90% of anything should be bad (& the precision-recall tradeoff) 2022-09-08T01:20:56.170Z

Comment by cartografie on Briefly thinking through some analogs of debate · 2022-09-12T02:50:48.697Z · LW · GW

1. You query whether Debate favours short arguments over long arguments because "the weakest part of an argument is a min function of the number of argument steps."
   
   This is a feature, not a bug.
   
   It's true that long arguments are more debatable than short arguments because they contain more inferential steps and each step is debatable.
   
   But additionally, long arguments are less likely to be sound than short arguments because they contain more inferential steps and each step is 100% certain.
   
   So "debate" still tracks "unlikely".
    
2. "An efficient Debate argument is not a guarantee of truth-tracking, if the judge is biased."
   
   Correct. The efficient market hypothesis for Debate basically corresponds to coherent probability assignments. Cf. the Garrabrant Inductor. I feel like you're asking a solution to the No Free Lunch Theorem here. At some point we have to pray that the prior assumptions of the Debaters assigns high likelihood to the actual world. But that's true of any method of generating beliefs, even idealised bayesianism.

Comment by cartografie on 90% of anything should be bad (& the precision-recall tradeoff) · 2022-09-09T12:39:02.441Z · LW · GW

yes, thanks v much. edited.

Comment by cartografie on 90% of anything should be bad (& the precision-recall tradeoff) · 2022-09-08T16:29:31.619Z · LW · GW

The precision-recall tradeoff definitely varies from one task to another. I split tasks into "precision-maxxing" (where false-positives are costlier than false-negatives) and "recall-maxxing" (where false-negatives are costlier than false-positives).

I disagree with your estimate of the relative costs in history and in medical research. The truth is that academia does surprisingly well at filtering out the good from the bad.

Suppose I select two medical papers at random — one from the set of good medical papers, and one from the set of crap medical papers. If a wizard offered to permanently delete both papers from reality, that would rarely be a good deal because the benefit of deleting the crap paper is negligible compared to the cost of losing the good paper. 

But what if the wizard offered to delete $M$ crap papers and one good paper? How large must $M$ be before this is a good deal? The minimal acceptable $M$ is $C_{FN}/C_{FP}$, so ${\tau }^{\star }=C_{FP}/(C_{FP}+C_{FN})=1/(1+M)$. I'd guess that $M$ is at least 30, so ${\tau }^{\star }$ is at most 3.5%.

Comment by cartografie on 90% of anything should be bad (& the precision-recall tradeoff) · 2022-09-08T16:05:34.691Z · LW · GW

Moreover, even if the post shouldn't have been published with hindsight, that does not entail the post shouldn't have been published without hindsight.

Comment by cartografie on 90% of anything should be bad (& the precision-recall tradeoff) · 2022-09-08T16:01:24.012Z · LW · GW

You are correct that precision is (in general) higher than the threshold. So if Alice publishes anything with at least 10% likelihood of being good, then more than 10% of her poems will be good. Whereas, if Alice aims for a precision of 10% then her promising threshold will be less than 10%.

Unless I've made a typo somewhere (and please let me know if I have), I don't claim the optimal promising threshold ${\tau }^{\star }$ = 10%.  You can see in Graph 5 that I propose a promising threshold of 3.5%, which gives a precision of 10%.

I'll edit the article to dispel any confusion. I was wary of giving exact values for the promising threshold, because ${\tau }^{\star }=3.5$ yields 10% precision only for these graphs, which are of course invented for illustrative purposes.