended as an abstraction of how recommendation systems modulate interaction strengths, note its relation to content-ranking mechanisms, and discuss the limitations of the abstraction. A full empirical validation against platform-specific ranking algorithms lies outside the scope of the present theoretical framework, but the added discussion will make the interpretive step transparent. revision: partial

  3. Referee: [SBM theoretical analysis] In the SBM analysis, the quantitative measure of sensitivity (how small an intervention produces echo chambers) is not derived explicitly from the model equations; it is unclear whether the reported threshold depends on the particular choice of the administrator's objective or on the block-model parameters.

    Authors: We will revise the SBM section to provide an explicit derivation of the sensitivity threshold directly from the closed-form opinion-dynamics solution under the administrator's objective. The derivation will show the dependence on both the objective function and the SBM parameters (block sizes, intra- and inter-block probabilities), thereby clarifying the origin of the reported thresholds. revision: yes

Circularity Check

0 steps flagged

No significant circularity; outcomes from explicit simulations and SBM analysis

full rationale

The paper modifies the Friedkin-Johnsen model by adding an administrator who adjusts edge weights, then demonstrates echo-chamber formation via direct simulations on Reddit/Twitter networks and separate theoretical analysis on stochastic block model graphs. No derivation step reduces by the paper's own equations to a fitted parameter renamed as a prediction, nor relies on self-citation chains or ansatzes smuggled from prior work. The central results are generated from the stated dynamics and optimization rather than tautologically re-derived from inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim depends on the appropriateness of the Friedkin-Johnsen base model, the modeling choice that the administrator acts by small edge-weight perturbations, and the assumption that minimizing a global disagreement metric produces the observed clustering; no explicit free parameters or new physical entities are named in the abstract.

free parameters (1)
  • administrator intervention scale
    The magnitude of allowed edge-weight changes is a tunable parameter whose value determines whether the polarization effect appears.
axioms (1)
  • domain assumption The Friedkin-Johnsen opinion dynamics model accurately describes how opinions evolve in social networks.
    The paper modifies this classic model rather than deriving it.
invented entities (1)
  • network administrator no independent evidence
    purpose: Models the content-filtering actor that adjusts edge weights to achieve an objective.
    Introduced as an additional actor whose incentives drive the edge changes.

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Works this paper leans on

65 extracted references · 65 canonical work pages · 1 internal anchor

  1. [1]

    Community detection and stochastic block models

    Emmanuel Abbe. Community detection and stochastic block models. Foundations and Trends in Communications and Information Theory, 14(1-2):1–162, 2018

    work page 2018

  2. [2]

    Opinion dynamics with varying suscep- tibility to persuasion

    Rediet Abebe, Jon Kleinberg, David Parkes, and Charalampos E Tsourakakis. Opinion dynamics with varying suscep- tibility to persuasion. In KDD 2018, pages 1089–1098. ACM, 2018

    work page 2018

  3. [3]

    The political blogosphere and the 2004 US election: divided they blog

    Lada A Adamic and Natalie Glance. The political blogosphere and the 2004 US election: divided they blog. InProceedings of the 3rd International Workshop on Link Discovery (LinkKDD) , pages 36–43, 2005

    work page 2004

  4. [4]

    Aggarwal

    Charu C. Aggarwal. Recommender Systems: The Textbook . Springer Publishing Company, Incorporated, 1st edition,

    work page

  5. [5]

    ISBN 3319296574, 9783319296579

    work page

  6. [6]

    Maximizing the diversity of exposure in a social network

    Cigdem Aslay, Antonis Matakos, Esther Galbrun, and Aristides Gionis. Maximizing the diversity of exposure in a social network. In 2018 IEEE International Conference on Data Mining (ICDM) , pages 863–868. IEEE, 2018

    work page 2018

  7. [7]

    The ’Filter Bubble’ explains why Trump won and you didn’t see it coming

    Drake Baer. The ’Filter Bubble’ explains why Trump won and you didn’t see it coming. Science of Us, 2016

    work page 2016

  8. [8]

    How social media reduces mass political polarization

    Pablo Barberá. How social media reduces mass political polarization. evidence from germany, spain, and the us. Job Market Paper, New York University, 46, 2014

    work page 2014

  9. [9]

