Large language models, trained on personal data, are increasingly able to mimic individual personalities. These ``AI clones'' or ``AI agents'' have the potential to transform how people search for matches in contexts ranging from marriage to employment. This paper presents a theoretical framework to study the tradeoff between the substantially expanded search capacity of AI representations and their imperfect representation of humans. An individual's personality is modeled as a point in $k$-dimensional Euclidean space, and an individual's AI representation is modeled as a noisy approximation of that personality. I compare two search regimes: Under in person search, each person randomly meets some number of individuals and matches to the most compatible among them; under AI-mediated search, individuals match to the person with the most compatible AI representation. I show that a finite number of in-person encounters yields a better expected match than search over infinite AI representations. Moreover, when personality is sufficiently high-dimensional, simply meeting two people in person is more effective than search on an AI platform, regardless of the size of its candidate pool.

翻译：基于个人数据训练的大型语言模型，正日益能够模拟个体人格。这些“AI克隆”或“AI代理”有潜力改变人们在从婚姻到就业等各种情境下的匹配搜索方式。本文提出了一个理论框架，用以研究AI表征在极大扩展搜索能力与其对人类的不完美表征之间的权衡。个体的个性被建模为$k$维欧几里得空间中的一个点，而个体的AI表征则被建模为该个性的一个有噪声近似。我比较了两种搜索机制：在面对面搜索机制下，每个人随机遇见一定数量的个体，并与其中最兼容者匹配；在AI中介搜索机制下，个体与AI表征最兼容的人匹配。我证明了有限次数的面对面相遇，其产生的预期匹配质量优于对无限数量AI表征的搜索。此外，当个性维度足够高时，仅仅与两个人面对面相遇，也比在任何规模的AI平台候选池中进行搜索更为有效。