In mathematical terms, the map from problem space to reference classes is a projection and has no canonical choice (you apply the projection by choosing to lose information), whereas the map from causal structures to problem space is an imbedding and has such a choice (and the choice gains information).
In mathematical terms, the map from problem space to reference classes is a projection and has no canonical choice (you apply the projection by choosing to lose information), whereas the map from causal structures to problem space is an imbedding and has such a choice (and the choice gains information).