Still doesn’t seem like the thing that Bayes alone could possibly answer. It seems more like a question about differential equations or dynamical systems or something of the kind. All Bayes’ theorem tells you is the relationship between certain conditional probabilities.
I guess the stupid question is does it follow from Bayes that if you keep measuring the same probability over and over that you will converge on the ‘actual’ probability.
That’s more like the Bernstein-von Mises theorem, I think. But that only applies if what you’re doing is actually Bayesian updating, and it’s not obvious to me that that’s necessarily happening in the system you describe. (The actors might happen to be doing that, but you haven’t said anything about how they make their decisions. Or there might be some more “automatic” bit of the system that’s equivalent to Bayesian updating—e.g., maybe some of the money flows might adjust themselves in ways that correspond to Bayesian updating—but I don’t see any reason to expect that from what you’ve said.)
This was really helpful and gives me some great stuff to look at.
Thank you.
My theory is that actors in an economy spend cash on things and some of those things produce lasting value in the economy and some don’t. Each actors probability of making a valuable choice that leads to overall growth is unknown. If we reward those that make a valuable voice with fresh cash, they then have the opportunity to succeed or fail again. If we do this over and over the ‘right’ probabilities will emerge and we will see who the ‘best spenders’ are by who has the biggest rewards flowing back.
We optimize for value creation and in the long run have a system with better and better information.
I’m not sure I’ve correctly understood your question, but it’s hard to see how anything much like that could follow from Bayes’ theorem on its own.
Question updated. Any more clear?
Still doesn’t seem like the thing that Bayes alone could possibly answer. It seems more like a question about differential equations or dynamical systems or something of the kind. All Bayes’ theorem tells you is the relationship between certain conditional probabilities.
I guess the stupid question is does it follow from Bayes that if you keep measuring the same probability over and over that you will converge on the ‘actual’ probability.
That’s more like the Bernstein-von Mises theorem, I think. But that only applies if what you’re doing is actually Bayesian updating, and it’s not obvious to me that that’s necessarily happening in the system you describe. (The actors might happen to be doing that, but you haven’t said anything about how they make their decisions. Or there might be some more “automatic” bit of the system that’s equivalent to Bayesian updating—e.g., maybe some of the money flows might adjust themselves in ways that correspond to Bayesian updating—but I don’t see any reason to expect that from what you’ve said.)
This was really helpful and gives me some great stuff to look at.
Thank you.
My theory is that actors in an economy spend cash on things and some of those things produce lasting value in the economy and some don’t. Each actors probability of making a valuable choice that leads to overall growth is unknown. If we reward those that make a valuable voice with fresh cash, they then have the opportunity to succeed or fail again. If we do this over and over the ‘right’ probabilities will emerge and we will see who the ‘best spenders’ are by who has the biggest rewards flowing back.
We optimize for value creation and in the long run have a system with better and better information.
That is interesting....what do you mean ‘on its own’. Are there some other things that affect the application of Bayes to a system?
Let me think about reforming the question now that I’m not on an iphone.