Selective Control under Noisy Perception: Governance Failures Hidden by Aggregate Metrics in Modular Networks

Igor Itkin

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Selective Control under Noisy Perception: Governance Failures Hidden by Aggregate Metrics in Modular Networks

Igor Itkin

arXiv:2606.14819v1Jun 12, 2026cs.MAphysics.soc-ph

TL;DR

Standard aggregate metrics may miss harms when noisy moderation errors affect users who bridge communities. Using an agent-based network model and a position-weighted governance loss, the paper finds usefulness remains stable while governance loss more than doubles under false-positive-heavy noise.

Problem
Existing metrics do not combine network-position-dependent classification errors with distinct failure modes such as missed threats and suppressed coordination.
Method
An agent-based model places learning agents in modular networks, generates three content types, applies noisy classification, and evaluates aggregate usefulness alongside bridge-specific governance loss.
Results
Usefulness remains near 2.21 across noise regimes, while governance loss more than doubles from 0.039 under oracle classification to 0.088 under false-positive-heavy noise.
Takeaways & Limitations
Governance loss diagnoses whether missed danger, suppressed coordination, or control cost dominates when aggregate usefulness averages away bridge-specific errors.
Takeaways & Limitations
Structural-position effects appear only with non-saturating contagion at inter-community density p_out = 0.03, while the base-density cascade remains untested.

Abstract

from arXiv · show

A content-moderation system can score well on every standard accuracy metric and still cause real harm, if its mistakes fall on the few users who connect otherwise separate communities. We show this in an agent-based model where N=240 learning agents on a community-structured network each post harmless, productive, or dangerous content, and a regulator removes or penalizes whatever a noisy classifier flags. Overall usefulness barely moves as the noise changes (one-way ANOVA, p=0.96): by aggregate measures, nothing looks wrong. The damage instead concentrates on these bridge users, whose useful posts are wrongly suppressed and whose dangerous posts are wrongly spared. A governance loss (L_gov) that prices these two mistakes separately from the cost of enforcement more than doubles under false-positive-heavy noise. Aggregate accuracy hides who is harmed, and the cheap quantity to audit is how many connections a user has (degree), a near-perfect proxy for the betweenness that defines a bridge (r=0.96).

1 Introduction

The paper shows that network position can hide governance failures from aggregate usefulness metrics, and introduces a governance loss that exposes bridge-concentrated classification errors and their distinct costs. It further examines adaptive targeting, institutional delay, and evolving content in a controlled agent-based model.

Model and motivation: A stochastic block model places agents in densely connected communities linked by sparse bridge nodes, while tabular Q-learning models adaptation among harmless, productive, and dangerous content.The regulator acts on noisy classifier labels rather than directly observing agents’ true states.
Governance loss: Lgov = LFN +LFP +Lcontrol separates missed dangerous activity, suppressed productive activity, and control expenditure while incorporating exposure weighting, bridge sensitivity, convex control cost, and decomposability.The metric is designed to distinguish failure modes that aggregate usefulness combines.
Aggregate metrics and bridge errors: Usefulness stays within 2.211–2.216 across noise regimes (one-way analysis of variance, p = 0.96), while governance loss more than doubles under false-positive-heavy noise (0.039 →0.088, Cohen’s d = 2.41).The governance-loss ordering holds across all 27 weighting configurations tested.
Adaptive governance: An adaptive bridge-targeting bandit fails to ease off under noisy classification, indicating that adaptive governance needs rewards aligned with governance loss rather than raw bridge error rates.This contribution addresses the tradeoff between targeting bridge errors and avoiding harmful suppression.
Delay and noise: Institutional delay and classification noise act through independent pathways: delay destabilizes the alarm feedback loop, whereas noise causes governance failure through bridge errors.A regulator facing both must address the mechanisms separately rather than treating them as compounding effects.
Endogenous content: An endogenous-content extension couples enforcement, behavior, and classifier ground truth in a feedback loop that the fixed-type model cannot capture.Content types evolve with agent behavior in this extension.

2 Related Work

Related work connects network structure, adaptive governance, content-moderation errors, opinion dynamics, and delay–noise interactions, while identifying governance loss as a position-weighted, cost-sensitive metric. Unlike fixed cost-sensitive learning, it derives weights from betweenness and separates named failure modes.