    Find your place: Simple distributed algorithms for community detection

    Luca Becchetti, Andrea Clementi, Emanuele Natale, Francesco Pasquale, and Luca Trevisan. Find your place: Simple distributed algorithms for community detection. In SODA 2017, pages 940–959, 2017

    work page 2017

  10. [10]

    A. Beck. On the convergence of alternating minimization for convex programming with applications to iteratively reweighted least squares and decomposition schemes. SIAM Journal on Optimization , 25(1):185–209, 2015. doi: 10.1137/13094829X. URL https://doi.org/10.1137/13094829X

    work page doi:10.1137/13094829x 2015

  11. [11]

    Bertsekas

    D.P. Bertsekas. Nonlinear Programming. Athena Scienti/f_ic, 1999. 15

    work page 1999

  12. [12]

    How bad is forming your own opinion? Games and Economic Be- havior, 92:248 – 265, 2015

    David Bindel, Jon Kleinberg, and Sigal Oren. How bad is forming your own opinion? Games and Economic Be- havior, 92:248 – 265, 2015. ISSN 0899-8256. doi: https://doi.org/10.1016/j.geb.2014.06.004. URL http://www. sciencedirect.com/science/article/pii/S0899825614001122

    work page doi:10.1016/j.geb.2014.06.004 2015

  13. [13]

    Polarized we govern?, 2014

    Sarah Binder. Polarized we govern?, 2014

    work page 2014

  14. [14]

    Boggs and Jon W

    Paul T. Boggs and Jon W. Tolle. Sequential quadratic programming. Acta Numerica , 4:1–51, 1995. doi: 10.1017/S0962492900002518

    work page doi:10.1017/s0962492900002518 1995

  15. [15]

    Your results may vary: Will the information superhighway turn into a cul-de-sac because of automated /f_ilters?The Wall Street Journal, 2011

    Paul Boutin. Your results may vary: Will the information superhighway turn into a cul-de-sac because of automated /f_ilters?The Wall Street Journal, 2011

    work page 2011

  16. [16]

    difference

    Jennifer Brundidge. Encountering “difference” in the contemporary public sphere: The contribution of the internet to the heterogeneity of political discussion networks. Journal of Communication, 60(4):680–700, 11 2010

    work page 2010

  17. [17]

    Carletti, D

    T. Carletti, D. Fanelli, S. Grolli, and A. Guarino. How to make an efficient propaganda. Europhysics Letters, 74(2):222, 2006

    work page 2006

  18. [18]

    Allison J. B. Chaney, Brandon M. Stewart, and Barbara E. Engelhardt. How algorithmic confounding in recommen- dation systems increases homogeneity and decreases utility. In Proceedings of the 12th ACM Conference on Rec- ommender Systems , RecSys ’18, pages 224–232, New York, NY, USA, 2018. ACM. ISBN 978-1-4503-5901-6. doi: 10.1145/3240323.3240370. URL htt...

    work page doi:10.1145/3240323.3240370 2018

  19. [19]

    Quantifying and minimizing risk of con/f_lict in social networks

    Xi Chen, Jefrey Lijffijt, and Tijl De Bie. Quantifying and minimizing risk of con/f_lict in social networks. In KDD 2018, pages 1197–1205, 2018

    work page 2018

  20. [20]

    The normalized friedkin-johnsen model (a work-in-progress report)

    Xi Chen, Jefrey Lijffijt, and Tijl De Bie. The normalized friedkin-johnsen model (a work-in-progress report). In ECML PKDD 2018-PhD Forum, 2018

    work page 2018

  21. [21]

    Political polarization on twitter

    Michael D Conover, Jacob Ratkiewicz, Matthew Francisco, Bruno Gonçalves, Filippo Menczer, and Alessandro Flam- mini. Political polarization on twitter. In Fifth international AAAI conference on weblogs and social media , 2011

    work page 2011

  22. [22]

    Biased assimilation, homophily, and the dynamics of polarization

    Pranav Dandekar, Ashish Goel, and David T Lee. Biased assimilation, homophily, and the dynamics of polarization. Proceedings of the National Academy of Sciences , 110(15):5791–5796, 2013

    work page 2013

  23. [23]

    Modeling opinion dynamics in social networks

    Abhimanyu Das, Sreenivas Gollapudi, and Kamesh Munagala. Modeling opinion dynamics in social networks. In Proceedings of the 7th ACM International Conference on Web Search and Data Mining , pages 403–412. ACM, 2014

    work page 2014

  24. [24]

