## Tuesday, June 15, 2010

### Best guess at objective probability

I think I may have once thought that epistemic probabilities are something like one's best guess at the objective probability. But that's obviously mistaken. Suppose Sally tells me that the objective probability of some future event is 0.8. Sam tells me the probability is 0.2. God tells me that either Sally or Sam is right. Moreover, I know that that Sally tends to be right 60% of the time. What should my epistemic probability of the event be? Well, my "best guess at the objective probability" is 0.8—what Sally says, since she's right 60% of the time. But obviously my epistemic probability should be (0.6)(0.8)+(0.4)(0.2)=0.56. Which I know is at least 0.24 away from the actual objectively probability.