Bayesian Rational Search Engine User

A user faces a list returned by a search system, ordered by a noisy proxy for relevance, and decides sequentially whether to pay a fixed cost to inspect another item or stop with the best she has uncovered. She does not enter the page knowing how good its items are, so each inspection both produces a candidate item and refines her belief about the page's underlying quality. We show the optimal policy is a standout rule: the user stops as soon as her best find exceeds her posterior mean of an average item on the page by a depth-dependent threshold. The induced dynamics collapse to a one-dimensional Markov chain, which yields the full distribution of inspection depth through a closed-form recursion. The model uncovers three hidden mechanisms (trust, commit, and cut-losses) on why users stop and yields a rich set of testable implications. Moreover, the Bayesian-rational view delivers a novel learning-to-rank likelihood: an observed depth censors the latent relevance path into a polyhedron of survival inequalities, whose Gaussian probability is a differentiable function of any feature-based relevance prediction.