Fisher Meets Bayes: The Value of Randomisation for Bayesian Inference of Causal Effects

Abstract

For a Bayesian agent with beliefs about the relationship between covariates and potential outcomes, deterministically selecting an assignment that yields optimal covariate balance rationally dominates randomisation. However, randomisation—by enabling control over the probabilities of erroneous causal conclusions due to unknown covariate imbalances—offers insurance against the possibility that an agent's beliefs may be misleading. For the most part, such rational justifications for optimum assignment have presupposed the framework of Bayesian inference, while such epistemic justifications for randomisation have presupposed the framework of significance testing. In this paper, I build on a conception of balance that seems inextricable from the significance testing framework, Fisherian balance, to show that it implies an analogous epistemic justification for randomisation within the framework of Bayesian inference. Consequently, for the choice between optimum and random assignment, this paper shows that epistemic justifications need not be wedded to significance testing nor must Bayesian inference be wedded to rational justifications.