I would dispute some of his word choices (“evidence-strength” and “the increased evidence” in particular seem nonsensical or at least non-standard) but I can sort of interpret what he wrote to be the same general idea as mine.
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.
Insight doesn’t exactly “count as evidence”. Rather, when you acquire insight, you improve the evidence-strength of the best algorithm available for assigning hypothesis probabilities.
Initially, your best hypothesis-weighting algorithms are “ask an expert” and “use intuition”.
If I give you the insight to prove some conclusion mathematically, then the increased evidence comes from the fact that you can now use the “find a proof” algorithm. And that algorithm is more entangled with the problem structure than anything else you had before.
What do you think of Liron’s definition?
I would dispute some of his word choices (“evidence-strength” and “the increased evidence” in particular seem nonsensical or at least non-standard) but I can sort of interpret what he wrote to be the same general idea as mine.
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.
I think he nailed it.