    Davis and W

    C. Davis and W. Kahan. The rotation of eigenvectors by a perturbation. iii. SIAM Journal on Numerical Analysis , 7(1): 1–46, 1970. doi: 10.1137/0707001. URL https://doi.org/10.1137/0707001

    work page doi:10.1137/0707001 1970

  25. [25]

    Learning a linear in/f_luence model from transient opinion dynamics

    Abir De, Sourangshu Bhattacharya, Parantapa Bhattacharya, Niloy Ganguly, and Soumen Chakrabarti. Learning a linear in/f_luence model from transient opinion dynamics. InProceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management , CIKM ’14, pages 401–410, New York, NY, USA, 2014. ACM. ISBN 978-1-4503-2598-1. d...

    work page doi:10.1145/2661829.2662064 2014

  26. [26]

    Reaching a consensus

    Morris H DeGroot. Reaching a consensus. Journal of the American Statistical Association , 69(345):118–121, 1974

    work page 1974

  27. [27]

    Eugene Stanley, and Walter Quattrociocchi

    Michela Del Vicario, Antonio Scala, Guido Caldarelli, H. Eugene Stanley, and Walter Quattrociocchi. Modeling con/f_ir- mation bias and polarization. Scienti/f_ic reports, 7, 2017

    work page 2017

  28. [28]

    Apple CEO Tim Cook urges college grads to ‘push back’ against algorithms that promote the ‘things you already know, believe, or like’

    Lisa Eadicicco. Apple CEO Tim Cook urges college grads to ‘push back’ against algorithms that promote the ‘things you already know, believe, or like’. Business Insider, 2019

    work page 2019

  29. [29]

    Opinion formation games with aggrega- tion and negative in/f_luence

    Markos Epitropou, Dimitris Fotakis, Martin Hoefer, and Stratis Skoulakis. Opinion formation games with aggrega- tion and negative in/f_luence. InAlgorithmic Game Theory - 10th International Symposium, SAGT 2017, L’Aquila, Italy, September 12-14, 2017, Proceedings , pages 173–185, 2017

    work page 2017

  30. [30]

    The death of the newsfeed

    Benedict Evans. The death of the newsfeed. https://www.ben-evans.com/benedictevans/2018/4/2/the-death-of-the- newsfeed, 2018

    work page 2018

  31. [31]

    Filter bubbles, echo chambers, and online news consumption

    Seth Flaxman, Sharad Goel, and Justin M Rao. Filter bubbles, echo chambers, and online news consumption. Public Opinion Quarterly, 80(S1):298–320, 2016. 16

    work page 2016

  32. [32]

    Social in/f_luence and opinions

    Noah E Friedkin and Eugene C Johnsen. Social in/f_luence and opinions. Journal of Mathematical Sociology , 15(3-4): 193–206, 1990

    work page 1990

  33. [33]

    Balancing information exposure in social net- works

    Kiran Garimella, Aristides Gionis, Nikos Parotsidis, and Nikolaj Tatti. Balancing information exposure in social net- works. In Advances in Neural Information Processing Systems 30 (NeurIPS) , pages 4663–4671. 2017

    work page 2017

  34. [34]

    Quantifying contro- versy on social media

    Kiran Garimella, Gianmarco De Francisci Morales, Aristides Gionis, and Michael Mathioudakis. Quantifying contro- versy on social media. Trans. Soc. Comput. , 1(1):3:1–3:27, January 2018. ISSN 2469-7818. doi: 10.1145/3140565. URL http://doi.acm.org/10.1145/3140565

    work page doi:10.1145/3140565 2018

  35. [35]

    Daniel Geschke, Jan Lorenz, and Peter Holtz. The triple-/f_ilter bubble: Using agent-based modelling to test a meta- theoretical framework for the emergence of /f_ilter bubbles and echo chambers.British Journal of Social Psychology , 58 (1):129–149, 2019

    work page 2019

  36. [36]

    Opinion maximization in social networks

    Aristides Gionis, Evimaria Terzi, and Panayiotis Tsaparas. Opinion maximization in social networks. In Proceedings of the 13th SIAM International Conference on Data Mining, May 2-4, 2013. Austin, Texas, USA. , pages 387–395, 2013

    work page 2013

  37. [37]

