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.

翻译：用户面对搜索引擎返回的列表，该列表按相关性噪声代理排序，用户依次决定是否支付固定成本以检查下一项，或停止并保留已发现的最佳结果。她进入页面时并不知晓各项质量优劣，因此每次检查既产生一个候选结果，又更新她对页面整体质量的信念。我们证明最优策略是一个"杰出法则"：当用户的最佳发现超过页面平均项的后验均值达到一个深度依赖阈值时，她便停止搜索。由此引发的动态过程坍缩为一维马尔可夫链，通过闭式递推获得检查深度的完整分布。该模型揭示了用户停止搜索的三种隐藏机制（信任、承诺与止损），并产生丰富的可检验含义。此外，贝叶斯理性视角提供了一种新颖的学习排序似然函数：观测到的截断深度将潜在相关性路径截断为生存不等式的多面体，其高斯概率是任意基于特征的相关性预测的可微函数。