Apply Bayes’ rule anyway. The result will not be perfect and you should be aware of that, but in majority of situations it’s still an improvement over intuitive guesses.
How do you determine the relevant probabilities? What if you’re looking for, say, the probability of a nuclear attack occurring anywhere in the world in the next 20 years?
Q: Once we find a bias, how can we fix it?
Retreat to more formalised reasoning, if possible.
Yes, but that doesn’t remove the bias. Surely if it’s at all possible to remove a bias, that’s better than circumventing it through formal reasoning, because formal reasoning is much slower than intuition.
How do you determine the relevant probabilities? What if you’re looking for, say, the probability of a nuclear attack occurring anywhere in the world in the next 20 years?
Such as? I am probably unable to give you a wholly general prescription for P(X | nuclear war is going to happen) valid for all X; I have even no idea how such a prescription should look like even if infinite computation power was available, if you don’t want me to classify all sorts of information and all sorts of hypotheses relevant to a nuclear attack. Of course it would be nice to have some general prescription allowing to mechanically detect what information is relevant, but I think this a problem different from Bayesian updating.
“Apply Bayes’ rule anyway” is not a method of reasoning unless we have some way of determining what the numbers are. If we don’t have a method for finding the numbers, then we still have work to do before calling Bayes’ rule a method of reasoning.
I haven’t said we haven’t some way of determining the numbers. I have said that I can’t concisely formulate a rule whose domain of definition is the set of all possible information. What you are asking for is basically outlining a large part of the code of a general artificial intelligence. This is out of reach, but it doesn’t mean we can’t update at all. Some probabilities plugged in will almost certainly be generated by intuition, but I don’t think method of reasoning has to remove all arbitrariness to be called such.
What you are asking for is basically outlining a large part of the code of a general artificial intelligence.
Kind of! I’m asking for the best algorithm for human intelligence we can come up with. I guess that indeed, the phrase “apply Bayes’ rule” is significantly better than nothing at all.
How do you determine the relevant probabilities? What if you’re looking for, say, the probability of a nuclear attack occurring anywhere in the world in the next 20 years?
Yes, but that doesn’t remove the bias. Surely if it’s at all possible to remove a bias, that’s better than circumventing it through formal reasoning, because formal reasoning is much slower than intuition.
What information you are updating from?
All information available to me.
Such as? I am probably unable to give you a wholly general prescription for P(X | nuclear war is going to happen) valid for all X; I have even no idea how such a prescription should look like even if infinite computation power was available, if you don’t want me to classify all sorts of information and all sorts of hypotheses relevant to a nuclear attack. Of course it would be nice to have some general prescription allowing to mechanically detect what information is relevant, but I think this a problem different from Bayesian updating.
“Apply Bayes’ rule anyway” is not a method of reasoning unless we have some way of determining what the numbers are. If we don’t have a method for finding the numbers, then we still have work to do before calling Bayes’ rule a method of reasoning.
I haven’t said we haven’t some way of determining the numbers. I have said that I can’t concisely formulate a rule whose domain of definition is the set of all possible information. What you are asking for is basically outlining a large part of the code of a general artificial intelligence. This is out of reach, but it doesn’t mean we can’t update at all. Some probabilities plugged in will almost certainly be generated by intuition, but I don’t think method of reasoning has to remove all arbitrariness to be called such.
Kind of! I’m asking for the best algorithm for human intelligence we can come up with. I guess that indeed, the phrase “apply Bayes’ rule” is significantly better than nothing at all.