Whose hotel does the AI recommend? An algorithm audit of reputation signals in LLM-assisted hotel selection

Travelers increasingly ask large language model (LLM) assistants which hotel to book, making these systems gatekeepers of property visibility -- yet what moves their recommendations is undocumented. We conduct a pre-specified algorithm audit using a randomized choice-based conjoint: across personas, prompt templates, and twelve open-weight and proprietary models, assistants choose among five hotels whose guest rating, review volume and recency, management response, chain affiliation, price, eco-certification, and list position are independently randomized. We estimate the average marginal component effect of each signal on the probability of recommendation. Guest rating and price dominate (a top rating raises selection by 31.6 percentage points; a high price lowers it by 30.0), reproducing human valence-and-price primacy but over-weighting eco-certification and ignoring management response. List position -- a content-free artifact -- shifts recommendations causally, worth about \$12 per night. Stated reasons track revealed weights imperfectly. The findings ground generative engine optimization and the accountability of AI infomediaries in causal evidence.