Enforcement on networks: Network topology shapes cooperation, punishment, reward, equilibrium selection, and heterogeneous roles in modular communities.Prior work includes canonical agent-based modeling of civil violence, where enforcement level affects rebellion.
Adaptive regulators and bilevel learning: Adaptive regulators face bilevel learning because agents best-respond while regulators learn from agent behavior.The AI Economist demonstrated co-adaptation through two-level deep reinforcement learning, while meta-gradient incentive design targets cooperation among selfish agents.
Content moderation and algorithmic governance: Aggregate moderation metrics treat errors on peripheral and high-betweenness nodes identically despite position-dependent consequences.Prior governance research characterizes algorithmic moderation as introducing position-independent classification errors into governance decisions.
Opinion dynamics and endogenous type change: Reinforcement-learning agents on modular networks can develop stable polarization through social feedback, paralleling Q-learning agents on stochastic block models.Opinion-dynamics research also examines external and institutional influence and Bayesian updating under fixed cognitive biases.
Gap: Governance loss weights misclassifications by network position and consequences rather than counting them uniformly.Its weights derive from betweenness instead of a fixed cost matrix, and it decomposes errors into missed threats, suppressed coordination, and control cost.

3 Model

The model places Q-learning agents with latent content types on a modular network governed by selective enforcement based on noisy labels and network position. It formalizes bridge structure, classification noise, enforcement targeting, and bridge-specific error metrics for evaluating governance failures.

Model overview: The regulator observes predicted labels rather than true content types and applies selective enforcement whose intensity depends on predicted label and network position.The model input includes a confusion matrix, bridge-targeting multiplier, and Q-learning agent architecture.
Network and bridges: Agents occupy a directed modular stochastic-block network, while bridge nodes are those in the top betweenness-centrality quantile and mediate cross-community information flow.Betweenness is computed on the network’s undirected projection despite directed edges representing asymmetric influence.
Agents and content: Each agent chooses loyal, moderate, or radical actions through tabular Q-learning, while its fixed latent content type is harmless, productive, or dangerous and remains unobservable to the regulator.Action and content type are distinct: radical action can produce either productive innovation or genuinely dangerous content.
Perception noise: Noisy labels are generated from a confusion matrix, with oracle, default, false-positive-heavy, and false-negative-heavy regimes determining classification uncertainty.The false-positive-heavy regime raises H→D from 0.02 to 0.20 and P→D from 0.15 to 0.35.
Selective enforcement: Bridge targeting increases scrutiny of structurally central nodes classified as dangerous, with multiplier values swept across {1.0, 1.35, 1.8}.The policy is intended to reduce cascade risk under accurate classification but can impose collateral costs when false positives are frequent.
Evaluation metrics: The model defines aggregate usefulness alongside bridge risk, bridge false positives, and bridge false negatives to distinguish overall payoff from position-specific governance errors.FPB counts non-dangerous bridge nodes misclassified as dangerous, while FNB counts dangerous bridge nodes misclassified as non-dangerous.

4 Governance Loss

Governance loss exposes network-position-specific failures that aggregate accuracy obscures by separately weighting bridge-node false negatives, false positives, and control costs. In the diagnostic example, FP-heavy noise more than doubles governance loss while aggregate usefulness remains unchanged.

4 Governance Loss: Governance loss weights classification errors by network position and decomposes them into false-negative, false-positive, and control-cost components.The metric is designed to make distinct governance failure modes separately inspectable.
4 Governance Loss: Bridge-specific errors matter because a false negative on a bridge can enable dangerous content to propagate across communities, unlike the same error on an isolated peripheral node.The metric therefore permits bridge-restricted inspection independent of population-level error rates.
4 Governance Loss: The product form makes error costs depend on relevant activity, so false-negative and false-positive components vanish when dangerous activity or enforcement is absent.Each error rate is multiplied by the activity it fails to address.
4 Governance Loss: The three components capture undetected dangerous bridge activity, suppressed productive bridge activity, and the opportunity cost of control intensity.The control-cost term is quadratic, reflecting increasing marginal costs from higher enforcement intensity.
4 Governance Loss: 2.3×: Under FP-heavy noise, governance loss rises from the oracle baseline 0.039 to 0.088, while aggregate usefulness remains unchanged at ≈2.21.The increase is +0.050 absolute, with Cohen’s d = 2.41, under λFN = λFP = λu = 1.

5 Experiments

Across noise conditions, aggregate usefulness remains statistically equivalent to the perfect-classification oracle, while bridge-specific errors and governance loss diverge sharply. These hidden costs are concentrated in false-positive suppression of productive bridges and false-negative exposure to dangerous bridge activity.

Baselines: The oracle condition (M = I) is the baseline and lower bound for governance loss, equal to pure control cost because FPB = FNB = 0.All Cohen’s d effect sizes are computed relative to this perfect-classification baseline.
Aggregate usefulness: 2.213 mean usefulness under the oracle versus 2.211–2.216 across noisy conditions yields no significant difference (F = 0.10, p = 0.96).The maximum spread is 0.005, or 0.2% of the mean, and TOST confirms equivalence to the oracle.
Bridge-specific errors: 0.228 FPB under FP-heavy noise is three times the default 0.077, while 0.152 FNB under FN-heavy noise is three times the default 0.050.These bridge-specific divergences are diluted in population aggregates because bridges comprise a small fraction of nodes.
Governance loss: Governance loss decomposes false-negative exposure, false-positive suppression, and control cost into interpretable components that usefulness and punished fraction miss.Outcome-level metrics are blind to noise regime (p > 0.68), whereas the components identify which failure mode dominates.
Governance loss: 0.088 Lgov under FP-heavy noise exceeds 0.057 under FN-heavy noise and 0.039 under the oracle, driven respectively by LFP and LFN.The FP-heavy effect relative to the oracle is Cohen’s d = 2.41, versus Cohen’s d = 0.96 for FN-heavy noise.
Targeting dilemma: Under FP-heavy noise, aggressive targeting trends worse than no targeting, while under FN-heavy noise stronger targeting gives the lowest governance loss.The FP-heavy comparison is m=1.0: Lgov=0.087 versus m=1.8: 0.090, but the gap is within noise (t=0.56, p=0.58).

6 Discussion

Aggregate usefulness remains invariant across noise and punishment regimes because bridge-specific errors are diluted across the population, while Lgov diagnoses harms that outcome-level metrics conceal. The discussion therefore prioritizes governance-loss-aligned rewards and classifier accuracy, while treating several mechanisms as directional or model-specific.

Aggregate metrics and dilution: Usefulness remains invariant across punishment costs from 0.5× to 15× base (p > 0.34), because bridge-specific punishment is diluted across the population.Bridge nodes constitute 12% of the population; FP-heavy noise adds approximately 0.028 to the punishment rate, a 14% perturbation relative to ≈0.20.
Governance-loss interpretation: Lgov detects bridge-specific errors by construction but diagnoses them by separating missed threats, suppressed coordination, and control cost in one scalar.The alternative-metrics comparison shows blindness is specific to outcome-level metrics, whereas population-level FP/FN rates can detect the effect.
Limits of demonstrated effects: The radicalization-suppression effect is significant in Erdős–Rényi and modular topologies but absent in scale-free, while governance-loss penalties remain within cross-seed noise at the tested sample size.The paper therefore presents this trap as a directional mechanism rather than a demonstrated noise-dependent effect.
Adaptive governance: The adaptive bandit converges to m ≈1.50 regardless of noise regime because its reward observes reduced dangerous bridge activity but not the enforcement cost of false positives.A governance-loss-aligned reward would make the adaptive regulator and diagnostic metric complements rather than substitutes.
Delay and endogenous dynamics: FP-heavy noise adds ≈0.05 to Lgov at every delay, while runaway trajectories remain 6% →16% →30% at delays 0 →6 →8 across noise regimes.Delay affects stability through the alarm-feedback loop, whereas noise affects governance loss through an independent pathway; endogenous content produces mild polarization.
Accuracy and targeting: Classifier accuracy cuts Lgov from ≈0.089 to ≈0.037, making accuracy a first-order lever while targeting intensity is second-order and only weakly accuracy-dependent.At α = 0, governance loss rises with m; at α = 1, the lowest loss occurs at m∗= 1.6, but precise complementarity is not established.

7 Conclusion · Appendix

Aggregate usefulness remains near 2.21 despite noisy governance, while bridge-weighted Lgov exposes concentrated harms, separates their mechanisms, and more than doubles from oracle classification. The contribution is diagnostic but scope-limited: bridge weighting depends on network structure and contagion dynamics, with degree often serving as its practical proxy.

