It Can’t Be A Coincidence!

Recently, co-bloggers Scott Sumner and Kevin Corcoran had a series of excellent posts on causation, coincidence, and identities (Scott’s post is here and Kevin’s are here, here, and here).  I want to add my two cents to the conversation with some readings and thoughts for interested readers.

A theme that runs through both their posts is the idea of coincidence: that two events happen together without any apparent causation.  Coincidence happens quite frequently.  Two silly examples:

July 14 I bowled the best two games of my life: 161 and 157.  Even the third game, at 118, was better than average.  My average is 110, so this was quite an improvement.  It was also the first time in months I carried a $5 bill in my pocket.  Did the $5 in my pocket cause my bowling game to improve?  It can’t be a coincidence!
On July 3, the Boston Red Sox visited Donald Trump in the White House.  Then, they won 10 games in a row and went from bottom dwellers to just a few games behind the division-leading Toronto Blue Jays.  Did Trump boost the Sox?  It can’t be a coincidence!

Of course, both these examples are silly.  Anyone claiming a $5 bill and merely being in Trump’s presence caused these events would get laughed out of a room.  Indeed, there is plenty of counterevidence to indicate the combination of time and place is a coincidence: the Washington Nationals visited Trump in 2019 after their World Series victory and they’ve had a losing record ever since.  It’s unlikely Trump caused either the Red Sox’s win streak or the Nationals losing streak.

Distinguishing causation from coincidence requires a good theory.  Theory helps us see what is coincidence and what is causation.  Theory, rigorously tested, is a vital lens to understanding the world.  Bad theory leads to confusing coincidence with causation.

Of course, this is not to say that even rigorously-tested theories are ultimately correct.  Miasma theory, for example, survived millennia of testing.  Indeed, a lot of evidence existed to support it: bad air tended to congregate around disease.  And the bad air often preceded the disease outbreak.  But, after some careful study and a bit of luck, miasma theory eventually unraveled.  John Snow hypothesized that certain diseases were not caused by bad air, but rather something else (he would die before germs were discovered, but he could see their existence in the data).  The bad air was not causing the disease, but rather caused by the disease.  (For interested readers, I highly recommend The Ghost Map by Steven Johnson.)

Determining causation is quite a tricky problem.  Judea Pearl, a brilliant statistician at UCLA, has a series of books exploring causation from a statistical point of view.  His technical book is called Causality and it is a difficult read. While no one will confuse me with a top-tier statistician, even those who are well-versed in the subject find it difficult.

For those of us who are not Turing Prize winners, he has a more accessible book: The Book of Why. In this book, he goes over the history of thought in causation and where we are now.  Short version: We really don’t know when two things are causal.  We do our best, but it’s quite a difficult problem.  All models of causation have assumptions, some quite strong, and we can never be sure they actually hold.

Which brings me to my final point: the phrase “It can’t be a coincidence!” is quite likely the least scientific phrase in the English language.  Not just because it is often invoked by conspiracy theorists or poor thinkers looking to push their latest half-baked idea, but also because it invokes a level of certainty one cannot have.  Coincidences happen all the time.  There is some probability that the causation is a coincidence.  Even a claim of statistical significance (eg “P<0.05”) is a statement of probability (subject to the aforementioned modeling assumptions).  Those who invoke such certainly usually do so because they lack sufficient theory and evidence to justify their claim.

When we consider the assumptions required to show causation, it should cause us to be humble enough to say, “It’s possible I am wrong.”

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