Going from a Representative Agent to Counterfactuals in Combinatorial Choice

TL;DR

This paper introduces a nonparametric counterfactual inference method for decision-making problems involving combinatorial choices, using a representative agent model and linear programming techniques to ensure flexibility and accuracy.

Contribution

It characterizes the set of representable selection probabilities and develops a novel nonparametric approach for counterfactual prediction in combinatorial choice models.

Findings

Method accurately predicts counterfactuals in synthetic data.

Linear programming verification of data consistency is efficient.

Approximations remain effective even under model misspecification.

Abstract

We study decision-making problems where data comprises points from a collection of binary polytopes, capturing aggregate information stemming from various combinatorial selection environments. We propose a nonparametric approach for counterfactual inference in this setting based on a representative agent model, where the available data is viewed as arising from maximizing separable concave utility functions over the respective binary polytopes. Our first contribution is to precisely characterize the selection probabilities representable under this model and show that verifying the consistency of any given aggregated selection dataset reduces to solving a polynomial-sized linear program. Building on this characterization, we develop a nonparametric method for counterfactual prediction. When data is inconsistent with the model, finding a best-fitting approximation for prediction reduces to solving a compact mixed-integer convex program. Numerical experiments based on synthetic data demonstrate the method's flexibility, predictive accuracy, and strong representational power even under model misspecification.