Fundamental Impossibility Results in AI Safety: Trading Off between Desiderata

This paper explores the idea of promoting well-being and safety in human-AI interactions by forcing AI agents explicitly to empower humans and to manage the power balance between humans and AI agents in a desirable way. Using a principled, partially axiomatic approach based on desirable properties, we design a parametrizable and decomposable objective function for AI systems that represents an inequality- and risk-averse long-term aggregate of human power. It can take into account models of human bounded rationality and social norms, and crucially, considers a wide variety of possible human goals. We prove how certain desiderata enforce particular functional forms and restrict parameter ranges. We exemplify the consequences of softly maximizing this metric in several paradigmatic situations and describe what instrumental sub-goals it will likely imply.

Artificial Intelligence (AI) safety systems combine character shaping (e.g., Reinforcement Learning from Human Feedback [RLHF], Constitutional AI), which modifies behavioral distributions at training time, with rule enforcement (e.g., output filters, safety classifiers), which blocks harmful outputs at inference time, yet little formal analysis exists on how their optimal balance should change as deployment scales increase. We introduce a stylized comparative-statics model that parameterizes safety design as a resource allocation alpha in [0,1] between these two approaches, incorporating scale-dependent filter degradation, common-mode failures, and character fragility -- the risk that shaped behavior degrades or collapses under novel conditions. Under a multiplicative Pareto damage model, we derive closed-form expected harm and supplement it with tail-risk (CVaR) analysis via Monte Carlo simulation. Across three scenarios (optimistic, moderate, pessimistic), the optimal alpha* is interior or at the rules-only boundary and shifts weakly toward character shaping as deployment scale T grows, from negligible (Delta alpha* = +0.01) to pronounced (Delta alpha* = +0.21) depending on scenario. The dominant parameter is the baseline character fragility rate p^(0)_frag, which shifts alpha* by 0.50 across its range -- far exceeding the effect of tail severity, filter quality, or common-mode failure probability. CVaR and expected-harm optima converge at large T. These results suggest that safety architecture decisions depend less on deployment scale per se than on the reliability of character shaping under distributional shift.

As AI systems become more capable, training procedures that optimize for downstream outcomes risk introducing implicit agency: goal-directed behavior that designers never specified. We present a formal safety argument for the Scientist AI (SAI) Predictor, trained to approximate the Bayesian posterior conditioned on a dataset of "epistemically contextualized" natural-language statements. We argue that such a Predictor can honestly predict agents, actions, and their consequences without itself being an agent that selects outputs to achieve goals. This rests on data representation and on the training procedure. Epistemic contextualization of text distinguishes latent factual claims from communication acts, so expressions of goals are treated as evidence to be explained rather than drives the model adopts. With a posterior-seeking training objective, this is intended to drive the Predictor toward calibrated, cautious predictions. Training proceeds so downstream effects of deploying a prediction never serve as a reward signal; any agency the system needs is supplied by explicit scaffolding constrained by guardrails. We prove that, under assumptions on the training dynamics and on the argued sparsity of dangerous Predictors, the probability that training produces a Predictor whose guarded deployment carries residual harm above a specified threshold is small: a dangerous Predictor would have to underestimate harm in a coordinated way across many queries while such coordinated patterns are rare under the initialization distribution and receive no direct training signal. Safety and accuracy are jointly supported in this framework, since the constraints that secure accuracy are the same ones that make coordinated deception costly. These guarantees against misalignment and agency arising from within the Predictor itself do not preclude the use of the Predictor as part of an agentic system.