First I ask you, “give me a probability distribution on the outcomes of a future event”. Then you observe some relevant data. Then I ask you again for a probability distribution on outcomes.
If I can compare your prior probabilities with your posterior probabilities, I can infer what likelihood ratios you assigned to the evidence, i.e. P(E|H1) : P(E|H2) : P(E|H3).
If I trusted your rationality, I’d take my prior and do a Bayesian update using your implied likelihood ratios. But I scoff at your implied likelihood ratios, because I know the likelihood values are determined by the operation of some intuitive algorithm that is unequipped for the domain. So instead of using your implied likelihood ratios wholesale, I need some other way of analyzing how your conclusions should affect my conclusions.
Insight, almost by definition, gives you a better mental algorithm for assigning posterior probabilities to hypotheses and making predictions—i.e. an algorithm with a higher expected Bayes-score (defined in Eliezer’s Technical Explanation).
Your algorithm provides “increased evidence” to me, an outside observer, because now I will do something closer to trusting your implied likelihood ratios, and I will rationally allow your analysis of the evidence to have more sway over my own.
The “outside observer” is actually you as well. You’re the one who knows to listen to your analysis more if it’s an insightful one.
I originally wanted to answer the question, “When does an insight count as evidence?” So now I have given a precise description of the relationship between insight and evidence.
First I ask you, “give me a probability distribution on the outcomes of a future event”. Then you observe some relevant data. Then I ask you again for a probability distribution on outcomes.
If I can compare your prior probabilities with your posterior probabilities, I can infer what likelihood ratios you assigned to the evidence, i.e. P(E|H1) : P(E|H2) : P(E|H3).
If I trusted your rationality, I’d take my prior and do a Bayesian update using your implied likelihood ratios. But I scoff at your implied likelihood ratios, because I know the likelihood values are determined by the operation of some intuitive algorithm that is unequipped for the domain. So instead of using your implied likelihood ratios wholesale, I need some other way of analyzing how your conclusions should affect my conclusions.
Insight, almost by definition, gives you a better mental algorithm for assigning posterior probabilities to hypotheses and making predictions—i.e. an algorithm with a higher expected Bayes-score (defined in Eliezer’s Technical Explanation).
Your algorithm provides “increased evidence” to me, an outside observer, because now I will do something closer to trusting your implied likelihood ratios, and I will rationally allow your analysis of the evidence to have more sway over my own.
The “outside observer” is actually you as well. You’re the one who knows to listen to your analysis more if it’s an insightful one.
I originally wanted to answer the question, “When does an insight count as evidence?” So now I have given a precise description of the relationship between insight and evidence.