Goal revelation: a bridge between information-theoretic empowerment and capability-based human power

Researchers propose goal revelation, a mutual-information measure linking two kinds of power measures in Markov games: information-theoretic empowerment and capability-based individual human power. The Fano inequality yields a lower bound B(s) on goal revelation from individual power, while empowerment forms an upper bound, giving the inequality chain B(s) ≤ I(G;ξ|s) ≤ I(A_h→ξ|s) ≤ E_h(s). Each quantity in the chain can be large while the next is zero, corresponding to two failure modes: an assistant maximizing empowerment may prefer interfaces with broad influence over goal-irrelevant degrees of freedom over interfaces that let the human achieve all goals; an assistant maximizing goal revelation cannot distinguish a normal interface from one that has been rewired so that every goal yields the wrong result, because relabeling goals leaves mutual information unchanged while driving all achievement probabilities to zero, so positive guarantees can only come from the achievement end. The paper gives a lower bound on satisfaction computable from two statistics of interaction logs, for monitoring the power users retain in deployed systems; simulations in stochastic environments show the three quantities are correlated but far from interchangeable.