As it stands now, I can’t accept this solution, simply because it doesn’t inform the right decision.
Imagine you were Beauty and q(y) was 1, and you were offered that bet. What odds would you take?
Our models exist to serve our actions. There is no such thing as a good model that informs the wrong action. Probability must add up to winning.
Or am I interpreting this wrong, and is there some practical reason why taking 1⁄2 odds actually does win in the q(y) = 1 case?
Yes, there is. I’ll be writing about that soon.
As it stands now, I can’t accept this solution, simply because it doesn’t inform the right decision.
Imagine you were Beauty and q(y) was 1, and you were offered that bet. What odds would you take?
Our models exist to serve our actions. There is no such thing as a good model that informs the wrong action. Probability must add up to winning.
Or am I interpreting this wrong, and is there some practical reason why taking 1⁄2 odds actually does win in the q(y) = 1 case?
Yes, there is. I’ll be writing about that soon.