The action cannot causally affect the state, but somehow taking a1 gives us evidence that we’re in the preferable state s1. That is, P(s1|a1)>P(s1|a2) and u(a1,s1)>u(a2,s2).
I’m actually unsure if CDT-theorists take this as true. If you’re only looking at the causal links between your actions, P(s1|a1) and P(s1|a2) are actually unknown to you. In which case, if you’re deciding under uncertainty about probabilities, so you strive to just maximize payoff. (I think this is roughly correct?)
I think the reason why many people think one should go to the doctor might be that while asserting P(s1|a1,K) > P(s1|a2,K), they don’t upshift the probability of being sick when they sit in the waiting room.
Does s1 refer to the state of being sick, a1 to going to the doctor, and a2 to not going to the doctor? Also, I think most people are not afraid of going to the doctor? (Unless this is from another decision theory’s view)?
With regards to this part:
I’m actually unsure if CDT-theorists take this as true. If you’re only looking at the causal links between your actions, P(s1|a1) and P(s1|a2) are actually unknown to you. In which case, if you’re deciding under uncertainty about probabilities, so you strive to just maximize payoff. (I think this is roughly correct?)
Does s1 refer to the state of being sick, a1 to going to the doctor, and a2 to not going to the doctor? Also, I think most people are not afraid of going to the doctor? (Unless this is from another decision theory’s view)?