So, my observation is that without meta-distributions (or A_p), or conditioning on a pile of past information (and thus tracking /more/ than just a probability distribution over current outcomes), you don’t have the room in your knowledge to be able to even talk about sensitivity to new information coherently. Once you can talk about a complete state of knowledge, you can begin to talk about the utility of long term strategies.
For example, in your example, one would have the same probability of being paid today if 20% of employers actually pay you every day, whilst 80% of employers never paid you. But in such an environment, it would not make sense to work a second day in 80% of cases. The optimal strategy depends on what you know, and to represent that in general requires more than a straight probability.
There are different problems coming from the distinction between choosing a long term policy to follow, and choosing a one shot action. But we can’t even approach this question in general unless we can talk sensibly about a sufficient set of information to keep track of about. There are two distinct problems, one prior to the other.
Jaynes does discuss a problem which is closer to your concerns (that of estimating neutron multiplication in a 1-d experiment 18.15, pp579. He’s comparing two approaches, which for my purposes differ in their prior A_p distribution.
So, my observation is that without meta-distributions (or A_p), or conditioning on a pile of past information (and thus tracking /more/ than just a probability distribution over current outcomes), you don’t have the room in your knowledge to be able to even talk about sensitivity to new information coherently. Once you can talk about a complete state of knowledge, you can begin to talk about the utility of long term strategies.
For example, in your example, one would have the same probability of being paid today if 20% of employers actually pay you every day, whilst 80% of employers never paid you. But in such an environment, it would not make sense to work a second day in 80% of cases. The optimal strategy depends on what you know, and to represent that in general requires more than a straight probability.
There are different problems coming from the distinction between choosing a long term policy to follow, and choosing a one shot action. But we can’t even approach this question in general unless we can talk sensibly about a sufficient set of information to keep track of about. There are two distinct problems, one prior to the other.
Jaynes does discuss a problem which is closer to your concerns (that of estimating neutron multiplication in a 1-d experiment 18.15, pp579. He’s comparing two approaches, which for my purposes differ in their prior A_p distribution.