Reconciling Model Multiplicity for Downstream Decision Making

We consider the problem of model multiplicity in downstream decision-making, a setting where two predictive models of equivalent accuracy cannot agree on what action to take for a downstream decision-making problem. Prior work attempts to address model multiplicity by resolving prediction disagreement between models. However, we show that even when the two predictive models approximately agree on their individual predictions almost everywhere, these models can lead the downstream decision-maker to take actions with substantially higher losses. We address this issue by proposing a framework that calibrates the predictive models with respect to both a finite set of downstream decision-making problems and the individual probability prediction. Specifically, leveraging tools from multi-calibration, we provide an algorithm that, at each time-step, first reconciles the differences in individual probability prediction, then calibrates the updated models such that they are indistinguishable from the true probability distribution to the decision-makers. We extend our results to the setting where one does not have direct access to the true probability distribution and instead relies on a set of i.i.d data to be the empirical distribution. Furthermore, we generalize our results to the settings where one has more than two predictive models and an infinitely large downstream action set. Finally, we provide a set of experiments to evaluate our methods empirically. Compared to existing work, our proposed algorithm creates a pair of predictive models with improved downstream decision-making losses and agrees on their best-response actions almost everywhere.