The notion of exchangeability has been recognized in the causal inference
literature in various guises, but only rarely in the original Bayesian meaning
as a symmetry property between individual units in statistical inference. Since
the latter is a standard ingredient in 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 relate the Bayesian notion of
exchangeability to alternative conditions for unconfounded inferences, commonly
stated using potential outcome variables, and define causal contrasts in the
presence of exchangeability in terms of limits of posterior predictive
expectations for further exchangeable units. We demonstrate that this reasoning
also carries over to longitudinal settings where parametric inferences are
susceptible to the so-called null paradox. We interpret the paradox in terms of
an exchangeability assumption made on too coarse a scale