The Probability Ranking Principle (PRP) has been considered as the foundational standard in the design of information retrieval (IR) systems. The principle requires an IR module's returned list of results to be ranked with respect to the underlying user interests, so as to maximize the results' utility. Nevertheless, we point out that it is inappropriate to indiscriminately apply PRP through every stage of a contemporary IR system. Such systems contain multiple stages (e.g., retrieval, pre-ranking, ranking, and re-ranking stages, as examined in this paper). The \emph{selection bias} inherent in the model of each stage significantly influences the results that are ultimately presented to users. To address this issue, we propose an improved ranking principle for multi-stage systems, namely the Generalized Probability Ranking Principle (GPRP), to emphasize both the selection bias in each stage of the system pipeline as well as the underlying interest of users. We realize GPRP via a unified algorithmic framework named Full Stage Learning to Rank. Our core idea is to first estimate the selection bias in the subsequent stages and then learn a ranking model that best complies with the downstream modules' selection bias so as to deliver its top ranked results to the final ranked list in the system's output. We performed extensive experiment evaluations of our developed Full Stage Learning to Rank solution, using both simulations and online A/B tests in one of the leading short-video recommendation platforms. The algorithm is proved to be effective in both retrieval and ranking stages. Since deployed, the algorithm has brought consistent and significant performance gain to the platform.
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