January 14, 2014

# Causation, counterfactuals, and Lotto

A story in the Herald illustrates a subtle technical and philosophical point about causation. One of Saturday’s Lotto winners says

“I realised I was starving, so stopped to grab a bacon and egg sandwich.

“When I saw they had a Lotto kiosk, I decided to buy our Lotto tickets while I was there.

“We usually buy our tickets at the supermarket, so I’m glad I followed my gut on this one,” said one of the couple, who wish to remain anonymous.

Assuming it was a random pick, it’s almost certainly true that if they had not bought the ticket at that Lotto kiosk at that time, they would not have won.  On the other hand, if Lotto is honest, buying at that kiosk wasn’t a good strategy — it had no impact on the chance of winning.

There is a sense in which buying the bacon-and-egg sandwich was a cause of the win, but it’s not a very useful sense of the word ’cause’ for most statistical purposes.

Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »

• Nick Iversen

Depends on how the random pick was generated. If each kiosk has an random pick generator in it that is independent of any other kiosk and has a predetermined sequence of random numbers (independent of time the pick was made) then it is conceivable that that kiosk and no other in NZ had a winning random pick in it. So at some point the next person who rolled up to that kiosk was going to get the winning numbers. So the decision to use that machine was critical.

On the other hand if the random picks are truly random then any machine at any time could produce a winning pick and so the choice of machine is irrelevant.

• Thomas Lumley

No, that’s exactly the point. Whether or not the random picks were ‘truly random’ (and whatever that means), it’s still true that

(a) If they had not bought the ticket then, they would almost certainly have got a different set of numbers and not won; but

(b) buying the ticket then did not increase their chance of winning in any meaningful sense; it was not a good strategy.