Emergence of Stereotypes and Affective Polarization from Belief Network Dynamics#

One-sentence summary. An agent-based belief-network model shows that two minimal ingredients — social influence and a drive for internal coherence — are sufficient to spontaneously generate stereotypes and strong affective polarization, even without ideological disagreement or network homophily.

Metadata at a Glance#

• Authors & Affiliations: Seckin, Aiyappa, Menczer, Flammini (Indiana U.); Vlasceanu (Stanford); Ahn (U. Virginia). Corresponding: oseckin@iu.edu, yyahn@virginia.edu.
• Field / Subfield: Computational Social Science / Opinion Dynamics / Social Cognition
• Type of work: Theoretical — agent-based modeling
• Status: Preprint (arXiv, 11 Apr 2026)

1. Core Questions#

• Q1. How do seemingly unrelated beliefs become associated — i.e., how do stereotypes emerge — without any underlying causal link?
• Q2. How do such emergent associations drive affective polarization (ingroup favoritism, outgroup animosity) in the absence of ideological conflict?

2. Motivation & Gap#

• Mainstream accounts attribute polarization to ideological disagreement, motivated reasoning, homophily, or echo chambers — yet affective polarization empirically exceeds substantive disagreement, and minimal-group experiments show arbitrary categorization alone can spark bias.
• Classical opinion-dynamics models treat opinions as isolated scalars, missing the fact that beliefs form mutually constraining networks.
• Earlier belief-network models (Rodriguez+2016; Aiyappa+2024) updated only directly communicated beliefs, with no mechanism for coherence-driven updates on related beliefs after an interaction.

3. Key Contributions#

1. An extended belief-network ABM combining direct social influence with endogenous coherence updates on related beliefs, selected via two-step weighted random walks over the belief graph.
2. Stereotypes emerge spontaneously around a neutral concept — group identity + coherence pressure suffice; no underlying reality needed.
3. Affective polarization (ingroup +1 / outgroup −1) arises as a downstream effect, without agents initially knowing neighbors’ group affiliations.
4. Polarization emerges in a well-mixed network — homophily and echo chambers are not required.
5. Parameter sweep identifies the regime: α > 0.5 (social influence) and β > 0 (coherence); very large β reduces polarization because beliefs crystallize before they can align with group identity.

4. Background & Prior Work#

• Social Balance Theory (Heider 1946): triad stability via sign product — basis of the coherence term.
• Cognitive Dissonance (Festinger 1957): motivation for coherence-seeking.
• Belief-network tradition: Converse 1964; Martin 2002; Friedkin+2016; Vlasceanu+2024 (bending); Rodriguez+2016; Aiyappa+2024 (direct precursor).
• Associative diffusion (Goldberg & Stein 2018); opinion cascades (Macy+2019).
• Minimal group paradigm (Tajfel+1971); false consensus effect (Ross+1977).

5. Method / Model#

• Approach: Two-layer ABM — a social graph of agents, each holding an internal belief graph.
• Core setup: N=100 agents on M=200 random edges. Each agent’s belief network contains self, a neutral concept (latte), Group A, Group B, and other agents. Self→own-group = +1, self→other-group = −1 (fixed); all other beliefs initialized near zero, N(0, 10⁻⁵).
• Key equations:
• Triad energy: E = −b(c_x,c_y)·b(c_x,c_z)·b(c_y,c_z) (Eq. 1).
• Dissonance d(B_i) = mean triad energy (Eq. 2).
• Per-step update: b ← b + f (social) + g (coherence).
• Social influence: f ~ N(α·(b_j − b_i), σ) (Eq. 5).
• Coherence update: g ~ N(−β·∂d/∂b, σ) — gradient descent on dissonance, applied to an adjacent edge chosen via two-step weighted random walk.
• Beliefs clipped to [−1, 1].
• Parameters: α = β = 1, σ = 0.1 (defaults); swept over [0, 3].
• Null conditions: α = 0 or β = 0. Also tested a reinforcement-style influence term — results qualitatively unchanged.

6. Dataset / Experimental Setup#

• Source: Pure simulation (Julia for the model, Python for analysis). No empirical dataset.
• Scale: N=100, M=200, 2.5×10⁶ time steps per run, 10 runs per parameter cell.
• Code: https://github.com/rachithaiyappa/emerging_beliefs
• Limitations of the setup: No empirical calibration; no ground truth (latte is neutral by construction).

7. Key Results#

• Stereotype formation (Fig. 3): Group A converges to +latte, Group B to −latte. Opinion polarization P_O goes 0 → ~2 (max).
• Affective polarization (Fig. 4): Ingroup valence → +1, outgroup → −1; P_A goes 0 → ~2.
• Internal dissonance drops toward −1 (Fig. 3h): populations settle into coherent, stable belief systems — coherence locks in the polarized state.
• Phase diagram (Fig. 5): Polarization requires α > 0.5 and β > 0; excessive β suppresses it (premature crystallization).
• False-consensus minority: A small fraction misinfer a neighbor’s group from positive interactions — consistent with Ross+1977.

