The best thing to do in this problem, when you’re not sure what priors you should assign, is to work backwards and figure out what priors you need to arrive at one solution or the other. In this case:
Let P = Pr(Julia Roberts goes to Paris). Then E(Stay) = 10(1-P) = 10 − 10P and E(Go) = 5P + 6(1-P) = 6 + P. So E(Stay) > E(Go) if 10 − 10 P > 6 + P or 4 > 11 P or P < 4⁄11.
Now, instead of trying to decide “what does the Holy Doctrine of Indifference direct us to do in this situation” we can think about the real question: is the probability that Julia Roberts goes to Paris less than 4/11?
The best thing to do in this problem, when you’re not sure what priors you should assign, is to work backwards and figure out what priors you need to arrive at one solution or the other. In this case:
Let P = Pr(Julia Roberts goes to Paris). Then E(Stay) = 10(1-P) = 10 − 10P and E(Go) = 5P + 6(1-P) = 6 + P. So E(Stay) > E(Go) if 10 − 10 P > 6 + P or 4 > 11 P or P < 4⁄11.
Now, instead of trying to decide “what does the Holy Doctrine of Indifference direct us to do in this situation” we can think about the real question: is the probability that Julia Roberts goes to Paris less than 4/11?