5-second level case study: Value of information
This post started off as a comment to Vaniver's post Value of Information: Four Examples. This post also heavily builds on Eliezer's post The 5-Second Level. The five second level is the idea that to develop a rationality skill, you need to automatically recognize a problem and then apply a stored, actionable procedural skill to deal with it, all in about five seconds or so. In here, I take the value of information concept and develop it into a five second skill, summarizing my thought process as I do so. Hopefully this will help others develop things into five second skills.
So upon reading this, I thought "the value of information seems like a valuable concept", but didn't do much more. A little later, I thought, "I want to make sure that I actually apply this concept when it is warranted. How do I make sure of that?" In other words, "how do I get this concept to the five second level?" Then I decided to document my thought process in the hopes of it being useful to others. This is quite stream-of-consciousness, but I hope that seeing my thought process helps to learn from it. (Or to offer me valuable criticism on how I should have thought.)
First off, "how do I apply this concept?" is too vague to be useful. A better question would be, "in what kinds of situations might this concept be useful?". With a bit of thought, it was easy to find at least three situations, ones where I am:
1. ...tempted to act now without gathering more information, despite the VoI being high.
2. ...tempted to gather more information, despite the VoI being low.
3. ...not sure of whether I should seek information or not.
#3 implies that I'm already reflecting on the situation, and am therefore relatively likely to remember VoI as a possible mental tool anyway. So developing a five-second level reaction for that one isn't as important. But in #1 and #2 I might just proceed by default, never realizing that I could do better. So I'll leave #3 aside, concentrating on #1 and #2.
Now in these situations, the relevant thing is that the VoI might be "high" or "low". Time to get more concrete - what does that mean? Looking at Vaniver's post, the VoI is high if 1) extra information is likely to make me choose B when I had intended on choosing A, and 2) there's a high payoff in choosing correctly between A and B. If at least 2 is false, VoI is low. The intermediate case is the one where 2 is true but 1 is false, in which case it depends on how extreme the values are. E.g. only a 1% chance of changing my mind given extra information might sometimes imply a high VoI, if the difference between the correct and incorrect choice is a million euros, say.
So sticking just to #1 for simplicity, and because I think that's a worse problem for me, I'd need to train myself to immediately notice and react if:
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