Will Lowe
LightNews LightNews
banner
conjugateprior.org
Will Lowe
@conjugateprior.org
3.4K followers 740 following 9.7K posts

Señor Research Scientist, NPC at the Hertie School in Berlin 🇩🇪 via Princeton, Mannheim, Edinburgh and a bunch of other ivory towers that will probably be billiard balls and decorative boxes by the end of the decade.

Rome Statute appreciator. .. more

Videos
Computer science 32%
Political science 28%
Posts Replies Media Videos
Pinned
conjugateprior.org
Will Lowe @conjugateprior.org · Apr 15
For Monty Hall problem aficionados: a #causal DAG, with explanation in the alt text.

Who knew that the M in M-bias stood for Monty?
A DAG for the Monty Hall problem. G, the door Monty opens, is a function of your first door choice D_F and of where the car is C. Conditioning on G, which happens because it determines your door choices when you have the opportunity to switch, induces collider bias between C and D_F, such that they are now less likely to be equal. (Why? because G cannot be C and G cannot be D_F. These are in the same 'direction' so, conditional on G, D_F is less likely to be C.) You decide to switch conditional on G, which you just observed, and D_F, because that defines what you can switch to. Conditional on G you now know D_F is less likely to be equal to C. So you switch. Note: In the original problem, W is a deterministic function of C and D_S so it's slightly cheeky to put it in a DAG, but I'm going to do so anyway. The argument doesn't require it, but if you want to think informally about opening paths to W from D_F via C, it's helpful. That makes this problem a variation on M-bias (or a clipped wing butterfly bias, if you prefer insects to goats).