Whose doctor does the AI recommend? An algorithm audit of reputation and demographic signals in large language model-assisted physician choice

Patients increasingly ask large language model (LLM) assistants which doctor to see, making these systems AI infomediaries: algorithms that intermediate one person's choice among other people and thereby decide, silently and at scale, which physicians become visible. We report a prespecified randomized algorithm audit of what causally moves those recommendations. Seven models (six open-weight; gpt-4o-mini) each chose among five synthetic family-medicine physician cards whose attributes were independently randomized across 3,024 choice sets, three patient personas, nine prompt paraphrases and nine experimental arms, yielding 40,068 scored responses; gender and ethnicity were signaled through names following correspondence-audit methodology. Reputation signals dominate: raising a rating from 3.9 to 4.7 increases choice probability by 31.4 percentage points (pp), and raising the fee from 90 to 190 lowers it by 20.0 pp. Demographic parity is rejected, but not in the direction human audit studies predict: female-signaled names gain 2.5 pp, and Hispanic-, South-Asian- and Black-signaled names gain 1.3-2.9 pp over White-signaled names, tilts worth 7-14 per visit in fee-equivalent terms, and a content-free first-listed position is worth 11. Yet models mentioned gender or ethnicity in at most 0.03% of their stated reasons and abstained in 0.39% of trials, so these effects are invisible in the models' own explanations, and transparency obligations relying on model self-report would not detect them. One reasoning model failed the prespecified auditability gate outright. The frozen design makes the audit repeatable: any new model can be assessed against identical stimuli, making recurring behavioural audit, rather than self-reported explanation, the monitoring technology fit for purpose.