8. Figures / Tables Worth Remembering#

• Fig. 1: Two-layer architecture + balanced/unbalanced triads.
• Fig. 2: One simulation step — pair selection, social influence, two-step random-walk coherence update.
• Fig. 3: Latte stereotype emergence + P_O and ⟨d(B_i)⟩ over time.
• Fig. 4: Ingroup/outgroup valence evolution; P_A time series.
• Fig. 5: α–β heatmaps showing the non-monotonic effect of β.

9. Interpretation & Implications#

• Reframes polarization as an emergent property of how humans organize beliefs under uncertainty, not as disagreement over values.
• Offers a cognitively grounded alternative to homophily-based opinion dynamics.
• Provides a candidate mechanism for COVID-19 vaccine polarization: coherence-driven alignment around political identity through associative chains (e.g., lockdowns ↔ freedom ↔ mandates), independent of genuine efficacy disagreement.
• Domain-agnostic — same dynamics could underlie polarization in climate, science denial, culture.

10. Limitations#

• Author-acknowledged: well-mixed network; only two fixed groups; a single tracked neutral concept; no reality-checking; random (non-selective) transmission; equal-influence agents; no distinction between beliefs and meta-beliefs (no theory of mind).
• Additional observations:
• No empirical calibration of α, β; the COVID illustration is narrative, not quantitative.
• Small population (N=100); scaling behavior is not systematically examined.
• The two-step-walk definition of “adjacency” is a modeling choice — alternative walk lengths could change spread dynamics.

11. Open Questions & Future Work#

• Empirically test whether exposure to a few ingroup members’ behavior seeds group-level stereotypes (experiments or observational studies).
• Add community structure / homophily — amplifier or accelerator?
• Overlapping, fluid identities; multiple interacting neutral concepts.
• Introduce theory of mind / second-order beliefs.
• Asymmetric influence, opinion leaders, selective exposure.

12. Connections#

• Related papers:
• Aiyappa, Flammini & Ahn (2024) Science Advances — direct methodological precursor (ref [47]).
• Rodriguez, Bollen & Ahn (2016) PLoS ONE — belief evolution under coherence + conformity (ref [48]).
• Goldberg & Stein (2018) — associative diffusion (ref [27]).
• Macy et al. (2019, 2021) — opinion cascades, tipping points (refs [28, 43]).
• Vlasceanu et al. (2024) — bending model (ref [19]).
• DellaPosta, Shi & Macy (2015) — “Why do liberals drink lattes?” — the empirical puzzle motivating the model (ref [17]).
• Potential applications: modeling partisan animosity; cultural-marker formation; misinformation spread through associative chains.
• Contrasts with: homophily-based / structural-separation accounts of polarization (refs [72–75]); motivated-reasoning and ideological-distance accounts.

13. Key Takeaways#

• The one idea to carry forward: polarization and stereotypes can be emergent from coherence-seeking in belief networks — no echo chambers, no substantive disagreement, not even knowledge of others’ identities required.
• Methodological nugget: the two-step weighted random walk is a clean, reusable primitive for selecting “related” beliefs in any belief-network model.

14. Quotes / Snippets#

“Our model shows that polarization can emerge in the complete absence of any underlying truth… the associations that drive division need not be normatively meaningful, politically relevant, or even accurate.” (p. 10)

“Even in a well-mixed network… polarization emerges purely from cognitive dynamics, without requiring echo chambers or social sorting.” (p. 10)

“This reframes polarization not as an outcome of disagreement over values, but as an emergent property of how humans organize beliefs under uncertainty.” (p. 10)

15. Glossary#

• Belief network (B_i): An agent’s signed, weighted graph of concept–concept associations; b_i(c_x, c_y) ∈ [−1, 1].
• Social Balance Theory: A triad is stable iff the product of its three edge signs is positive.
• Internal dissonance d(B_i): Mean triad energy; lower = more coherent.
• Social influence (α): Strength with which a receiver’s belief drifts toward the sender’s.
• Coherence pressure (β): Strength of the dissonance-reducing gradient step.
• Endogenous update: Coherence-driven change to a related belief, triggered but not directly communicated by an interaction.
• Opinion polarization P_O(c): |mean(A) − mean(B)| opinion gap on concept c; range [0, 2].
• Affective polarization P_A: Mean (ingroup − outgroup) valence gap; range [0, 2].
• False consensus effect: Overestimating how widely one’s beliefs are shared; appears in the model as the minority of sign-flipping agents.

BibTeX#

@article{seckin2026emergence,
  title   = {Emergence of Stereotypes and Affective Polarization from Belief Network Dynamics},
  author  = {Seckin, Ozgur Can and Aiyappa, Rachith and Vlasceanu, Madalina and Menczer, Filippo and Flammini, Alessandro and Ahn, Yong-Yeol},
  journal = {arXiv preprint arXiv:2604.10251},
  year    = {2026},
  url     = {https://arxiv.org/abs/2604.10251},
  note    = {cs.SI}
}