January 31, 2022

Are probability distributions for potential responses real and necessary for causal inference?

Philip Dawid, statistics, Cambridge emeritus
Ilya Shpitser, computer science, Johns Hopkins
Thomas Richardson, statistics, Washington
Sylvia Wenmackers, philosophy, KU Leuven

Many statistical models hypothesize a joint probability distribution for an individual’s potential responses to different treatments even when only one treatment can be given. These models include structural equation and functional models as well as the potential response model popularized by Don Rubin in the 1970s. For more than two decades, Phil Dawid has advocated the more parsimonious decision-theoretic approach, in which a probability distribution for the individual’s response is given conditional on each possible treatment but no joint distribution is hypothesized.

Joint distributions for potential responses allow us to work fully within the familiar framework of probability measures. Their disadvantage, Dawid argues, is the confusion introduced by the introduction of meaningless assumptions (such as “treatment-unit additivity assumption”) and meaningless quantities (such the variance of the difference between an individual’s responses to two possible treatments). Discussion of confounding also becomes confusing in the context of probability distributions for unobservable and meaningless quantities. Dawid’s solution is to generalize the theory of conditional independence and DAGs from probability measures to decision models.

Dawid and other authors distinguish between studying the effects of causes (causal investigation as a guide to action) and studying the causes of effects (assignment of responsibility for outcomes already observed).  In the latter case, Dawid is more open to “counterfactual” questions that the joint distribution of potential outcomes might help us answer, such as “given what happened when Mr. Defendant did A, what would likely have happened if he had done B instead.”

Questions for the panel:

1. Dawid’s decision-theoretic language for studying the effects of causes has not been widely used in statistical practice.  What are the obstacles to its adoption?
2. Is Dawid’s framework more difficult to use with observational studies than with experimental studies?
3. Do standard interpretations of probability (for example, the six interpretations Alan Hájek discusses in the Stanford Encyclopedia of Philosophy) generalize from probability measures to Dawid’s decision models?
4. Why do some statisticians find counterfactuals useful?
5. Can we assign responsibility for outcomes without using counterfactuals? (See Glenn Shafer (2001): Causality and responsibility, Cardozo Law Review 22:101-123.)

References

1. A. Philip Dawid (2000), Causal inference without counterfactuals (with discussion), Journal of the American Statistical Association 95:407-448
2. A. Philip Dawid (2015), Statistical causality from a decision-theoretic perspective, Ann. Rev. Stat. Appl. 2:273-303
3. A. Philip Dawid (2021), Decision-theoretic foundations for statistical causality, Journal of Causal Inference 9:39-77
4. A. Philip Dawid (2007), Counterfactuals, hypotheticals and potential responses: a philosophical examination of statistical causality. In Causality and Probability in the Sciences, F. Russo and J. Williamson (eds.), London, College Publications, pp. 503-532.