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

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'?

• In this case, Z is summer, since blockbusters unlikely to win awards are typically released in the summer months to take advantage of heavy moviegoing. Similarly, people like to swim when the weather is warm. May 14, 2020 at 1:56

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.

• Causation and correlation are notions from different domains, but I do not think one is more fundamental than the other unless we say mathematics is less fundamental than causation. Though I am no philosopher, so what do I know. May 14, 2020 at 7:42
• I think Pearl would definitely claim that causation is more fundamental. May 14, 2020 at 17:58
• Yeah, perhaps I should have kept quiet. I do not have any solid arguments. May 14, 2020 at 18:21
• Hey, it's only big people can admit mistakes! I've certainly made many ... May 14, 2020 at 18:28
• Thank you for your kind words! I might not deserve them. I did not mean to say I am retracting my claim or changing my opinion of the matter, just that I do not have solid argument to present at the moment. I do not even know if Pearl's arguments are convincing. My problem is, I do not have the time to engage in this question fully, so perhaps I should have kept quiet rather than starting the argument without being ready to go through with it. May 16, 2020 at 10:20