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arxiv: 2506.01169 · v2 · submitted 2025-06-01 · 📡 eess.SY · cs.SY

Dynamical models for distributed social power perception in Friedkin-Johnsen influence networks

Ye Tian , Angela Fontan , Yu Kawano , Wei Zhang , Kenji Kashima , Karl H. Johansson This is my paper

Pith reviewed 2026-05-19 11:47 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords social power perceptionFriedkin-Johnsen dynamicsinfluence networksdistributed estimationopinion dynamicsreflected appraisalconvergence analysis
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The pith

Social power can be perceived accurately through distributed local updates in Friedkin-Johnsen influence networks.

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

The paper develops a mechanism for agents in social influence networks to perceive their social power without needing global knowledge. Individuals update perceptions of their own influence using the Friedkin-Johnsen opinion dynamics and only local neighbor information about stubbornness and assigned weights. Rigorous analysis shows convergence to the true social power both when influence weights remain fixed and when they coevolve with perceptions. This matters because global computation of social power usually demands full network data that is unavailable or expensive in large groups. The approach remains effective from arbitrary starting perceptions, in disconnected networks, and across different timescales.

Core claim

The central claim is that a distributed perception mechanism built on Friedkin-Johnsen opinion dynamics lets each individual estimate true social power from repeated local interactions. Each person begins with an independent initial perception and updates it using only knowledge of neighbors' stubbornness and the influence weights those neighbors assign. The dynamical analysis identifies equilibria and invariant sets, then establishes conditions under which perceptions converge to the globally correct social power values in the static case of fixed weights and in the reflected-appraisal case where weights adjust together with the perceptions.

What carries the argument

The distributed perception update rule derived from Friedkin-Johnsen opinion dynamics, which lets each individual revise its power estimate from local neighbor stubbornness and weight information.

If this is right

  • Perceptions converge to true social power when influence weights are fixed in static networks.
  • Perceptions also converge when influence weights coevolve with perceptions under reflected appraisal.
  • Convergence holds even from extreme initial perceptions and in disconnected networks.
  • The mechanism stays reliable under variations in update timescales.

Where Pith is reading between the lines

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

  • The approach points toward decentralized power ranking in large online communities that avoids collecting full network data at a central point.
  • If local knowledge of neighbor weights is noisy or incomplete, convergence may slow or fail, suggesting value in extensions that learn those weights on the fly.
  • The same local-update structure could apply to other distributed estimation tasks in multi-agent systems such as tracking resource shares or consensus values.

Load-bearing premise

Each individual must know its neighbors' stubbornness and the influence weights they accord.

What would settle it

A concrete network example or simulation in which agents follow the local update rule yet their power perceptions fail to converge to the true globally computed social power would disprove the convergence result.

Figures

Figures reproduced from arXiv: 2506.01169 by Angela Fontan, Karl H. Johansson, Kenji Kashima, Wei Zhang, Ye Tian, Yu Kawano.

Figure 1
Figure 1. Figure 1: Trajectories of system (7) with 3 individuals and various initial perceptions. If W(γ) is irreducible with dominant left eigenvector ω, then limk→∞ p(k) = ω1 ⊤ n p(0). Thus, p(k) converges to ω if and only if 1 ⊤ n p(0) = 1, where ω is the social power allocation of the DeGroot model (8). We notice key differences between systems (9) and (7): (i) In system (9), the perception weight i accords to j is Wji(γ… view at source ↗
Figure 2
Figure 2. Figure 2: Trajectories of systems (11), (5) and (6) with [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Trajectories of system (11) with 3 individuals and initial perceived social power (0.3, 0.4, 0.5)⊤, (0.8, 0.2, 0)⊤ and (0.9, 0.8, 0.6)⊤, respectively. Corollary 2: (Monotonicity and exponential convergence with fully stubborn center node) Suppose that Assumption 1 holds and G(C) is a star topology with fully stubborn center node 1. For system (11) and the equilibrium p ∗ P , let µ = j∈Vp p ∗ jej and ν = X … view at source ↗
read the original abstract

