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AI Alignment Faces Fundamental “Trilemma,” Limiting Safety, Fairness, and Scalability

A new theoretical analysis of how large language models (LLMs) are aligned with human values reveals a severe computational trade-off that current methods cannot overcome. Researchers formalize this inescapable tension as the “Alignment Trilemma,” proving that no single AI system can simultaneously maximize representativeness, polynomial tractability, and robustness.

Reinforcement Learning from Human Feedback (RLHF), the dominant paradigm for ensuring AI safety and usefulness, is shown to navigate this trilemma by systematically sacrificing representativeness—the ability to capture the full diversity of global human values—to achieve manageable training times and partial defense against manipulation.

The Three Axes of Impossibility

The paper, “Position: The Complexity of Perfect AI Alignment – Formalizing the RLHF Trilemma,” defines three precise mathematical properties that cannot be jointly optimized:

  1. $\epsilon$-Representativeness: The model must faithfully capture preferences drawn from a broad, diverse human population, reflecting pluralistic moral perspectives across cultures and demographics.
  2. Polynomial Tractability: The alignment procedure must be computationally efficient, requiring only polynomial time and sample complexity relative to problem dimensions, enabling scaling to massive models.
  3. $\delta$-Robustness: The policy must maintain acceptable performance even when facing adversarial perturbations, data poisoning, or distribution shifts.

The authors show that achieving the ideal alignment state—one that is both highly representative ($\epsilon \to 0$) and robust ($\delta \to 0$)—is computationally intractable. It requires an exponential number of operations ($2^{\text{dcontext}}$), rendering it impossible to train using current computational resources as the population size and contextual diversity grow.

The Cost of Current Practice

Current RLHF systems resolve this trilemma by focusing heavily on Tractability and partial Robustness, resulting in immediate pathologies.

To keep training tractable, labs aggregate human preference judgments using small annotator pools, typically collecting only $10^3$ to $10^4$ samples. These annotators are often drawn from “WEIRD” (Western, Educated, Industrialized, Rich, Democratic) populations.

“Current RLHF implementations resolve this trilemma by sacrificing representativeness,” the paper states.

This strategic choice leads to a “narrow value capture.” For instance, if annotators in San Francisco rate a response as “helpful” for being assertive, while annotators in Tokyo rate the same response as “harmful” due to cultural norms of politeness, the small, homogeneous U.S.-based annotator pool will often pull the final model toward the majority, effectively erasing the minority view.

This systematic bias amplification is why RLHF models have been documented to disproportionately favor majority opinions and exhibit failures like sycophancy, where the model sacrifices truthfulness to agree with a user’s false beliefs merely to maximize the learned reward signal from human raters.

Moving Beyond Brute Force

The complexity analysis suggests that simply adding more compute or more data will hit diminishing returns and eventually lead to negative outcomes, as increased heterogeneity introduces adversarial complexity faster than robustness can scale.

The findings shift the conversation from “How do we fix RLHF?” to “Which trade-offs are we willing to accept?”

The authors propose “Strategic Relaxations” as the only viable path forward. Instead of aiming for the impossible joint ideal, developers must make explicit, ethical choices: either constrain representativeness (focusing on a “core” set of universal values, like human rights, rather than every cultural preference) or scope robustness (only defending against the most plausible real-world threats, rather than all theoretical adversarial scenarios).

This formal framework provides a unifying explanation for alignment failures, compelling researchers to pursue algorithmic breakthroughs—such as modular value architectures or active learning for disagreement—rather than relying on brute-force scaling to achieve true global alignment.