Thurner, Hofer & Korbel — Why more social interactions lead to more polarization in societies (PNAS)

Stefan Thurner, Markus Hofer and Jan Korbel, PNAS 2025, doi 10.1073/pnas.2517530122. Read in full through firecrawl after PNAS returned 403 to a direct fetch. The scraped text does not carry the issue date, so the year here is from the citation record rather than from the page.

Arrived 2026-09-05 by Telegram as a psypost write-up. Read the dispute page with this one — polarization-connectivity-dispute. Two independent groups have attacked the paper in PNAS and the authors have replied to both, and none of that reaches the trade coverage.

The claim

Two trends coincide: over two decades the number of close social connections roughly doubled, and Western opinion polarized. The paper argues they are the same event — that a society passes a critical connectivity above which polarization is not gradual but a phase transition.

"Increasing social connectivity, often seen as a unifying force between people, can lead to polarization."

The model

Each individual holds an opinion vector s_i of G binary entries (±1 per issue); their ideology is the mean, s̄_i. A fixed Poissonian small-world network says who knows whom; what changes is the sign of each tie. Alignment between two people is the normalised dot product a_ij = G⁻¹ s_i·s_j — positive means friends, negative means enemies.

Everyone minimises cognitive dissonance:

H(i) = −α Σ_{friends} a_ij + (1−α) Σ_{enemies} a_ij

Run as a Metropolis algorithm: flip one random opinion of one random person, accept if stress falls, accept with a probability governed by β if it rises. Change the sign of a_ij and the friendship flips with it.

The two mechanisms are named and are both borrowed from social psychology: homophily (friends converge, similar people befriend) and social balance (Heider triads settle into +++ or +−−;

- − and − − − carry tension). The paper's argument for why it needs both is that models with only one give the wrong answer — voter models converge on consensus, and bounded-confidence models predict polarization at low connectivity, the opposite of what is claimed here.

Radicalized influencers are a fraction γ of nodes with fixed extreme opinions (half all +1, half all −1) that never update their opinions but do update their friendships.

The numbers

The transition. Without influencers (γ=0), polarization ψ = Var(a_ij) stays low and then jumps discontinuously at a critical degree ⟨k⁺⟩ ≈ 5. Community structure flips with it: below the threshold, clusters of ≤2% of nodes sit scattered with neutral ideologies; above it, two groups of roughly 50% each with opposed ideologies (Leiden algorithm).

Influencers change the order of the transition, not just its position. At γ = 0.02 the jump becomes continuous — and polarization then appears at lower connectivities. Higher β (sensitivity to social stress) also moves the onset earlier.

The empirical fit. US polarization from Pew rises from ψ ≈ 0.11 before 2010 to 0.19 by 2017. Connectivity across GSS/ESS/SSND-family surveys in the US, Germany, the Netherlands and Norway rises from ⟨k⁺⟩ ≈ 2.2 in 2004 to ≈ 4.1 in 2024, about 100%. Feeding only that connectivity curve into the model, with everything else fixed (α=0.5, β=2.7, γ=0.02, N=10⁵, ε=0.175), reproduces the timing and size of the polarization rise. The connectivity inflection lands just after the iPhone, Android and public Facebook (2008), and Facebook passing every other US site for traffic (2010).

Hysteresis. Once past the threshold, cutting connectivity back below it does not undo the polarization; ⟨k⁺⟩ has to fall substantially further. Without influencers the rise is discontinuous and the fall continuous. With influencers the hysteresis is weaker.

Where the parameters come from, which is the soft joint

α = 0.5 weights aligning with friends and misaligning with enemies equally. β = 2.7 is assumed, not measured: the paper cites prior work putting β between 1 and 2 for topics like car brands and investments, and then sets a higher value for politics on the stated hypothesis that people are more socially sensitive about political beliefs. γ = 0.02 assumes radicals are rare. The authors run robustness checks in the SI, and they are explicit that this is where the assumption sits.

What it is and is not

It is a mechanism with a falsifiable structure: a first-order transition, a critical degree, an order change under influencers, and hysteresis are all things a real society could fail to show. It is not a measurement of any society. Every number above except the Pew and survey series is generated by simulation, and the fit to the empirical curve comes from a model whose most consequential parameter was chosen on a hypothesis about political feeling.

That is also the honest reading of the "empirically, polarization started to increase exactly with the advent of smartphones and social media" line in the significance statement — the coincidence is in the data, the mechanism connecting the two is in the model.

polarization-connectivity-dispute · psypost-polarization-model · replication-crisis · synthesis