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Current practice for evaluating recommender systems typically focuses on point estimates of user-oriented effectiveness metrics or business metrics, sometimes combined with additional metrics for considerations such as diversity and novelty. In this paper, we argue for the need for researchers and practitioners to attend more closely to various distributions that arise from a recommender system (or other information access system) and the sources of uncertainty that lead to these distributions. One immediate implication of our argument is that both researchers and practitioners must report and examine more thoroughly the distribution of utility between and within different stakeholder groups. However, distributions of various forms arise in many more aspects of the recommender systems experimental process, and distributional thinking has substantial ramifications for how we design, evaluate, and present recommender systems evaluation and research results. Leveraging and emphasizing distributions in the evaluation of recommender systems is a necessary step to ensure that the systems provide appropriate and equitably-distributed benefit to the people they affect. 

There is increasing attention to evaluating the fairness of search system ranking decisions. These metrics often consider the membership of items to particular groups, often identified using protected attributes such as gender or ethnicity. To date, these metrics typically assume the availability and completeness of protected attribute labels of items. However, the protected attributes of individuals are rarely present, limiting the application of fair ranking metrics in large scale systems. In order to address this problem, we propose a sampling strategy and estimation technique for four fair ranking metrics. We formulate a robust and unbiased estimator which can operate even with very limited number of labeled items. We evaluate our approach using both simulated and real world data. Our experimental results demonstrate that our method can estimate this family of fair ranking metrics and provides a robust, reliable alternative to exhaustive or random data annotation. 

We introduce the concept of \emph{expected exposure} as the average attention ranked items receive from users over repeated samples of the same query. Furthermore, we advocate for the adoption of the principle of equal expected exposure: given a fixed information need, no item should receive more or less expected exposure than any other item of the same relevance grade. We argue that this principle is desirable for many retrieval objectives and scenarios, including topical diversity and fair ranking. Leveraging user models from existing retrieval metrics, we propose a general evaluation methodology based on expected exposure and draw connections to related metrics in information retrieval evaluation. Importantly, this methodology relaxes classic information retrieval assumptions, allowing a system, in response to a query, to produce a \emph{distribution over rankings} instead of a single fixed ranking. We study the behavior of the expected exposure metric and stochastic rankers across a variety of information access conditions, including \emph{ad hoc} retrieval and recommendation. We believe that measuring and optimizing expected exposure metrics using randomization opens a new area for retrieval algorithm development and progress.