  Ranking systems are ubiquitous in modern Internet services, including online
marketplaces, social media, and search engines. Traditionally, ranking systems
only focus on how to get better relevance estimation. When relevance estimation
is available, they usually adopt a user-centric optimization strategy where
ranked lists are generated by sorting items according to their estimated
relevance. However, such user-centric optimization ignores the fact that item
providers also draw utility from ranking systems. It has been shown in existing
research that such user-centric optimization will cause much unfairness to item
providers, followed by unfair opportunities and unfair economic gains for item
providers.
  To address ranking fairness, many fair ranking methods have been proposed.
However, as we show in this paper, these methods could be suboptimal as they
directly rely on the relevance estimation without being aware of the
uncertainty (i.e., the variance of the estimated relevance). To address this
uncertainty, we propose a novel Marginal-Certainty-aware Fair algorithm named
MCFair. MCFair jointly optimizes fairness and user utility, while relevance
estimation is constantly updated in an online manner.
  In MCFair, we first develop a ranking objective that includes uncertainty,
fairness, and user utility. Then we directly use the gradient of the ranking
objective as the ranking score. We theoretically prove that MCFair based on
gradients is optimal for the aforementioned ranking objective. Empirically, we
find that on semi-synthesized datasets, MCFair is effective and practical and
can deliver superior performance compared to state-of-the-art fair ranking
methods. To facilitate reproducibility, we release our code
https://github.com/Taosheng-ty/WSDM22-MCFair.