Social power quantifies the ability of individuals to influence others and plays a central role in social influence networks. Yet, computing social power typically requires global knowledge and significant computational or storage capability, especially in large-scale networks with stubborn individuals. In this paper, we propose a distributed perception mechanism based on the Friedkin-Johnsen opinion dynamics that enables individuals to estimate their true social power through local interactions. The mechanism starts from independent initial perceptions and relies only on local information: each individual only needs to know its neighbors' stubbornness and the influence weights they accord. We provide rigorous dynamical system analysis that characterizes equilibria, invariant sets, and convergence. Conditions are established for convergence to the true social power in both the static setting with fixed influence weights and the reflected-appraisal setting where influence weights coevolve with perceptions. The proposed mechanism remains reliable under extreme initial perceptions, disconnected influence networks, reflected-appraisal coupling, and variations in timescales. Numerical examples illustrate our results.

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

0 major / 3 minor

Summary. The paper proposes a distributed perception mechanism based on the Friedkin-Johnsen opinion dynamics that enables agents in influence networks to estimate their true social power through local interactions. The mechanism starts from independent initial perceptions and uses only local information consisting of neighbors' stubbornness parameters and the influence weights they assign. Rigorous dynamical-systems analysis is provided to characterize equilibria, invariant sets, and convergence conditions, with results established for both the static setting (fixed influence weights) and the reflected-appraisal setting (where influence weights coevolve with perceptions). The analysis covers robustness to extreme initial perceptions, disconnected networks, and variations in timescales.

Significance. If the central claims hold, the work offers a meaningful contribution by providing a fully distributed alternative to centralized social-power computation in large networks containing stubborn agents. The explicit use of standard dynamical-systems tools to derive equilibria, invariant sets, and convergence conditions, together with the treatment of both static and reflected-appraisal cases, supplies concrete, falsifiable predictions about perception trajectories. These features strengthen the manuscript's value for the systems-and-control community working on social-influence models.

minor comments (3)
  1. [Preliminaries / Notation] In the notation section, the distinction between an agent's perception vector and the true social-power vector should be emphasized with an explicit remark that the former is the quantity being updated while the latter is the target equilibrium; this would reduce the chance of reader confusion when the two appear in the same equation.
  2. [Numerical examples] The numerical examples would benefit from a short table listing the exact stubbornness values and the row-stochastic weight matrices used in each simulation; without it, reproducing the reported trajectories requires additional effort.
  3. [Discussion / Conclusion] A brief remark on the computational cost of the local update rule (relative to a centralized eigenvector computation) would help readers assess practicality for very large networks.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our manuscript, the recognition of its contribution to distributed social-power perception in Friedkin-Johnsen networks, and the recommendation for minor revision. No specific major comments were provided in the report, so we have no individual points to address. We will incorporate any minor editorial improvements suggested by the editor or production staff in the revised version.

Circularity Check

0 steps flagged

Standard dynamical-systems analysis with no reduction of claims to fitted inputs or self-referential definitions

full rationale

The paper applies classical Lyapunov and invariance arguments to the Friedkin-Johnsen model under an explicit local-information assumption (each agent knows neighbors' stubbornness and row-stochastic weights). The equilibria and convergence statements are derived directly from the closed-loop vector field and do not collapse to a parameter fit, a renaming of an empirical pattern, or a load-bearing self-citation chain. The central result therefore retains independent mathematical content once the modeling assumptions are granted.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard Friedkin-Johnsen opinion dynamics as a domain model plus generic properties of discrete-time dynamical systems for convergence analysis; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Opinion updates follow the Friedkin-Johnsen model with stubborn individuals.
    The mechanism is explicitly built on this established opinion dynamics framework.
  • domain assumption Local information on neighbor stubbornness and influence weights is available and accurate.
    The distributed update rule requires this local knowledge as stated in the abstract.

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