  We develop a mathematical and interpretative foundation for the enterprise of
decision-theoretic statistical causality (DT), which is a straightforward way
of representing and addressing causal questions. DT reframes causal inference
as "assisted decision-making", and aims to understand when, and how, I can make
use of external data, typically observational, to help me solve a decision
problem by taking advantage of assumed relationships between the data and my
problem.
  The relationships embodied in any representation of a causal problem require
deeper justification, which is necessarily context-dependent. Here we clarify
the considerations needed to support applications of the DT methodology.
Exchangeability considerations are used to structure the required
relationships, and a distinction drawn between intention to treat and
intervention to treat forms the basis for the enabling condition of
"ignorability". We also show how the DT perspective unifies and sheds light on
other popular formalisations of statistical causality, including potential
responses and directed acyclic graphs.
