While large language models (LLMs) perform well on well-defined tasks, effective
prompts are challenging when tasks depend on users’ soft traits and latent prefer-
ences. We formalize this friction by introducing preference uncertainty—capturing
soft information—into a cheap talk framework (Crawford and Sobel, 1982) and model soft
information communication with AI as the investor’s optimal stopping problem with
Brownian information flow. We propose a novel empirical methodology to test theoret-
ical predictions...