  Machine learning models are often used to inform real world risk assessment
tasks: predicting consumer default risk, predicting whether a person suffers
from a serious illness, or predicting a person's risk to appear in court. Given
multiple models that perform almost equally well for a prediction task, to what
extent do predictions vary across these models? If predictions are relatively
consistent for similar models, then the standard approach of choosing the model
that optimizes a penalized loss suffices. But what if predictions vary
significantly for similar models? In machine learning, this is referred to as
predictive multiplicity i.e. the prevalence of conflicting predictions assigned
by near-optimal competing models. In this paper, we present a framework for
measuring predictive multiplicity in probabilistic classification (predicting
the probability of a positive outcome). We introduce measures that capture the
variation in risk estimates over the set of competing models, and develop
optimization-based methods to compute these measures efficiently and reliably
for convex empirical risk minimization problems. We demonstrate the incidence
and prevalence of predictive multiplicity in real-world tasks. Further, we
provide insight into how predictive multiplicity arises by analyzing the
relationship between predictive multiplicity and data set characteristics
(outliers, separability, and majority-minority structure). Our results
emphasize the need to report predictive multiplicity more widely.