    The polarization of contemporary american politics

    Christopher Hare and Keith T Poole. The polarization of contemporary american politics. Polity, 46(3):411–429, 2014

    work page 2014

  38. [38]

    Opinion dynamics and bounded con/f_idence: Models, analysis and simulation

    Rainer Hegselmann and Ulrich Krause. Opinion dynamics and bounded con/f_idence: Models, analysis and simulation. Journal of Arti/f_icial Societies and Social Simulation, 5:1–24, 2002

    work page 2002

  39. [39]

    Opinion dynamics and bounded con/f_idence models, analysis, and simulation

    Rainer Hegselmann, Ulrich Krause, et al. Opinion dynamics and bounded con/f_idence models, analysis, and simulation. Journal of Arti/f_icial Societies and Social Simulation, 5(3), 2002

    work page 2002

  40. [40]

    Stochastic blockmodels: First steps

    Paul W Holland, Kathryn Blackmond Laskey, and Samuel Leinhardt. Stochastic blockmodels: First steps. Social net- works, 5(2):109–137, 1983

    work page 1983

  41. [41]

    The /f_ilter bubble and its effect on online personal health information.Croatian medical journal, 57(3): 298, 2016

    Harald Holone. The /f_ilter bubble and its effect on online personal health information.Croatian medical journal, 57(3): 298, 2016

    work page 2016

  42. [42]

    Will the global village fracture into tribes? rec- ommender systems and their effects on consumer fragmentation

    Kartik Hosanagar, Daniel Fleder, Dokyun Lee, and Andreas Buja. Will the global village fracture into tribes? rec- ommender systems and their effects on consumer fragmentation. Management Science , 60(4):805–823, 2014. doi: 10.1287/mnsc.2013.1808. URL https://doi.org/10.1287/mnsc.2013.1808

    work page doi:10.1287/mnsc.2013.1808 2014

  43. [43]

    Jasper Jackson. Eli pariser: activist whose /f_ilter bubble warnings presaged Trump and Brexit: Upworthy chief warned about dangers of the internet’s echo chambers /f_ive years before 2016’s votes.The Guardian, 2017

    work page 2016

  44. [44]

    Maximizing the spread of in/f_luence through a social network

    David Kempe, Jon Kleinberg, and Éva Tardos. Maximizing the spread of in/f_luence through a social network. In KDD 2003, pages 137–146, 2003

    work page 2003

  45. [45]

    The contribution of social network sites to exposure to political difference: The relationships among snss, online political messaging, and exposure to cross-cutting perspectives

    Yonghwan Kim. The contribution of social network sites to exposure to political difference: The relationships among snss, online political messaging, and exposure to cross-cutting perspectives. Computers in Human Behavior , 27(2): 971–977, 2011

    work page 2011

  46. [46]

    Layman, Thomas M

    Geoffrey C. Layman, Thomas M. Carsey, and Juliana Menasce Horowitz. Party polarization in american politics: Char- acteristics, causes, and consequences. Annual Review of Political Science , 9(1):83–110, 2006

    work page 2006

  47. [47]

    Social media, network heterogeneity, and opinion polarization

    Jae Kook Lee, Jihyang Choi, Cheonsoo Kim, and Yonghwan Kim. Social media, network heterogeneity, and opinion polarization. Journal of communication, 64(4):702–722, 2014

    work page 2014

  48. [48]

    Lord, Lee Ross, and Mark R

    Charles G. Lord, Lee Ross, and Mark R. Lepper. Biased assimilation and attitude polarization: The effects of prior theories on subsequently considered evidence. Journal of personality and social psychology , 37(11):2098, 1979

    work page 2098

  49. [49]

    Eigenvector Computation and Community De- tection in Asynchronous Gossip Models

    Frederik Mallmann-Trenn, Cameron Musco, and Christopher Musco. Eigenvector Computation and Community De- tection in Asynchronous Gossip Models. In Proceedings of the 45th International Colloquium on Automata, Languages and Programming (ICALP), pages 159:1–159:14, 2018

    work page 2018

  50. [50]

    Measuring and moderating opinion polarization in social networks

    Antonis Matakos, Evimaria Terzi, and Panayiotis Tsaparas. Measuring and moderating opinion polarization in social networks. Data Min. Knowl. Discov., 31(5):1480–1505, September 2017. ISSN 1384-5810. doi: 10.1007/s10618-017-0527-9. URL https://doi.org/10.1007/s10618-017-0527-9

    work page doi:10.1007/s10618-017-0527-9 2017

  51. [51]

