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

Jaime Ruiz-Serra, Tomáš Gavenčiak, Jobst Heitzig

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 $\mathbb{I}(G;ξ\mid s)$ between the human's latent goal and the realised trajectory. Empowerment caps revelation from above, so that $B(s) \le \mathbb{I}(G;ξ\mid s) \le \mathbb{I}(\mathbf{A}_h \to ξ\mid s) \le \mathfrak{E}_h(s)$. 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…