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Cited by 288Social Media and PoliticsElectoral Systems and Political ParticipationOpinion Dynamics and Social Influence

The DOI matches its Crossref record; 122 of the 122 references it cites were found in a registry or an index; 20 of the 56 sources its claims cite were checked for support.

How digital media drive affective polarization through partisan sorting

Open access
Törnberg, Petter·2022·Proceedings of the National Academy of Sciences
DOI 10.1073/pnas.2207159119PMC PMC9586282
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Abstract

Politics has in recent decades entered an era of intense polarization. Explanations have implicated digital media, with the so-called echo chamber remaining a dominant causal hypothesis despite growing challenge by empirical evidence. This paper suggests that this mounting evidence provides not only reason to reject the echo chamber hypothesis but also the foundation for an alternative causal mechanism. To propose such a mechanism, the paper draws on the literatures on affective polarization, digital media, and opinion dynamics. From the affective polarization literature, we follow the move from seeing polarization as diverging issue positions to rooted in sorting: an alignment of differences which is effectively dividing the electorate into two increasingly homogeneous megaparties. To explain the rise in sorting, the paper draws on opinion dynamics and digital media research to present a model which essentially turns the echo chamber on its head: it is not isolation from opposing views that drives polarization but precisely the fact that digital media bring us to interact outside our local bubble. When individuals interact locally, the outcome is a stable plural patchwork of cross-cutting conflicts. By encouraging nonlocal interaction, digital media drive an alignment of conflicts along partisan lines, thus effacing the counterbalancing effects of local heterogeneity. The result is polarization, even if individual interaction leads to convergence. The model thus suggests that digital media polarize through partisan sorting, creating a maelstrom in which more and more identities, beliefs, and cultural preferences become drawn into an all-encompassing societal division.

Overview

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Written from the paper’s full text.

TL;DR

The paper proposes a computational model in which digital media drive affective polarization not through echo chambers but through nonlocal interaction that aligns local political cultures into partisan sorting. Simulations show that increasing nonlocal interaction can sharply raise sorting when influence homophily is high, while purely local interaction keeps sorting low.

Key findings

  • In example runs with high influence homophily (h = 8; n = 10, |A| = 196, c = 4, m = 10), γ = 1 quickly reaches a high sorting value ψ; γ = 0.5 rises more slowly and settles around ψ = 0.3; γ = 0 remains near the expected ψ = 0.
  • Across 8,000 simulation runs varying γ and h, low influence homophily (h = 1) produces no partisan sorting regardless of γ; high homophily (h = 8) produces a rapid increase in sorting past a threshold of nonlocal interaction; intermediate homophily (h = 4) shows bistability between low- and high-sorting end states.
  • The same general γ–ψ relationship appears on random regular, scale-free, and connected caveman networks (1,600 runs over the parameter space), though the clique-dominated caveman network requires higher γ before sorting rises.
  • With n = 10 dynamic attributes and m = 10 possible states, the chance that two groups share at least one attribute is about 65% (1 − (9/10)^10 ≈ 0.65), which can prevent sorting from reaching 1 and affects convergence probability.

Methods

  • Agent-based opinion-dynamics model: agents on a graph (primarily a two-dimensional torus lattice with Moore neighborhood), each with n dynamic attributes taking integer values 1–m and a fixed partisan attribute S (k = 2); partisanship is weighted by c = 4. Each asynchronous update selects a random agent; interlocutors are local neighbors with fraction γ replaced by nodes sampled randomly from the entire network; influence follows an urn model based on relative similarity with homophily parameter h; sorting ψ is the fraction of shared dynamic attributes among same-party agents minus that among different-party agents.
  • Simulations: 8,000 runs varying γ and h (Fig. 2 reports h = 1, 4, 8), plus 1,600 runs on three common network structures (random regular, scale-free, connected caveman). Convergence is operationalized as no update during 10 runs across the full number of agents, or after 1,000,000 iterations.
  • Analysis: final ψ as a function of γ; PCA on the matrix of distances between agents and ridgeline plots to visualize group distributions over time; grid visualizations treating dynamic attributes as a base-m number.

Limitations

  • Stated: partisan affiliation is treated as fixed, assuming it changes on a slower timescale; the model focuses on k = 2 bipolarization (though expandable to k > 2); nonlocal interlocutors are chosen without self-similarity bias, leaving selective-exposure-like bias to future research; the torus lattice is a poor representation of real-world networks, though other network structures are tested; convergence is challenging to prove analytically, so an empirically chosen stopping metric is used.
  • Stated: the model is minimal and theoretical; it does not directly measure affective polarization but uses sorting ψ as a proxy linked in the literature; no empirical validation against real-world digital media data is presented.
  • Evident: parameter choices (c = 4, h values, n = 10, m = 10, |A| = 196 or 625) and simulation stopping rules may affect results; causal claims about digital media are model-derived, not empirically tested; the paper notes academic debate about how far political divisions dominate cultural life, and cites a study finding most lifestyle preferences remain shared across the political divide.

