Green and grue causal variables

The causal Bayes net framework specifies a set of axioms for causal discovery. This article explores the set of causal variables that function as relata in these axioms. Spirtes (2007) showed how a causal system can be equivalently described by two different sets of variables that stand in a non-trivial translation-relation to each other, suggesting that there is no "correct" set of causal variables. I extend Spirtes' result to the general framework of linear structural equation models and then explore to what extent the possibility to intervene or a preference for simpler causal systems may help in selecting among sets of causal variables.