If 2 variables are dependent, then there always exists a 3rd variable that causally influences both

Question

In the book elements of causal inference (Peters et al). They mention this principle:

Principle 1.1 (Reichenbach’s common cause principle) If two random variables X and Y are statistically dependent, then there exists a third variable Z that causally influences both. (As a special case, Z may coincide with either X or Y.) Furthermore, this variable Z screens X and Y from each other in the sense that given Z, they become independent.

It is known that there is a high correlation between number of people who drowned by falling into a pool and films nicolas cage appeared in. What could possible be the Z variable for this case that influences both?

Or more generally: on what grounds Reichenbach states that 'there always exists a third variable Z'?

Answer 1

One can always come up with examples just as you did. However, such obviously irrelevant variables are not really what Reichenbach has in mind with his dictum.

You could preface the Reichenbach principle with this qualifier: among variables that could reasonably be connected, if they are correlated, then there is a causal relationship linking them.

This is the reason the aphorism, "Correlation does not imply causation" ought to be replaced with Reichenbach's principle: "No correlation without causation." Or at least, "Correlation usually implies causation."

Causation is more fundamental than correlation, and it's certainly much easier for humans to reason about than correlation.