Settlement factorization theory ensures AI advice integrity within factor 2

Language models increasingly mediate paid advice environments where agents submit open-ended forecasts, recommendations, or plans, and a principal later pays contributors based on outcomes. A critical challenge is preventing advisers from manipulating the evaluation process—no adviser should write the answer key used to judge their own report. Nicolas Della Penna's new paper from arXiv (2607.04382) formalizes this 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: 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. This shows factorization is a normal form, and own-report leakage epsilon—measured in total variation—is an intrinsic invariant of any mechanism. The invariant has an exact price: with payment kernels of label sensitivity L, truthful margins degrade by at most 2L epsilon, with the constant tight (half own-label manipulation, half pandering to a biased evaluator). Faithful advice survives outside decision interests D whenever the externalized margin satisfies gamma > D + 2L epsilon. The paper also shows that settling a crowd dilutes every margin exponentially in informational redundancy, while a factorized leave-one-out label sustains constant margins 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; differential privacy of the evaluator in the paid report certifies epsilon by construction.