Rankings are ubiquitous across many applications, from search engines to hiring committees. In practice, many rankings are derived from the output of predictors. However, when predictors trained for classification tasks have intrinsic uncertainty, it is not obvious how this uncertainty should be represented in the derived rankings. Our work considers ranking functions: maps from individual predictions for a classification task to distributions over rankings. We focus on two aspects of ranking functions: stability to perturbations in predictions and fairness towards both individuals and subgroups. Not only is stability an important requirement for its own sake, but -- as we show -- it composes harmoniously with individual fairness in the sense of Dwork et al. (2012). While deterministic ranking functions cannot be stable aside from trivial scenarios, we show that the recently proposed uncertainty aware (UA) ranking functions of Singh et al. (2021) are stable. Our main result is that UA rankings also achieve multigroup fairness through successful composition with multiaccurate or multicalibrated predictors. Our work demonstrates that UA rankings naturally interpolate between group and individual level fairness guarantees, while simultaneously satisfying stability guarantees important whenever machine-learned predictions are used.

我们的研究考虑了排名函数：将分类任务的个别预测映射为排名分布，重点关注对预测扰动的稳定性以及对个体和子群体的公平性。我们展示了最近提出的基于不确定性的排名函数在稳定性方面的表现，并且通过与多准确预测或多校准预测器的成功组合，实现了多组公平性。我们的研究表明，基于不确定性的排名在组和个体级公平性保证之间自然插值，并且同时满足在使用机器学习预测时重要的稳定性要求。

不确定预测下的排序稳定性和多组公平性