I am not sure you actually justified your claim, that OR follows from the laws of probability with no empirical input.
I wanted to say the same thing.
The OP uses the example of age, but I like the example of shade of eye color better. If h is height and s is shade of eye color, then
weight = alpha * a + beta * s
Then if beta is anything other than 0, your estimate will, on expectation, be worse. This feels correct, and it seems like this should be demonstrable, but I haven’t really tried.
Waveman says:
I wanted to say the same thing.
The OP uses the example of age, but I like the example of shade of eye color better. If h is height and s is shade of eye color, then
weight = alpha * a + beta * s
Then if beta is anything other than 0, your estimate will, on expectation, be worse. This feels correct, and it seems like this should be demonstrable, but I haven’t really tried.