The traditional Bayesian treatment of rational agents assumes that the only way an agent can get new information is by getting some new observation that is known with probability 1. However, we would like a theory of rationality that can allow for agents that also get more information by thinking longer. In such a situation, some of the constraints imposed by traditional Bayesian reasoning no longer apply. This detailed post explores what constraints remain, and what types of updating are allowable under this more permissive definition of rationality.
Planned opinion:
I particularly enjoyed this post; it felt like the best explanation in relatively simple terms of a theory of rationality that is more suited to bounded agents that cannot perfectly reason about an environment larger than they are. (Note “simple” really is relative; the post still assumes a lot of technical knowledge about traditional Bayesianism.)
Planned summary for the Alignment Newsletter:
Planned opinion: