Revision as of 17:27, 13 October 2025

Abstract

We introduce Authority Entropy, an index that quantifies the distribution of authority stances within dialogue windows and tests its predictive value for compliance, convergence speed, and equilibrium stability. Using a multilingual lexicon of authority-bearing constructions anchored in the regla compilada as an operational constraint set, we train a strictly causal classifier that maps text to stance probabilities over {low, neutral, high}. Authority Entropy is computed per sliding window, together with its slope and volatility, and related to behavioral endpoints through survival models and doubly robust estimators. The study spans synthetic arenas with controllable payoffs, open multi-party tasks with outcome labels, and consented human–model interactions. Baselines include sentiment, toxicity, politeness, formality, and power taggers. Stress tests apply adversarial edits that alter authority cues while preserving semantics to assess sensitivity of entropy and downstream effects. Primary outcomes are compliance rate, convergence time, payoff stability, and regret, reported with leakage audits, calibration checks, and confidence intervals. Results target a public specification of the index, a causal benchmark and leaderboard, and open tooling to visualize instability regimes over time. The contribution is a portable, language-aware measure that links local authority structure to cooperative dynamics without right context leakage. Acknowledgment / Editorial Note This article is published with editorial permission from LeFortune Academic Imprint, under whose license the text will also appear as part of the upcoming book AI Syntactic Power and Legitimacy. The present version is an autonomous preprint, structurally complete and formally self-contained. No substantive modifications are expected between this edition and the print edition. LeFortune holds non-exclusive editorial rights for collective publication within the Grammars of Power series. Open access deposit on SSRN is authorized under that framework, if citation integrity and canonical links to related works (SSRN: 10.2139/ssrn.4841065, 10.2139/ssrn.4862741, 10.2139/ssrn.4877266) are maintained.

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