#10 | Necessary and Sufficient Causation

There’s a great sentence on page 260 of Judea Pearle’s The Book of Why:

“Responsibility and blame, regret and credit: these concepts are the currency of a causal mind.”

(Of course, the page number might vary depending on the version you have.)

The paragraph immediately preceding this sentence is great too and later in the chapter both necessary and sufficient causation are discussed. However, I needed to do a bit more work to develop my own understanding of these concepts.

Necessary causation

Let’s imagine the classic scenario where a child breaks a window with a ball.

• The child throwing the ball towards the window was a necessary cause of the window being broken, specifically, by the child throwing the ball. “You need to be more careful playing with your ball”.

• The parent purchasing the ball and giving it to the child was also a necessary cause of the window being broken by the child throwing the ball. “If I didn’t by her that ball I wouldn’t have to replace this window.”

• The house having a window was also a necessary cause of the window being broken by the ball. “Who put a window there in the first place?!”

While all are necessary causes of the window being broken by this particular child with this particular ball, the level of responsibility we intuitively associate with each is not the same. For instance, it’s totally reasonable for a house to have a window.

However, as the occurrence of necessary causes increases, so too does the probability of the outcome occurring. With the window in place, and the ball given to the child, the scene was set for the ball to hit the window. So how do we decide what caused the window to break? Who is responsible? How do we quantify this?

Sufficient Causation

Let’s say:

• The house having a window causes the probability of the window being broken by the child throwing the ball to become 1%.

• The parent buying the ball for the child makes the probability of the window being broken by the child thowing the ball become 5%.

• The child throwing the ball makes the probability of the window being broken by the child throwing the ball become 100%.

Intuitively, the degree to which each event is a sufficient cause is proportionate to the change in probabilities. The order of events is important, since the existing circumstances are a key input to the change in probability. A sufficient event will have necessary events enabling it.

So the parent buying the ball for the child is a necessary but not sufficient cause of the window being broken by the child throwing the ball. The child actually throwing the ball at the window is sufficient to cause the window to break.

Less specifically

The outcomes above are very specific.

• The window was broken by this specific child with this specific ball etc.

• When the outcome is less specific than the number of necessary causes decreases.

• Analysing a less specific outcome probably means that a specific event hasn’t occurred yet and the analysis relates to possible future outcomes.

If we are wondering could the window ever break, then the only necessary cause is that the window exists in the first place. The child throwing a ball at it is certainly sufficient to break the window but it’s not necessary because how the window breaks isn’t specified and there are lots of other ways the window could break.