    The politicization of climate change and polarization in the american public’s views of global warming, 2001–2010

    Aaron M McCright and Riley E Dunlap. The politicization of climate change and polarization in the american public’s views of global warming, 2001–2010. The Sociological Quarterly, 52(2):155–194, 2011. 17

    work page 2001

  52. [52]

    Spectral partitioning of random graphs

    Frank McSherry. Spectral partitioning of random graphs. In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS) , page 529, 2001

    work page 2001

  53. [53]

    Minimizing controversy and disagreement in social networks

    Cameron Musco, Christopher Musco, and Charalampos Tsourakakis. Minimizing controversy and disagreement in social networks. 2018. Proceedings of the 27th International World Wide Web Conference (WWW)

    work page 2018

  54. [54]

    Exploring the /f_ilter bubble: the effect of using recommender systems on content diversity

    Tien T Nguyen, Pik-Mai Hui, F Maxwell Harper, Loren Terveen, and Joseph A Konstan. Exploring the /f_ilter bubble: the effect of using recommender systems on content diversity. In Proceedings of the 23rd International World Wide Web Conference (WWW), pages 677–686. ACM, 2014

    work page 2014

  55. [55]

    The /f_ilter bubble: What the Internet is hiding from you

    Eli Pariser. The /f_ilter bubble: What the Internet is hiding from you. Penguin UK, 2011

    work page 2011

  56. [56]

    Russian cyber hacks on us electoral system far wider than previously known

    Michael Riley and Jordan Robertson. Russian cyber hacks on us electoral system far wider than previously known. Bloomberg, June, 13, 2017

    work page 2017

  57. [57]

    News use across social media platforms: Most americans continue to get news on social media, even though many have concerns about its accuracy.Pew Research Center Report, 2018

    Elisa Shearer and Katerina Eva Matsa. News use across social media platforms: Most americans continue to get news on social media, even though many have concerns about its accuracy.Pew Research Center Report, 2018. URL https:// www.journalism.org/2018/09/10/news-use-across-social-media-platforms-2018/

    work page 2018

  58. [58]

    Disciplined Multi-Convex Programming

    Xinyue Shen, Steven Diamond, Madeleine Udell, Yuantao Gu, and Stephen Boyd. Disciplined Multi-Convex Program- ming. arXiv e-prints, art. arXiv:1609.03285, Sep 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  59. [59]

    Social media use in 2018

    Aaron Smith and Monica Andersen. Social media use in 2018. Pew Research Center Report , 2018

    work page 2018

  60. [60]

    Social networks and health

    Kirsten P Smith and Nicholas A Christakis. Social networks and health. Annu. Rev. Sociol, 34:405–429, 2008

    work page 2008

  61. [61]

    Lecture notes on spectral partitioning in a stochastic block model

    Daniel Spielman. Lecture notes on spectral partitioning in a stochastic block model. http://www.cs.yale.edu/homes/spielman/561/lect21-15.pdf., 2015

    work page 2015

  62. [62]

    Jost, Jonathan Nagler, and Joshua A

    Cristian Vaccari, Augusto Valeriani, Pablo Barberá, John T. Jost, Jonathan Nagler, and Joshua A. Tucker. Of echo chambers and contrarian clubs: Exposure to political disagreement among german and italian users of twitter. Social Media + Society , 2(3):2056305116664221, 2016. doi: 10.1177/2056305116664221. URL https://doi.org/10. 1177/2056305116664221

    work page doi:10.1177/2056305116664221 2016

  63. [63]

    Van H. Vu. Spectral norm of random matrices. Combinatorica, 27(6):721–736, 2007

    work page 2007

  64. [64]

    Wainwright

    Martin J. Wainwright. High-Dimensional Statistics: A Non-Asymptotic Viewpoint . Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 2019

    work page 2019

  65. [65]

    de Vreese, and Natali Helberger

    Frederik Zuiderveen Borgesius, Damian Trilling, Judith Moeller, Balázs Bodó, Claes H. de Vreese, and Natali Helberger. Should we worry about /f_ilter bubbles?Internet Policy Review, Journal on Internet Regulation , 5(1), 2016. 18

    work page 2016