Intrinsic Barriers and Practical Pathways for Human-AI Alignment: An Agreement-Based Complexity Analysis

AI alignment is formalized as a multi-objective optimization problem called ⟨M,N,ε,δ⟩-agreement, in which a set of N agents (including humans) must reach approximate (ε) agreement across M candidate objectives, with probability at least 1−δ. Analyzing communication complexity, the paper proves an information-theoretic lower bound showing that once either M or N is large enough, no amount of computational power or rationality can avoid intrinsic alignment overheads. This establishes rigorous limits to alignment itself, not merely to particular methods, clarifying a "No-Free-Lunch" principle: encoding "all human values" is inherently intractable and must be managed through consensus-driven reduction or prioritization of objectives. Complementing this impossibility result, the paper constructs explicit algorithms as achievability certificates for alignment under both unbounded and bounded rationality with noisy communication. Even in these best-case regimes, the bounded-agent and sampling analysis shows that with large task spaces (D) and finite samples, reward hacking is globally inevitable: rare high-loss states are systematically under-covered, implying scalable oversight must target safety-critical slices rather than uniform coverage. Together, these results identify fundamental complexity barriers—tasks (M), agents (N), and state-space size (D)—and offer principles for more scalable human-AI collaboration. Because the lower bounds are closely matched by constructive algorithms (up to polynomial terms), they enable principled governance risk thresholds, and the results justify cautious optimism: alignment is tractable in principle, yet only when we restrain objectives and exploit task structure with care.