Large language models, trained on personal data, may soon be able to mimic individual personalities. These ``AI clones'' or ``AI agents'' have the potential to transform how people search over one another in contexts ranging from marriage to employment -- indeed, several dating platforms have already begun using AI clones to evaluate potential pairings between users. This paper presents a theoretical framework to study the tradeoff between the substantially expanded search capacity of AI clones, and their imperfect representation of humans. Individual personalities are modeled as points in $k$-dimensional Euclidean space, and their AI clones are modeled as noisy approximations of these personalities. I compare two search regimes: an ``in-person regime'' -- where each person randomly meets some number of individuals and matches to the most compatible among them -- against an ``AI representation regime'' -- in which individuals match to the person whose AI clone is most compatible with their AI clone. I show that a finite number of in-person encounters exceeds the expected payoff from search over infinite AI clones. Moreover, when the dimensionality of personality is large, simply meeting two people in person produces a better expected match than entrusting the process to an AI platform, regardless of the size of its candidate pool.