If I’m not mistaken, if A = “Dagon has bought a lottery ticket this week” and B = Dagon states “A”, then I still think p(A | B) > p(A), even if it’s possible you’re lying. I think the only way it would be less than the base rate p(A) is if, for some reason, I thought you would only say that if it was definitely not the case.
I think, in this context, you should give a lot more weight to the “possible” of my lies. If someone else had made a similar statement in rebuttal of your thesis, I’d model p(A|B) < p(A), In other contexts, B could even be uncorrelated to truth, due to ignorance or misunderstanding.
My primary objection isn’t that this is always or even mostly wrong, just that it’s a very simplistic model that’s incorrect often enough, for reasons that are very instance-specific, that it’s a poor heuristic.
Remember that what we decide “communicated well” to mean is up to us. So I could possibly increase my standard for that when you tell me “I bought a lottery ticket today” for example. I could consider this not communicated well if you are unable to show me proof (such as the ticket itself and a receipt). Likewise, lies and deceptions are usually things that buckle when placed under a high enough burden of proof. If you are unable to procure proof for me, I can consider that “communicated badly” and thus update in the other (correct) direction.
“Communicated badly” is different from “communicated neither well nor badly.” The latter might refer to when A is the proposition in question and one simply states “A” or when no proof is given at all. The former might refer to when the opposite is actually communicated—either because a contradiction is shown or because a rebuttal is made but is self-refuting, which strengthens the thesis it intended to shoot down.
Consider the situation where A is true, but you actually believe strongly that A is false. Therefore, because A is true, it is possible that you witness proofs for A that seem to you to be “communicated well.” But if you’re sure that A is false, you might be led to believe that my thesis, the one I’ve been arguing for here, is in fact false.
I consider that to be an argument in favor of the thesis.
If I’m not mistaken, if A = “Dagon has bought a lottery ticket this week” and B = Dagon states “A”, then I still think p(A | B) > p(A), even if it’s possible you’re lying. I think the only way it would be less than the base rate p(A) is if, for some reason, I thought you would only say that if it was definitely not the case.
I think, in this context, you should give a lot more weight to the “possible” of my lies. If someone else had made a similar statement in rebuttal of your thesis, I’d model p(A|B) < p(A), In other contexts, B could even be uncorrelated to truth, due to ignorance or misunderstanding.
My primary objection isn’t that this is always or even mostly wrong, just that it’s a very simplistic model that’s incorrect often enough, for reasons that are very instance-specific, that it’s a poor heuristic.
Remember that what we decide “communicated well” to mean is up to us. So I could possibly increase my standard for that when you tell me “I bought a lottery ticket today” for example. I could consider this not communicated well if you are unable to show me proof (such as the ticket itself and a receipt). Likewise, lies and deceptions are usually things that buckle when placed under a high enough burden of proof. If you are unable to procure proof for me, I can consider that “communicated badly” and thus update in the other (correct) direction.
“Communicated badly” is different from “communicated neither well nor badly.” The latter might refer to when A is the proposition in question and one simply states “A” or when no proof is given at all. The former might refer to when the opposite is actually communicated—either because a contradiction is shown or because a rebuttal is made but is self-refuting, which strengthens the thesis it intended to shoot down.
Consider the situation where A is true, but you actually believe strongly that A is false. Therefore, because A is true, it is possible that you witness proofs for A that seem to you to be “communicated well.” But if you’re sure that A is false, you might be led to believe that my thesis, the one I’ve been arguing for here, is in fact false.
I consider that to be an argument in favor of the thesis.