This is an interesting idea, that appeals to me owing to my earlier angle of attack on intuitions about "subjective anticipation".

The question then becomes, how would we program a robot to answer the kind of question that was asked of Sleeping Beauty?

This comment suggests one concrete way of operationalizing the term "credence". It could be a wrong way, but at least it is a concrete suggestion, something I think is lacking in other parts of this discussion. What is our criterion for judging either answer a "wrong" answer? More specifically still, how do we distinguish between a robot correctly programmed to answer this kind of question, and one that is buggy?

As in the robot-and-copying example, I suspect that which of 1/2 or 1/3 is the "correct" answer in fact depends on what (heretofore implicit) goals, epistemic or instrumental, we decide to program the robot to have.