7 Conclusion: 2.21 usefulness holds across noise regimes (one-way ANOVA p = 0.96), while bridge-weighted governance loss Lgov more than doubles under noisy classification.The conventional aggregate usefulness metric does not register the damage concentrated on bridge nodes.
7 Conclusion: Lgov separates missed danger at bridges, suppressed coordination at bridges, and enforcement cost into three terms of one scalar.This decomposition diagnoses which governance failure dominates in each noise regime.
7 Conclusion: An adaptive bandit targeting bridges harder when it detects danger never eases off under false-positive-heavy noise because its reward tracks bridge error rates rather than enforcement cost.The result motivates aligning adaptive-governance rewards with Lgov.
7 Conclusion: p = 0.91: in the base one-hop model, dangerous content on bridges spreads no further than elsewhere, so bridge weighting is not implied by those dynamics.The contribution’s structural interpretation changes when contagion permits multiple hops.
7 Conclusion: Cohen’s d > 3: under multi-hop contagion, structural position carries large consequence whenever the dangerous process does not saturate.This finding establishes a scope condition for when bridge position matters dynamically.
7 Conclusion: r = 0.96: degree is a near-collinear proxy for betweenness in modular networks, but degree weighting is preferable with low-degree cut vertices.The dilution arithmetic generalizes to modular systems, while the appropriate position weighting depends on topology.
7 Conclusion: Lgov’s demonstrated position weighting remains a diagnostic contribution, with learned transmission processes and formal resource-allocation optimization identified as next steps.The paper frames these extensions as natural beyond the current analysis.

A Model Parameters and Implementation

This appendix section provides the paper’s full model specification. Related appendices cover experimental design and statistical procedures, plus robustness, ODD-protocol alignment, and reproducibility details.

A Model Parameters and Implementation: The appendix provides the full model specification for the study.This material appears in the section on model parameters and implementation.
A Model Parameters and Implementation: Appendix B describes the experimental design and statistical procedures.
A Model Parameters and Implementation: Appendix C reports robustness checks, ODD-protocol alignment, and reproducibility details supporting the main text.

A.1 Simulation configuration … B.1 Experiment design grid

The study uses a 240-agent, six-community stochastic block model with Q-learning agents, noisy content labels, bridge-targeted enforcement, and a governance-loss measure. Eleven paired-seed experiments vary specified factors to isolate how noise and targeting affect outcomes.

A.1 Simulation configuration: N = 240 agents are partitioned into K = 6 communities in a stochastic block model, with bridge nodes defined as the top 12% by betweenness centrality.The network uses pin = 0.08 and pout = 0.004.
A.1 Simulation configuration: Agents use tabular Q-learning with α = 0.10, γ = 0.95, and ϵ = 0.08, while states encode local influence, alarm, punishment, and bridge membership.Repression uses ∆ = 6 steps, k = 10, Ac = 0.72, and λinfl = 0.22; Experiment 10 sweeps λinfl over [0.1, 1.0].
A.2 Simulation step loop: Each simulation step samples cached predicted labels, optionally updates endogenous content, applies repression, samples punishments, computes rewards, and records the alarm history.With new features disabled, the loop reduces to the fixed-type base model.
A.3 Noise regimes: Four noise regimes—Oracle, Default, FP-heavy, and FN-heavy—are defined by confusion matrices over content types {H, P, D}.Labels are sampled once per node per time step and cached for consistent observation, enforcement, and metric computation.
A.4 Bridge targeting: Bridge targeting applies multiplier m to bridge nodes predicted as dangerous, testing m = 1.0, m = 1.35, and m = 1.8 while fixing ut = 1.0.The fixed regulator force isolates targeting effects from overall enforcement level.
A.5 Governance loss computation: Governance loss combines dangerous-bridge false negatives, punished-bridge false positives, and squared mean usefulness with equal weights λFN = λFP = λu = 1.The product form weights error rates by the actual activity they fail to address.
B.1 Experiment design grid: Table 5 maps eleven experiments to varied factors, replication counts, and total runs, with seeds paired across conditions by graph realization.Per-experiment configurations add reward formulas, transition strengths, and interpolation schemes.

