2026/05/05 by Lauri Lovén · 1 citation
#cs.GT
We prove the True-KL0 property for a parametric family of heterogeneous scoring rules arising in scored elicitation mechanisms (AI oversight, forecasting, expert surveys). An agent with private type M>1, scored through a d-dimensional outcome interface, reports to a principal who evaluates via a power-p pseudospherical scoring rule, p ∈ (d,d+1); M captures the agent's information quality relative to a reference. Honest reporting is dominant-strategy optimal for every d and every p>1, without a prior over the agent's type: a consequence of strict properness and identifiability, with a quadratic misreport-loss rate. True-KL0, the property R(M,p,d)<1 for all M>1, d ∈ \2,3,4\, p ∈ (d,d+1), is the quantitative core: R is the Rayleigh quotient of the radial misreport channel of an annular oversight model, and True-KL0 certifies a uniform curvature-domination margin for that channel: 1-R ≥ 0.26 (R ≤ 0.7324, semi-rigorous numerical certificate). Two structural tools drive the proof: (i) a substitution y=(x+1)/(x-1) rewrites the loss integral IL as ∫1M F(y)(M2-y2)d/2 dy with M-independent weight F(y)>0; (ii) log-concavity of IL in M: algebraic for d=2 up to a small certified compact verification, via Prekopa's theorem plus semi-rigorous certificates for d ∈ \3,4\. True-KL0 then follows from elementary tail bounds plus a certified bound on M ∈ [1.001, 20]. We also characterise the dimensional boundary: True-KL0 holds for all p ∈ (d,d+1) when d ≤ 4; d=5 is the unique transition, with pcrit(5) ∈ [5.5718, 5.5750] (mpmath, not interval-certified); for d=6,7 (and conjecturally all d ≥ 6) no threshold exists: the bound fails at every sampled p ∈ (d,d+1).