Information design is typically studied through the lens of Bayesian signaling, where signals shape beliefs purely based on their correlation with the true state of the world. However, behavioral economics and psychology emphasize that human decision-making is more complex and can depend on how information is framed. This paper formalizes a language-based notion of framing and bridges this to the popular Bayesian-persuasion model. We model framing as a possibly non-Bayesian, linguistic way to influence a receiver's prior belief, while a signaling/recommendation scheme can further refine this belief in the classic Bayesian way. A key challenge in systematically optimizing in this framework is the vast space of possible framings and the difficulty of predicting their effects on receivers. Based on growing evidence that Large Language Models (LLMs) can effectively serve as proxies for human behavior, we formulate a theoretical model based on access to a framing-to-belief mapping. This model then enables us to precisely characterize when solely optimizing framing or jointly optimizing framing and signaling is tractable. We substantiate our theoretical analysis with an empirical study that leverages LLMs to optimize over the natural-language framing space using an iterative prompt optimization method combined with analytical solvers for optimal signaling schemes.

翻译：信息设计通常通过贝叶斯信号传递的视角进行研究，其中信号纯粹基于其与真实世界状态的相关性来塑造信念。然而，行为经济学和心理学强调，人类决策更为复杂，可能取决于信息的呈现方式。本文形式化了一种基于语言的呈现方式概念，并将其与流行的贝叶斯劝说模型相连接。我们将呈现方式建模为一种可能非贝叶斯的、语言化的影响接收者先验信念的方式，而信号传递/推荐方案可以进一步以经典贝叶斯方式细化这一信念。在此框架下系统优化的一个关键挑战在于可能的呈现方式空间极其庞大，且难以预测其对接收者的影响。基于大语言模型（LLMs）能有效替代人类行为的日益增长的证据，我们构建了一个基于呈现方式到信念映射的理论模型。该模型使我们能够精确刻画仅优化呈现方式或联合优化呈现方式与信号传递在何种情况下是可处理的。我们通过一项实证研究验证了理论分析，该研究利用LLMs，结合迭代提示优化方法与最优信号传递方案的解析求解器，在自然语言呈现空间中进行优化。