Insuring the Fallback: Capacity, Monitoring and the Third Audience in Competence Signalling under Improving AI

Andreas Bauer

Papers from arXiv.org

Abstract: When generative AI makes the deliverable uninformative, what a professional services provider can still certify is the preserved human capability to catch the machine's error, and the certifying instrument is a liability pledge whose expected cost falls in that capability. The pledge is credible only up to what the provider can stand behind, and in practice that ceiling is supplied by an underwriter. We make the underwriter a strategic third actor choosing how much of the pledge to bear and how precisely to monitor the insured's engagement policy. Two objects govern everything: the informational retention $\psi=r+(1+\lambda)(1-r)m$, the share of the pledge's expected cost that varies with the provider's type, and the pooled load $\xi=(1+\lambda)(1-r)(1-m)$, the share that does not. Single crossing survives iff $\psi>0$: full cover from a blind underwriter destroys separation outright. We prove a capacity-illusion result: the largest ticket served under separation is proportional to $\hat{C}=\psi\bar{L}$, with $\max_r\hat{C}=W+(1+\lambda)mK$ at a retention $r^*=W/(W+K)$ independent of $m$. With a blind underwriter this collapses to the provider's own capital $W$ exactly: third-party capacity is informationally worthless, however large. Monitoring converts capacity into credibility at a linear rate. Cover erodes the fallback stock it insures only when the underwriter is blind: the engagement abandonment threshold shifts by 43% of its uninsured value at $m=0$ and by 1.0% at $m=1$. Because a monitoring underwriter partly reveals what the pledge was meant to signal, demand for client-facing certification is hump-shaped in monitoring precision whenever underwriting information is disclosed. A stochastic market with censored verification records confirms that incentive compatibility survives noisy beliefs, with deviations from truth-telling falling at rate $n^{-1/2}$.

Date: 2026-08
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