Going from a Representative Agent to Counterfactuals in Combinatorial Choice

2025-05-29

AI Summary

This paper addresses nonparametric counterfactual inference under combinatorial choice settings using aggregate decision data. It considers binary choice frequency data drawn from multiple binary polytopes and proposes a representative agent model grounded in separable concave utility maximization. The contributions are threefold: (1) it establishes the first necessary and sufficient conditions for the representability of choice probabilities under this model; (2) it reformulates data consistency testing as a polynomial-size linear program; and (3) it develops an optimal approximate counterfactual prediction framework under model misspecification, integrating mixed-integer convex optimization with nonparametric calibration. In synthetic experiments, the method achieves high predictive accuracy, strong structural interpretability, and robustness to model misspecification.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Nonparametric counterfactual inference in combinatorial choice problems
• Characterizing selection probabilities via representative agent model
• Best-fitting approximation under model inconsistency using convex programming

Innovation

• Nonparametric counterfactual inference using representative agent model
• Polynomial-sized linear program for consistency verification
• Compact mixed-integer convex program for best-fitting approximation