The standard example I’ve always seen for the “collider bias” is that we have a bunch of restaurants in our hypothetical city, and it seems like the better their food, the worse their drinks and visa-versa. This is (supposed to be) because places with bad food and drinks go out of business and there is a cap on effort that can be applied to food or drinks.
How would the self-defeating thing play in here? I don’t see yet why it shouldn’t, but I also don’t recognize a way for it to happen, either. Could you walk me through it?
I don’t think it would, in practice. One reason is that “bad/bad places go out of business” is a mechanism that doesn’t go via your preferences in the way that “you spend time with smart nice people” does. But if it did I think it would go like this.
You go to restaurants that have good food or good drinks or both. This induces an anticorrelation between food quality and drinks quality in the restaurants you go to. After a while you notice this. You care a lot about (let’s say) having really good food, and having got the idea that maybe having good drinks is somehow harmful to food quality you stop preferring restaurants with good drinks. Now you are just going to restaurants with good food, and not selecting on drinks quality, so the collider bias isn’t there any more (this is the bit that’s different if in fact there’s a separate selection that kills restaurants whose food and drink are both bad, which doesn’t correspond to anything in the interpersonal-relations scenario), so you decide you were wrong about the anticorrelation. So you start selecting on drink quality again, and the anticorrelation comes back. Repeat until bored or until you think of collider bias as an explanation for your observations.
The standard example I’ve always seen for the “collider bias” is that we have a bunch of restaurants in our hypothetical city, and it seems like the better their food, the worse their drinks and visa-versa. This is (supposed to be) because places with bad food and drinks go out of business and there is a cap on effort that can be applied to food or drinks.
How would the self-defeating thing play in here? I don’t see yet why it shouldn’t, but I also don’t recognize a way for it to happen, either. Could you walk me through it?
I don’t think it would, in practice. One reason is that “bad/bad places go out of business” is a mechanism that doesn’t go via your preferences in the way that “you spend time with smart nice people” does. But if it did I think it would go like this.
You go to restaurants that have good food or good drinks or both. This induces an anticorrelation between food quality and drinks quality in the restaurants you go to. After a while you notice this. You care a lot about (let’s say) having really good food, and having got the idea that maybe having good drinks is somehow harmful to food quality you stop preferring restaurants with good drinks. Now you are just going to restaurants with good food, and not selecting on drinks quality, so the collider bias isn’t there any more (this is the bit that’s different if in fact there’s a separate selection that kills restaurants whose food and drink are both bad, which doesn’t correspond to anything in the interpersonal-relations scenario), so you decide you were wrong about the anticorrelation. So you start selecting on drink quality again, and the anticorrelation comes back. Repeat until bored or until you think of collider bias as an explanation for your observations.
Thanks for the explanation how it’s different; now I understand what the original post meant.