Quantifying Theoretical AI Alignment Guarantees: Receiver-Utility Bounds in Bayesian Persuasion

2026-06-20

AI Summary

This study addresses the question of how much useful information a human receiver can extract from signals sent by an AI whose objectives are misaligned with their own. Within the Bayesian persuasion framework, the paper models the AI’s strategic distortion of information and analyzes the upper bound on the receiver’s expected utility when decisions are based solely on prior beliefs and received signals. The key contributions include the first proof that the receiver’s utility is at most 3/2 times the utility achievable by relying on the prior alone; for η-approximately independent priors, an additive loss bound of at most ηn is established; and a constructive six-bit counterexample demonstrates a utility ratio of 39/31, thereby disproving the conjectured universality of a 5/4 upper bound.

Abstract

Misalignment can change how information moves from an AI agent to a human user. We model this as an information advantage: the AI agent observes the world state, while the human receiver only knows a prior and must act after seeing the agent's signal. A strategic AI sender may withhold evidence or garble information in order to steer the human's decision. We ask how much useful information can still reach the human when the AI optimizes a misaligned objective. We study a Bayesian persuasion model in which the world state is a bit string, the human receiver wants to guess the bits correctly, and a single AI sender wants the receiver to guess as many bits as possible as $1$. For a prior $μ$, let $R_0(μ)$ be the receiver's utility from using only the prior, and let $R_{\max}(μ)$ be the largest receiver utility among signaling schemes that are optimal for the sender. We prove $R_{\max}(μ)/R_0(μ)\leq 3/2$. This bound improves for priors close to the independent product prior with the same marginals: if $μ(x)\geq (1-η)π_μ(x)$ for every state $x$, then $R_{\max}(μ)\leq R_0(μ)+ηn$. We also give a six-bit prior for which $R_{\max}(μ)/R_0(μ)=39/31>5/4$, so no universal $5/4$ bound is possible.

Problem

• AI alignment
• Bayesian persuasion
• information asymmetry
• receiver utility
• misaligned objectives

Innovation

• Bayesian persuasion
• AI alignment
• information asymmetry
• utility bounds
• strategic signaling