This problem doesn’t seem to be about trust at all, it seems to be about incomplete sharing of information. It seems weird to me to say Carla doesn’t completely trust Bob’s account if she is 100% sure he isn’t lying.
The sensitivity of the test—that aliens actually abduct people, given someone is telling her aliens abducted him—is 2.5% since she doesn’t really know his drug habits and hasn’t ruled out there’s a LARP she’s missing the context for.
I would describe this not as Carla not trusting Bob, but as her not having all of Bob’s information—Bob could just tell her that he doesn’t use drugs, or that he isn’t referring to a LARP, or any other things he knows about himself that Carla doesn’t that are causing her sensitivity to be lower, until their probabilities are the same. And, of course, if this process ends with Carla having the same probabilities as Bob, and Carla does the same with Dean, he will have the same probabilities as Bob as well.
I think this satisfies Aumann’s Agreement Theorem.
Well, if it does then Bob and Carla definitely have the same probabilities; that’s what the problem says, after all.
This problem doesn’t seem to be about trust at all, it seems to be about incomplete sharing of information. It seems weird to me to say Carla doesn’t completely trust Bob’s account if she is 100% sure he isn’t lying.
I would describe this not as Carla not trusting Bob, but as her not having all of Bob’s information—Bob could just tell her that he doesn’t use drugs, or that he isn’t referring to a LARP, or any other things he knows about himself that Carla doesn’t that are causing her sensitivity to be lower, until their probabilities are the same. And, of course, if this process ends with Carla having the same probabilities as Bob, and Carla does the same with Dean, he will have the same probabilities as Bob as well.
Well, if it does then Bob and Carla definitely have the same probabilities; that’s what the problem says, after all.