The question being asked here is really “what priors should I assign?”. I don’t think I have the answer, but allow me to restate the problem:
“The subject is known to be headed for one of three places, A, B and C. What is the probability they turn up in each place?” To which the answer is 1⁄3 each by indifference.
Now why did it look ok to us to merge B and C into one option, (B or C)? Because (in the original problem) B and C were cities located in the same country, the U.S., and that prior geographical information had been incorporated into the problem. When we condition on the knowledge that A is in one country (France) and B and C are in another (the U.S.) the problem is, well, no longer symmetrical. And I confess I’m now actually unsure how or if indifference or maximum entropy can be applied to this now asymmetric problem.
And I confess I’m now actually unsure how or if indifference or maximum entropy can be applied to this now asymmetric problem.
You have to use the information about the asymmetry, which in this case involves an actress and geopolitical boundaries. This isn’t a case where there’s an elegant ignorance prior, you just have to actually use your knowledge.
The question being asked here is really “what priors should I assign?”. I don’t think I have the answer, but allow me to restate the problem:
“The subject is known to be headed for one of three places, A, B and C. What is the probability they turn up in each place?” To which the answer is 1⁄3 each by indifference.
Now why did it look ok to us to merge B and C into one option, (B or C)? Because (in the original problem) B and C were cities located in the same country, the U.S., and that prior geographical information had been incorporated into the problem. When we condition on the knowledge that A is in one country (France) and B and C are in another (the U.S.) the problem is, well, no longer symmetrical. And I confess I’m now actually unsure how or if indifference or maximum entropy can be applied to this now asymmetric problem.
You have to use the information about the asymmetry, which in this case involves an actress and geopolitical boundaries. This isn’t a case where there’s an elegant ignorance prior, you just have to actually use your knowledge.