P(A|B) is defined as P(A & B) / P(B), and both P(A & B) and P(B) are straightforward things to bet on in a prediction market.
The problem is that you get some estimates P*(A&B) and P*(B), and P*(A&B)/P*(B) is not necessarily a good estimate for P(A&B)/P(B) even when each of the component estimates were good. It gets much worse when the estimates aren’t very good.
It gets worse still if what you really want is something more structured than a simple conditional probability, such as a credence for a causal relation. I suspect that there are many complications here that may be beyond the scope of any plausible prediction market structure.
P(A|B) is defined as P(A & B) / P(B), and both P(A & B) and P(B) are straightforward things to bet on in a prediction market.
The problem is that you get some estimates P*(A&B) and P*(B), and P*(A&B)/P*(B) is not necessarily a good estimate for P(A&B)/P(B) even when each of the component estimates were good. It gets much worse when the estimates aren’t very good.
It gets worse still if what you really want is something more structured than a simple conditional probability, such as a credence for a causal relation. I suspect that there are many complications here that may be beyond the scope of any plausible prediction market structure.