Honest Reporting in Scored Oversight: True-KL0 Property via the Prekopa Principle

A new paper by Lauri Lovén, published on arXiv (2605.03793), tackles a fundamental problem in mechanism design: how to ensure honest reporting in scored oversight systems like AI evaluation, forecasting competitions, and expert surveys. The paper proves the True-KL₀ property for a parametric family of heterogeneous scoring rules. In these systems, a d-dimensional agent with private information quality M>1 reports to a principal who evaluates using a power-p pseudospherical scoring rule with p in (d,d+1). The result is unconditional dominance: honest reporting maximizes the expected score for every M>1, regardless of the agent's belief distribution. This is a major improvement over traditional approaches that require explicit prior knowledge or complex incentive structures.

The proof relies on two structural tools. First, a substitution rewrites the loss integral into a form where all M-dependence is isolated in a convex factor. Second, Prekopa's theorem on log-concavity preservation shows the integral is log-concave in M, establishing unimodality of the gain ratio R(M,p,d). For d=2, the proof is fully algebraic; for d=3 and 4, it combines analytic reasoning with high-precision numerical verification. The dimensional boundary is also characterized: True-KL₀ holds unconditionally for all p in (d,d+1) when d≤4, but fails above a critical threshold p_crit(d) for d≥5. For d=5, the threshold lies between 5.5718 and 5.5750. The work has immediate implications for designing trustable AI oversight systems, scoring mechanisms, and any setting where honest reporting is paramount.