Russian roulette: The need for stochastic potential outcomes when utilities depend on counterfactuals

TL;DR

This paper argues that when utilities depend on counterfactuals, especially in medical decision-making, a stochastic potential outcome framework is necessary to avoid paradoxical decisions, challenging traditional deterministic models.

Contribution

It introduces the need for stochastic potential outcomes in models where utilities depend on unrealized potential outcomes, resolving paradoxes in decision analysis.

Findings

Asymmetric utility functions can lead to paradoxical decisions.

Allowing potential outcomes to be random variables resolves these paradoxes.

Stochastic potential outcomes are essential for accurate decision analysis with counterfactual-dependent utilities.

Abstract

It has been proposed in medical decision analysis to express the ``first do no harm'' principle as an asymmetric utility function in which the loss from killing a patient would count more than the gain from saving a life. Such a utility depends on unrealized potential outcomes, and we show how this yields a paradoxical decision recommendation in a simple hypothetical example involving games of Russian roulette. The problem is resolved if we abandon the stable unit treatment value assumption (SUTVA) and allow the potential outcomes to be random variables. This leads us to conclude that, if you are interested in this sort of asymmetric utility function, you need to move to the stochastic potential outcome framework. We discuss the implications of the choice of parameterization in this setting.