Goal Revelation as a Bridge Between Information-Theoretic Empowerment and Capability-Based Human Power

Abstract

Power matters for AI safety. Optimal agents tend to acquire power across a wide range of objectives (instrumental convergence). As we embed AI agents into socio-technical systems, humans risk gradual disempowerment. Both concerns call for a formal, quantitative measure of power. Two such measures in the context of Markov games are information-theoretic empowerment, the capacity of the channel from an agent's actions to future states, and capability-based individual power, a measure of goal attainment built from the probabilities that a human would attain each goal in a family of candidates were they pursuing it. We show where the two meet. From individual power, Fano's inequality yields a floor $B(s)$. This floor is a lower bound on what we term goal revelation, the mutual information $\mathbb{I}(G;\xi \mid s)$ between the human's latent goal and the realised trajectory. Empowerment caps revelation from above, so that $B(s) \le \mathbb{I}(G;\xi \mid s) \le \mathbb{I}(\mathbf{A}_h \to \xi \mid s) \le \mathfrak{E}_h(s)$. Each quantity can be large while the one below it stays at zero, highlighting the following failure modes. An assistant maximising empowerment can prefer an interface offering broad influence over goal-irrelevant degrees of freedom to one that lets the human attain every goal they might hold. An assistant maximising revelation cannot tell a working interface from one rewired so that every goal yields the wrong outcome, since relabelling goals leaves mutual information unchanged while zeroing every attainment probability. Positive guarantees therefore come only from the attainment end of the chain. A satisfaction floor, computable from two statistics of interaction logs, offers a way to monitor the power users retain in a deployed system, and simulations in random environments show the three quantities are correlated but far from interchangeable.