The Recursive Paradox: The Economic and Environmental Cost of Governing AI with AI in Financial and Sustainable Markets

When an AI system exhibits failures, the default industry response is to deploy a second AI to monitor, correct, or validate the first. We formalize this practice as recursive AI governance and argue that it creates a paradox: each additional governance layer increases computational, financial, and environmental costs without guaranteeing epistemic improvement, because a validator trained on the same data-generating process as the system it oversees inherits the same blind spots. We support the thesis with evidence from two domains. First, using ~420,000 Kalshi prediction-market contracts (Bixhili, 2026a), we show that apparently informative signals are largely arithmetic artifacts of price calibration and that no model family examined beat the market baseline out of sample — as theory predicts (Grossman & Stiglitz, 1980; Lo, 2004). Second, we quantify the resource bill of the governance layer (IEA, 2025; Li et al., 2023). We then assess the strongest objection — that a single unified "Monolith" could internalize all validation — and correct three mathematical overclaims common in this debate: parameter-set uniqueness does not hold; achievable loss is bounded below by the irreducible Bayes risk; and information theory penalizes multi-agent systems economically, not logically. The operative dichotomy is not "Monolith vs. Swarm" but anchored vs. self-referential: any system acting on an open, adversarial environment requires an external, manipulation-resistant feedback signal. In finance, that anchor is the market price itself, supplemented by human oversight.