  The algorithmic independence of conditionals, which postulates that the
causal mechanism is algorithmically independent of the cause, has recently
inspired many highly successful approaches to distinguish cause from effect
given only observational data. Most popular among these is the idea to
approximate algorithmic independence via two-part Minimum Description Length
(MDL). Although intuitively sensible, the link between the original postulate
and practical two-part MDL encodings is left vague. In this work, we close this
gap by deriving a two-part formulation of this postulate, in terms of
Kolmogorov complexity, which directly links to practical MDL encodings. To
close the cycle, we prove that this formulation leads on expectation to the
same inference result as the original postulate.
