arXiv:2502.05934v2 Announce Type: replace Abstract: We formalize AI alignment as a multi-objective optimization problem called $\langle M,N,\varepsilon,\delta\rangle$-agreement that generalizes prior approaches with fewer assumptions, in which a set of $N$ agents (including humans) must reach approximate ($\varepsilon$) agreement across $M$ candidate objectives with probability at least $1-\delta$. Using communication complexity, we prove an information-theoretic lower bound demonstrating that once either $M$ or $N$ is large enough, no interaction or rationality can avoid intrinsic alignment overheads. This barrier establishes rigorous intrinsic limits to alignment \emph{itself}, not merely to specific methods, clarifying a crucial no free lunch'' principle: encodingall human values'' inevitably leads to misalignment, requiring future methods to explicitly manage complexity through consensus-driven reduction or prioritization of objectives. Complementing this impossibility result, we provide explicit algorithms achieving alignment under both computationally unbounded and bounded rationality with noisy messages. Even in these best-case scenarios where alignment to arbitrary precision is theoretically guaranteed, our analysis identifies three critical scalability barriers: the number of tasks ($M$), agents ($N$), and task state space size ($D$); thereby highlighting fundamental complexity-theoretic constraints and providing guidelines for safer, scalable human-AI collaboration.
