Beyond Self-Resolution: Settlement Factorization for Robust Natural Language Mechanisms

Jul 16, 2026

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Language models increasingly mediate paid advice through open-ended forecasts, recommendations, plans, and evidence, where a principal uses submitted reports and later compensates contributors. The work formalizes a required separation: reports become hardened records, a public decision record Z uses all admissible advice, and each paid adviser is scored against an externally produced label conditional on Z. A revelation-principle analogue shows influence-free references within a factor of two, and defines an intrinsic own-report leakage invariant ε.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages33

Reading Time1 h 23 min

Abstract

Introduction

arXiv :2607 .04382v 1 [ cs .GT] 5 Jul 2026 Beyond Self-Resolution: Settlement Factorization for Robust Natural Language Mechanisms Nicolas Della Penna [nikete@grouplang.ai](nikete@grouplang.ai) July 2026 Abstract Language models increasingly mediate paid advice: agents submit open-ended forecasts, recommendations, plans, and evidence; a principal acts on the reports; and the mechanism later pays the contributors. Advice should influence the public decision, but no adviser should write the answer key used to evaluate it. We formalize the separation as settlement factorization: reports are hardened into official records, a public decision record Z may use all advice, and each paid adviser is scored against a label whose production is externalized from their own report, conditional on Z. The central result is an analogue of the revelation principle for this setting: resampling the paid report from a committed ghost distribution inside the settlement channel equips every mechanism with an influence-free reference within a factor of two of the best achievable, so factorization is a normal form, and own-report leakage ε—measured in total variation—is an intrinsic invariant of any mechanism, identified behaviorally by worst-case incentive erosion. The invariant has an exact price: with payment kernels of label sensitivity L, truthful margins degrade by at most 2Lε, and the constant is tight—half own-label manipulation, half pandering to a biased evaluator—so faithful advice survives outside decision interests D whenever the externalized margin satisfies γ > D + 2Lε . Settling a growing crowd on the shared decision record dilutes every margin exponentially in the informational redundancy, while afactorized leave-one-out label sustains a constant margin at unit stakes. Stakes outbid decision interests but never evaluator capture; randomized reference settlement makes integrity a threshold good priced per unit of total variation; and differential privacy of the evaluator in the paid report certifies ε by construction. 1 Introduction A model recommends which vendor to hire. A research agent proposes an experiment. A reviewer writes an assessment. A provider on an agent marketplace describes its skills, suggests a plan, and predicts whether the plan will work. In each case, a principal wants to reward useful language without delegating the entire institutional decision to the report itself. It is helpful to call these systems advice mechanisms. Their messages are richer than scalar forecasts. An adviser may provide factual claims, conditional predictions, a recommended action, a decomposition of the task, caveats, and supporting evidence in one report. The principal retains the right to combine the reports, apply a constitution, and choose an action. This is neither ordinary preference revelation nor mere text evaluation: the report is intended to change what the principal does. That intended influence creates a design boundary: The report may be evidence for the decision, but it must not write its own answer key. The first clause is why a leave-one-out decision rule is often inappropriate. Good advice should affect the public decision. The second clause is why a single unconstrained “judge the report and decide its reward” call is fragile. If adviser i can steer the label against which adviser i is scored, a high payment may reflect evaluator control rather than information, effort, or decision value. Della Penna (2024) isolates a positive regime in which a foundation model can interpret rich reports and directly implement allocations and transfers under strong accuracy and informationoverdetermination conditions.1 The present paper does not dispute that result. It asks what an institution should expose once it needs a robust, inspectable, and modular settlement process. The answer is settlement factorization. Reports are hardened into official advice records. A public decision record may use all admissible

FAQs

What problem does “settlement factorization” address in natural language advice mechanisms?

It enforces a separation between advice used to influence a public decision and the answer key/label used to evaluate and pay contributors, preventing advisers from steering their own scoring.

How does the paper relate to the revelation principle in this setting?

It provides an analogue stating that resampling paid reports from a committed ghost distribution yields an influence-free reference mechanism within a factor of two of the best achievable, effectively giving a normal form.

What is the role of own-report leakage ε and how is it measured?

Own-report leakage ε is an intrinsic invariant of any mechanism, measured via total variation, and it governs how much incentives erode, with payments degrading truthful margins by an amount tied to label sensitivity and ε.

Jul 16, 2026

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