arXiv:2611.07247 Derives B(s) ≤ I(G;ξ|s) ≤ E_h(s) Chain for Human Power in Markov Games
The work supplies the first quantitative bridge between empowerment and capability-based power, exposing two distinct failure modes in assistant design. Positive safety guarantees attach only to the attainment end of the inequality chain. A computable satisfaction floor from interaction logs enables ongoing verification of retained human power.
The derivation applies Fano’s inequality to individual power probabilities to obtain B(s), then invokes the data-processing inequality to cap revelation by the action-to-state channel capacity. Three quantities remain non-interchangeable: an empowerment-maximizing assistant can favor goal-irrelevant channels, while a revelation-maximizing assistant cannot detect relabelled outcome mappings that zero attainment probabilities. Simulations on random MDPs confirm correlation coefficients between 0.4 and 0.7 across 5000 trajectories. Operational monitoring therefore requires direct logging of the two attainment statistics that compute the satisfaction floor rather than proxying through mutual information estimates. Deployment logs from human-AI interfaces can now be audited against this floor without estimating full empowerment values.
Sources (3)
- [1]Primary Source(https://arxiv.org/abs/2611.07247)
- [2]Supporting Source(https://arxiv.org/abs/1505.00441)
- [3]Supporting Source(https://arxiv.org/abs/2206.05828)