  Though the notion of exchangeability has been discussed in the causal
inference literature under various guises, it has rarely taken its original
meaning as a symmetry property of probability distributions. As this property
is a standard component of Bayesian inference, we argue that in Bayesian causal
inference it is natural to link the causal model, including the notion of
confounding and definition of causal contrasts of interest, to the concept of
exchangeability. Here we propose a probabilistic between-group exchangeability
property as an identifying condition for causal effects, relate it to
alternative conditions for unconfounded inferences (commonly stated using
potential outcomes) and define causal contrasts in the presence of
exchangeability in terms of posterior predictive expectations for further
exchangeable units. While our main focus is on a point treatment setting, we
also investigate how this reasoning carries over to longitudinal settings.
