[Q_is_4_Quantum]

ChatGPT suggests (and cites your paper):

Give the humans an order 1,2,3,…, and let a referee read them in that order. Person k tosses one fair coin and reports H/T. The referee stops at the first time the reported heads exceed the reported tails. If N people were consulted, choose one of those N uniformly at random. Output heads iff that chosen person’s coin was heads.

For a one-pass version: instead of storing the whole consulted prefix, the referee can keep a single “currently marked” consulted person, and when the k-th consulted coin arrives, replace the mark by that new person with probability 1/k. When the process stops, the marked person is uniform among the consulted ones.