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Integrity signals

Registry

Crossref · 10.1073/pnas.2207159119

Cites

122 of 122 references verified0 citation errors · 0 not checkable

Statistics

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Figures

Fig. 1. Three example runs over time, for three parameters of γ. ψ is measured every 5,000 steps, over 500,000 time steps. Parameters are h = 8, n = 10, |A| =196, c = 4, m = 10. As the figure shows, the run with γ = 1 quickly reaches a high ψ-value. The medium-γ population gradually increases to a ψ of 0.3. The run with completely local interaction remains near the expected ψ value of 0.
Fig. 1. Three example runs over time, for three parameters of γ. ψ is measured every 5,000 steps, over 500,000 time steps. Parameters are h = 8, n = 10, |A| =196, c = 4, m = 10. As the figure shows, the run with γ = 1 quickly reaches a high ψ-value. The medium-γ population gradually increases to a ψ of 0.3. The run with completely local interaction remains near the expected ψ value of 0.CC BY-NC-ND · PubMed Central
Fig. 2. The level of polarization (ψ) as a function of the level of nonlocal interaction (γ) when the level of influence homophily is (A) low (h = 1), (B) medium (h = 4), and (C) high (h = 8). Each dot represents the final ψ of a single run. The red line shows the LOWESS (Locally Weighted Scatterplot Smoothing) curves for the distributions. Parameters are |A| = 196, c = 4, m = 10, n = 10. As the figure shows, the level of polarization increases sharply when γ passes a certain threshold. This suggests that increasing the number of interactions with individuals outside the local network can lead to bipolarization, even given individual convergence on the microlevel. When influence homophily is in between high and low (h = 4), the system exhibits bistability: for higher values of γ, the system can end up in low-polarization or high-polarization states, depending on initial conditions and stochastic dynamics.
Fig. 2. The level of polarization (ψ) as a function of the level of nonlocal interaction (γ) when the level of influence homophily is (A) low (h = 1), (B) medium (h = 4), and (C) high (h = 8). Each dot represents the final ψ of a single run. The red line shows the LOWESS (Locally Weighted Scatterplot Smoothing) curves for the distributions. Parameters are |A| = 196, c = 4, m = 10, n = 10. As the figure shows, the level of polarization increases sharply when γ passes a certain threshold. This suggests that increasing the number of interactions with individuals outside the local network can lead to bipolarization, even given individual convergence on the microlevel. When influence homophily is in between high and low (h = 4), the system exhibits bistability: for higher values of γ, the system can end up in low-polarization or high-polarization states, depending on initial conditions and stochastic dynamics.CC BY-NC-ND · PubMed Central
Fig. 3. The model applied on three common network structures, running with otherwise the same parameters as for Fig. 2C, with 1,600 runs over the parameter space. (A) A random regular graph, generated through the algorithm described in Steger and Wormald (112). Parameters used were 196 nodes and 8 edges. (B) A scale-free network, characterized by highly uneven degree distribution with some dominant nodes, generated with the algorithm described in ref. 113, based on Barabási–Albert growth model but adding that each random edge is followed by a chance of making an edge to one of its neighbors, thus capturing clustering. Parameters used were 196 nodes, 8 edges, and 0.01 probability of adding a triangle to any given edge. (C) The connected caveman, a highly cliqued graph structure used also in DellaPosta et al. (58), with 14 cliques of 14 nodes and 0.05 probability for reconnecting a given edge. As can be seen, strikingly, all network structures show the same general relationship between γ and ψ but with differences in the immediacy of the rise of sorting as a function of nonlocal interactions. In particular, the clique-dominated network in C requires a higher value of γ to become sorted.
Fig. 3. The model applied on three common network structures, running with otherwise the same parameters as for Fig. 2C, with 1,600 runs over the parameter space. (A) A random regular graph, generated through the algorithm described in Steger and Wormald (112). Parameters used were 196 nodes and 8 edges. (B) A scale-free network, characterized by highly uneven degree distribution with some dominant nodes, generated with the algorithm described in ref. 113, based on Barabási–Albert growth model but adding that each random edge is followed by a chance of making an edge to one of its neighbors, thus capturing clustering. Parameters used were 196 nodes, 8 edges, and 0.01 probability of adding a triangle to any given edge. (C) The connected caveman, a highly cliqued graph structure used also in DellaPosta et al. (58), with 14 cliques of 14 nodes and 0.05 probability for reconnecting a given edge. As can be seen, strikingly, all network structures show the same general relationship between γ and ψ but with differences in the immediacy of the rise of sorting as a function of nonlocal interactions. In particular, the clique-dominated network in C requires a higher value of γ to become sorted.CC BY-NC-ND · PubMed Central
