The Riskless Corner: Why Prudence Cannot Pay for Vigilance

Abstract

An auditing programme that models recurring internal-control failures as a no-collusion equilibrium has, until now, priced the monitor’s incentives as if he were risk-neutral — and one of its quietest results depended on it: the precision with which a court adjudicates a failure washes out of the monitor’s expected blame, by the tower property, so forensic quality never enters his incentives. This paper prices the variance of the blame a risk-averse monitor might be assigned, and shows that a single fact then organizes everything: the trap — abandoning the post — is riskless, because a failure is then certain and its blame fixed. Because the trap bears no risk, the lower boundary of the strategic-inattention fold cannot be moved by risk aversion or by adjudicator precision (an invariance that is preference-free, signal-free, and detection-free); and because the trap bears no risk, the monitor’s risk-adjusted ledger coincides with the material ledger there and, by concavity, lies below it everywhere else. The consequence is a chain inequality: a risk-averse monitor’s engaged post, however heavy his coverage, is never something he prefers on net — his vigilance is a local optimum sustained by the equilibrium’s basin, not by conviction, and once a shock carries him out it does not return. This separates prudence sharply from an internalized duty, which enters the ledger as a subsidy the corner’s risklessness denies to prudence: duty can pay for a held post; prudence can only defend one. Between these results, forensic quality proves two-faced — sharpening marginal blame at low coverage (eroding vigilance, and past a window of mid-quality forensics destroying it) while saturating it at high coverage (reviving vigilance as costly self-insurance against the court’s noise) — so that the penalty paradox acquires a bounded upper edge and an institution improving its forensics halfway can extinguish the vigilance it sought to sharpen. Pricing the whole wealth lottery rather than the charge alone leaves the chain inequality intact but dissolves the geometry: certain doom saturates as certain safety does, the floor sinks, and past a modest risk aversion the fold dies into a pure switch, below which a monitor abandons a post that is materially his to keep — fatalism in the strict sense that he refuses to escape a failure because it is nearly certain. The results are calibration-flagged throughout; the spine is established for general risk-averse expected utility and across signal structures and detection levels.