We would! Choosing priors is difficult and different people with different experience and views will have different (but still reasonable) priors. You may take

We would! Choosing priors is difficult and different people with different experience and views will have different (but still reasonable) priors. You may take personal (just use all your experience) or objective (try to come up with some scheme for assigning priors to types of situations) view on this problem. Work was done in both directions. It's more of a philosophical problem than math problem, although in many cases you want something specific: "I have no idea what the outcome might be but I think it's either extremely on the right or left so give me priori which converges fast to one or the other). Or in a coin example: "it's almost surely more or less fair, so I don't want to change my views after several unlucky flips".