Fig. 4. The final state of two simulations at opposite ends of the x axis of Fig. 2C. (A) γ = 0 and (B) γ = 1. The agents are represented as crosses or circles depending on their static attribute. The colors are chosen by treating the list of dynamic attributes as a base-m number and then normalizing the result (i.e., ∑l=1…nDi,lm^(l−1)/mⁿ), using this fraction to select a color from matplotlib’s cm_prism. This allows us to represent each configuration of dynamic attributes as a unique color, with agents with different static attributes having the same color if they have the same dynamic attributes. Parameters are |A| = 625, h = 8, c = 4, m = 10, n = 10. As can be seen, when γ is low, the agents converge locally within their groups, resulting in a low level of global sorting as local differences cancel out. When γ is high, the groups converge internally, leading to high level of sorting.
Fig. 4. The final state of two simulations at opposite ends of the x axis of Fig. 2C. (A) γ = 0 and (B) γ = 1. The agents are represented as crosses or circles depending on their static attribute. The colors are chosen by treating the list of dynamic attributes as a base-m number and then normalizing the result (i.e., ∑l=1…nDi,lm^(l−1)/mⁿ), using this fraction to select a color from matplotlib’s cm_prism. This allows us to represent each configuration of dynamic attributes as a unique color, with agents with different static attributes having the same color if they have the same dynamic attributes. Parameters are |A| = 625, h = 8, c = 4, m = 10, n = 10. As can be seen, when γ is low, the agents converge locally within their groups, resulting in a low level of global sorting as local differences cancel out. When γ is high, the groups converge internally, leading to high level of sorting.CC BY-NC-ND · PubMed Central
Fig. 5. (A and B) The same model runs as Fig. 4 A and B, respectively. The lines on the y axis represent time steps in the run, with each line representing 100,000 time steps. These ridgeline plots (also called joy plots) are a way of giving a sense of the distributions over time. The plots show the kernel density estimation of the probability density function by time step (y axis), applied on the one-dimensional PCA of the matrix of distances between each node in the model. The distributions of the two static groups are plotted separately as blue and red. The PCA reduces the dimensionality of the distances between each node, then representing them as a one-dimensional distribution. The figures reveal how the groups effectively bipolarize when the level of nonlocal interaction is high, while they separate into local cultures which counterbalance one another when nonlocal interaction is low.
Fig. 5. (A and B) The same model runs as Fig. 4 A and B, respectively. The lines on the y axis represent time steps in the run, with each line representing 100,000 time steps. These ridgeline plots (also called joy plots) are a way of giving a sense of the distributions over time. The plots show the kernel density estimation of the probability density function by time step (y axis), applied on the one-dimensional PCA of the matrix of distances between each node in the model. The distributions of the two static groups are plotted separately as blue and red. The PCA reduces the dimensionality of the distances between each node, then representing them as a one-dimensional distribution. The figures reveal how the groups effectively bipolarize when the level of nonlocal interaction is high, while they separate into local cultures which counterbalance one another when nonlocal interaction is low.CC BY-NC-ND · PubMed Central
Fig. 6. Ridge plots illustrating the dynamics of the model with low levels of influence homophily (h = 1). (A and B) The final state of the two simulations and (C and D) their dynamics over time, with each line representing 100,000 time steps. A and C have low nonlocal interaction (γ = 0), and B and D have high nonlocal interaction (γ = 1). Parameters are |A| = 625, n = 10, m = 10, h = 1, c = 4. As can be seen, the runs without nonlocal interaction converge locally, forming local cultures with members of both groups. This is in line with Axelrod’s original model of cultural diversity. The run with a high level of nonlocal interaction converges globally on a single set of attributes.
Fig. 6. Ridge plots illustrating the dynamics of the model with low levels of influence homophily (h = 1). (A and B) The final state of the two simulations and (C and D) their dynamics over time, with each line representing 100,000 time steps. A and C have low nonlocal interaction (γ = 0), and B and D have high nonlocal interaction (γ = 1). Parameters are |A| = 625, n = 10, m = 10, h = 1, c = 4. As can be seen, the runs without nonlocal interaction converge locally, forming local cultures with members of both groups. This is in line with Axelrod’s original model of cultural diversity. The run with a high level of nonlocal interaction converges globally on a single set of attributes.CC BY-NC-ND · PubMed Central