B.2 Per-experiment configurations

The section specifies configurations for three experiments beyond the shared settings, varying adaptive multipliers, delay and noise, and endogenous content dynamics. Together, these configurations define 2,650 experiment runs.

Experiment 4 (adaptive multiplier): Experiment 4 compares three static multipliers with an adaptive bandit across four noise regimes, totaling 800 runs.The bandit selects m ∈ {1.0, 1.2, 1.4, 1.6, 1.8, 2.0} with ϵ = 0.10 and reward rm = −FPB −2DB.
Experiment 5 (delay × noise): Experiment 5 crosses seven delay values with four noise regimes at fixed bridge multiplier m = 1.35, totaling 1,400 runs.The delay values are ∆∈{0, 2, 4, 6, 8, 10, 14}; other parameters match the shared settings.
Experiment 6 (endogenous content): Experiment 6 crosses exogenous and two endogenous content conditions with three noise regimes, totaling 450 runs.Endogenous content follows per-action Markov chains, with default β = 1.0 and fast β = 1.5.

B.3 Statistical methods

The analysis uses 50 random seeds with observations paired across noise conditions by seed, while reporting seed means, conservative independent-group ANOVA, and Cohen’s d relative to the oracle condition.

50 random seeds (1–50) are used, with observations paired by seed because each seed generates the same network graph across noise conditions.
Reported values are means across seeds, and Table 3’s ANOVA treats conditions as independent groups, a conservative choice because paired testing would yield larger F statistics.
Cohen’s d is computed as d = (¯xcondition−¯xoracle)/spooled, using the pooled standard deviation.

C Robustness, ODD Protocol, and Reproducibility … C.3 Secondary parameter magnitudes

The paper tests whether its governance-cost finding survives weighting and bridge-definition changes, documents the model through the ODD protocol, and identifies several secondary parameters as illustrative choices. Robustness checks preserve the main ranking and show FP-heavy governance loss remains about twice oracle loss across bridge thresholds.

C.1 Robustness checks: Across all 27 λFN, λFP, λu combinations, oracle classification has the lowest Lgov and FP-heavy noise the highest.Only default-versus-FN-heavy ordering reverses in 10 of 27 configurations when λFP ≫λFN down-weights missed threats.
C.1 Robustness checks: 0.082, 0.087, 0.100 versus 0.035, 0.039, 0.048 respectively: FP-heavy governance loss is roughly twice oracle loss for 5%, 12%, and 20% bridge fractions.Each bridge fraction was tested with 50 seeds.
C.2 ODD protocol alignment: The model’s stated purpose is to investigate governance failures produced by classification noise interacting with network structure and hidden by aggregate metrics.This purpose is presented as part of the ODD protocol alignment.
C.2 ODD protocol alignment: The model contains N=240 agents on a directed modular graph, one regulator, one interaction round per step, and runs lasting 500 steps.Agents have actions, Q-tables, true and predicted content types, bridge membership, charisma, detectability, and cost scales.
C.2 ODD protocol alignment: Each step applies noisy classification, Q-learning action selection, optional content transition, delayed-alarm enforcement, reward computation, and Q-table updating.The design includes emergence from noise–structure interaction, Q-learning adaptation, sensing, and stochasticity.
C.2 ODD protocol alignment: The model is self-contained, initializes a stochastic-block-model graph with zeroed Q-tables and independently sampled content types, and defines submodels in Sections 3–4.Sensitivity analysis includes the 27-configuration λ sweep and a cross-topology experiment.
C.3 Secondary parameter magnitudes: Secondary modifiers are illustrative values, including charisma (+0.2), detectability (+0.15), DB reward weight (2× the false-positive term), EMA rate (0.05), and P→D = 0.35.The stated motivation is that structurally central nodes are more influential and visible, while missed dangerous bridges are costlier failures.

C.4 Reproducibility

The simulation is reproducible because its code, configurations, outputs, and main-text results are stored in specified experiment directories. Each run also produces raw trajectories, per-seed summaries, and a configuration manifest.

C.4 Reproducibility: All simulation code, configuration files, and outputs are stored under experiments/.The main-text results are located in experiments/results/paper2/.
C.4 Reproducibility: Each run produces a raw trajectory CSV, a summary with per-seed metrics, and a configuration manifest.