  As artificial intelligence is increasingly affecting all parts of society and
life, there is growing recognition that human interpretability of machine
learning models is important. It is often argued that accuracy or other similar
generalization performance metrics must be sacrificed in order to gain
interpretability. Such arguments, however, fail to acknowledge that the overall
decision-making system is composed of two entities: the learned model and a
human who fuses together model outputs with his or her own information. As
such, the relevant performance criteria should be for the entire system, not
just for the machine learning component. In this work, we characterize the
performance of such two-node tandem data fusion systems using the theory of
distributed detection. In doing so, we work in the population setting and model
interpretable learned models as multi-level quantizers. We prove that under our
abstraction, the overall system of a human with an interpretable classifier
outperforms one with a black box classifier.
