An Axiomatic Foundation for Decisions with Counterfactual Utility

Economists Koch, Imai, and Strzalecki have published a paper on arXiv that provides an axiomatic foundation for decisions under counterfactual utility. Counterfactual utility evaluates decisions not only by realized outcomes but also by what would have happened under alternative choices, allowing decision-makers to encode regret or harm avoidance. However, recent work highlighted inconsistencies and transitivity failures, notably in the Russian roulette example and the Allais paradox. The authors extend the classic von Neumann-Morgenstern (vNM) framework to preferences defined on the space of all potential outcomes rather than just realized ones. They show expected counterfactual utility satisfies the vNM axioms on this extended domain, thus providing a coherent preference representation. This reconciles apparent paradoxes and resolves long-standing behavioral economics puzzles.

Furthermore, the paper examines how counterfactual preferences map onto realized outcomes through menu-dependent projections. It derives an additional axiom required to reduce counterfactual utilities to standard utilities, and establishes an axiomatic foundation for additive counterfactual utilities with necessary and sufficient conditions for point identification. Importantly, results hold for both deterministic and stochastic potential outcomes. This framework bridges theoretical economics, game theory (cs.GT), and statistics theory (math.ST), offering a rigorous basis for decision-making with regret and counterfactual reasoning. The work has implications for AI agents that need to consider alternative actions, as well as for behavioral economics models of choice under uncertainty.