  The harmful impacts of algorithmic decision systems have recently come into
focus, with many examples of systems such as machine learning (ML) models
amplifying existing societal biases. Most metrics attempting to quantify
disparities resulting from ML algorithms focus on differences between groups,
dividing users based on demographic identities and comparing model performance
or overall outcomes between these groups. However, in industry settings, such
information is often not available, and inferring these characteristics carries
its own risks and biases. Moreover, typical metrics that focus on a single
classifier's output ignore the complex network of systems that produce outcomes
in real-world settings. In this paper, we evaluate a set of metrics originating
from economics, distributional inequality metrics, and their ability to measure
disparities in content exposure in a production recommendation system, the
Twitter algorithmic timeline. We define desirable criteria for metrics to be
used in an operational setting, specifically by ML practitioners. We
characterize different types of engagement with content on Twitter using these
metrics, and use these results to evaluate the metrics with respect to the
desired criteria. We show that we can use these metrics to identify content
suggestion algorithms that contribute more strongly to skewed outcomes between
users. Overall, we conclude that these metrics can be useful tools for
understanding disparate outcomes in online social networks.
