A popular methodology for building binary decision-making classifiers in the
presence of imperfect information is to first construct a non-binary "scoring"
classifier that is calibrated over all protected groups, and then to
post-process this score to obtain a binary decision. We study the feasibility
of achieving various fairness properties by post-processing calibrated scores,
and then show that deferring post-processors allow for more fairness conditions
to hold on the final decision. Specifically, we show:
1. There does not exist a general way to post-process a calibrated classifier
to equalize protected groups' positive or negative predictive value (PPV or
NPV). For certain "nice" calibrated classifiers, either PPV or NPV can be
equalized when the post-processor uses different thresholds across protected
groups, though there exist distributions of calibrated scores for which the two
measures cannot be both equalized. When the post-processing consists of a
single global threshold across all groups, natural fairness properties, such as
equalizing PPV in a nontrivial way, do not hold even for "nice" classifiers.
2. When the post-processing is allowed to `defer' on some decisions (that is,
to avoid making a decision by handing off some examples to a separate process),
then for the non-deferred decisions, the resulting classifier can be made to
equalize PPV, NPV, false positive rate (FPR) and false negative rate (FNR)
across the protected groups. This suggests a way to partially evade the
impossibility results of Chouldechova and Kleinberg et al., which preclude
equalizing all of these measures simultaneously. We also present different
deferring strategies and show how they affect the fairness properties of the
overall system.
We evaluate our post-processing techniques using the COMPAS data set from
2016.

研究二进制决策制定分类器在存在不完美信息的情况下的流行方法是首先建立非二进制的 “评分” 分类器，该分类器在所有受保护的组中进行了校准，然后对该分数进行后处理以获得二进制决策。我们研究通过后处理校准分数实现各种公平性属性的可行性，然后表明推迟后处理器可以使更多的公平条件在最终决策上得以保持。