Potential Outcome Rankings for Counterfactual Decision Making

TL;DR

This paper introduces new metrics for counterfactual decision-making, enabling better ranking of potential outcomes and identification of optimal actions under uncertainty using causal reasoning.

Contribution

It proposes two novel metrics, PoR and PoB, along with identification theorems, bounds, and estimation methods for improved counterfactual decision analysis.

Findings

PoR reveals the most probable outcome rankings for individuals.

PoB identifies the most likely top outcome for an action.

Numerical experiments demonstrate estimator properties and real-world applicability.

Abstract

Counterfactual decision-making in the face of uncertainty involves selecting the optimal action from several alternatives using causal reasoning. Decision-makers often rank expected potential outcomes (or their corresponding utility and desirability) to compare the preferences of candidate actions. In this paper, we study new counterfactual decision-making rules by introducing two new metrics: the probabilities of potential outcome ranking (PoR) and the probability of achieving the best potential outcome (PoB). PoR reveals the most probable ranking of potential outcomes for an individual, and PoB indicates the action most likely to yield the top-ranked outcome for an individual. We then establish identification theorems and derive bounds for these metrics, and present estimation methods. Finally, we perform numerical experiments to illustrate the finite-sample properties of the estimators and demonstrate their application to a real-world dataset.