Verification

Claims the paper makes

18 Own interpretation · 13 No basis given · 8 Partly supported · 8 No full text of the sources · 8 Own result · 4 Supported so far · 2 Supported · 2 Sources not found · 2 Not checked yet · 1 Own method · accuracy not yet measured

Show all 39 claims

  • It may state two separate claims as one. 24
  • Probably not a substantial claim. 7
27 of 27

  • The authors state this as an assumption.

    Partisan affiliation is fixed throughout the model run, assuming it changes on a slower timescale than other attributes.

    “Each agent i also has a single attribute, Si, corresponding to partisan affiliation, which held fixed throughout the model run (see also ref. 58).”
    “We here treat partisan affiliation as fixed, assuming that it will change on a slower timescale than the other attributes.”

  • The authors state this as an assumption.

    Social similarity is relative to the larger social context.

    “The social similarity is in other words treated as relative: that is, how similar we see ourselves to a particular individual depends on the larger social context (for instance, while the differences between Trotskyists and Stalinists may appear as a large chasm for members of the Party, they may for outsiders appear as a matter of relatively trivial detail).”

  • The authors state this as an assumption.

    Nonlocal interlocutors are chosen without bias toward self-similarity.

    “While the selective exposure hypothesis would suggest that these individuals would be selected with a bias toward self-similarity, we will here let the choice be unbiased as we are seeking to examine whether sorting can appear without such empirically questioned assumptions.”
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Citations

Cites

Show all 110 references

Research works printed but not linked: 7

  1. C. R. Sunstein, Echo Chambers: Bush v. Gore, Impeachment, and Beyond (Princeton University Press, Princeton, NJ, 2001).
  2. A. Guess, B. Nyhan, B. Lyons, J. Reifler, Avoiding the echo chamber about echo chambers. Knight Foundation 2, 1–25 (2018).
  3. E. A. Nordlinger, Conflict Regulation in Divided Societies (Center for International Affairs, Harvard University, 1972).
  4. S. Levitsky, D. Ziblatt, How Democracies Die (Broadway Books, 2018).
  5. M. W. Macy J. A. Kitts A. Flache S. Benard "Polarization in dynamic networks: A Hopfield model of emergent structure" in Dynamic Social Network Modeling and Analysis R. Breiger K. Carley P. Pattison Eds. (National Academies Press Washington DC 2003) pp.162–173.
  6. R. P. Abelson “Mathematical models of the distribution of attitudes under controversy” in Contributions to Mathematical Psychology N. Fredericksen H. Gullicksen Eds. (Holt Rinehart and Winston New York NY 1964) pp.142–165.
  7. E. Klein, Why We’re Polarized (Simon and Schuster, 2020).

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Metadata

Authors
Törnberg, P.
Affiliations
University of Neuchâtel (CH)
Corresponding author
Törnberg, Petter
ORCID
Törnberg, Petter
Venue
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences
Published
2022-10-10
Volume
119
Issue
42
Pages
e2207159119-e2207159119
ISSN
  • 0027-8424 (ISSN-L)
  • 1091-6490
DOI
10.1073/pnas.2207159119
PMC
PMC9586282
OpenAlex
W4304098849
Semantic Scholar
ab19b3fdc1f28d16e01c7ca9fdd1ba217428a298
Cited by
288
References
110
Citations by year
2026: 76 · 2025: 75 · 2024: 79 · 2023: 52 · 2022: 6
FWCI
81.17
Type
journal article
Language
en
Open access
Licence
Locations
  • Proceedings of the National Academy of Sciences (publishedVersion, cc-by-nc-nd)
  • PubMed (publishedVersion)
  • UvA-DARE (University of Amsterdam) (acceptedVersion, cc-by-nc-nd)
  • PubMed Central (submittedVersion, cc-by-nc-nd)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
Funders
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (VI.Veni.201S.006)
Topics
  • Social Sciences › Communication › Social Media and Politics
  • Social Sciences › Political Science and International Relations › Electoral Systems and Political Participation
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Opinion Dynamics and Social Influence
Keywords
affective polarization, digital media, partisan sorting, opinion dynamics, nonlocal interactions, local interactions, political polarization, social media
MeSH terms
Attitude, Humans, Politics, Internet

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