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Traditionally, recommender systems operate by returning a user a set ofitems, ranked in order of estimated relevance to that user. In recent years,methods relying on stochastic ordering have been developed to create "fairer"rankings that reduce inequality in who or what is shown to users. Completerandomization -- ordering candidate items randomly, independent of estimatedrelevance -- is largely considered a baseline procedure that results in themost equal distribution of exposure. In industry settings, recommender systemsoften operate via a two-step process in which candidate items are firstproduced using computationally inexpensive methods and then a full rankingmodel is applied only to those candidates.  In this paper, we consider the effects of inequality at the first step andshow that, paradoxically, complete randomization at the second step can resultin a higher degree of inequality relative to deterministic ordering of items byestimated relevance scores. In light of this observation, we then propose asimple post-processing algorithm in pursuit of reducing exposure inequalitythat works both when candidate sets have a high level of imbalance and whenthey do not. The efficacy of our method is illustrated on both simulated dataand a common benchmark data set used in studying fairness in recommendersystems.

Random Isn't Always Fair: Candidate Set Imbalance and Exposure Inequality in Recommender Systems