nucleation

LIT-1146: Opinion Dynamics and the Evolution of Social Power in Influence Networks

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StatusActive — read 2026-10-24 (NOTE-1135) from the version of record posted on the last author's site, proofs skimmed; worth reading as the exact analysis of reflected appraisal under DeGroot dynamics. With fixed relative interpersonal weights, self-weights converge from every non-autocratic start to one equilibrium ordered by eigenvector centrality; power accumulates above a threshold, is autocratic exactly for a star and democratic exactly for a doubly stochastic network, and members no path of influence reaches end with none. Theorems about a model; the authors say its validity and robustness are not yet established.
Version2
Tagsnetwork-science, social-science
Cited as “paper” byNOTE-1135 — Jia, MirTabatabaei, Friedkin & Bullo — Opinion dynamics and the evolution of social power in influence networks
Cited as “source” byTHEORY-1232 — Under reflected appraisal across issues, whether power concentrates in one member depends on the single-issue step: with Friedkin–Johnsen anchoring on initial positions almost every random strongly connected group evolves to a single leader, and with DeGroot consensus the same random complete networks keep power spread, THEORY-916 — In the DeGroot–Friedkin model, where a group reaches DeGroot consensus on each issue and each member's self-weight on the next issue equals their control over the last, with fixed relative interpersonal weights that form a strongly connected network, self-weights converge from every non-autocratic start to one equilibrium ordered by the eigenvector centralities of those weights: power accumulates above a centrality threshold, is autocratic exactly when the network is a star and democratic exactly when it is doubly stochastic; and in the networks that are not strongly connected that the authors treat, members to whom some other member does not listen, even indirectly, end with none

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Jia, P., MirTabatabaei, A., Friedkin, N. E. & Bullo, F. (2015). SIAM Review 57(3):367–397.

Key takeaways

From the reading, NOTE-1135. Page numbers are the journal’s.

  • One parameter. “the evolution and limiting values of the self-weights depend only upon the network structure” (p. 374), through the eigenvector centralities c.
  • Convergence. Unless the network is a star, every non-autocratic start converges to one interior equilibrium ordered as c (Theorem 4.1, p. 380).
  • Accumulation. “social power tends to accumulate at the top of the hierarchy” (p. 367): above a threshold, power exceeds centrality (Proposition 4.2).
  • Extremes. Autocracy exactly for a star; democracy exactly for a doubly stochastic network: “If such structures are unusual, then so is a democratic equilibrium” (p. 376).
  • The unreached. “the individuals who are not globally reachable in G(C) have zero social power in the equilibrium influence networks” (p. 384).
  • Limits the authors state. “At the present time, we cannot assert robustness” (p. 386).

Why this is here

A15 of the exchange of 2026-10-16 put it first: perhaps the closest predecessor of the dual canvases, and the baseline QUESTION-117 asks CASE-092 to be compared with.

Added 2026-10-24, from the reading. It is also cited by CLAIM-448 (exchange of 2026-10-23/24) as the baseline for self-reinforcing authority. The reading confirms it and sharpens it: under DeGroot dynamics every issue ends in consensus, so the record is always coherent, its content is weighted toward the central, and members nobody listens to contribute nothing. That exclusion is by uptake, through a fixed network, not by a maintained regime of admission. Filed from it: THEORY-916.

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