I couldn’t figure out how to translate your English into math, or see how to do the math myself. For the reasons stated in Nick’s essay, I’m skeptical that it is feasible to fully “do the math” in problems like these. I suspect you may have done the math incorrectly, or applied simplifying assumptions that are not safe to make. My other top-level comment pointed out one important consideration that your math probably ignored.
I do think it’s useful to look at actual specific mechanisms and actual math, but I worry it’s easy to forget that the mechanism we’re looking at is just one among many that exist in reality and the math inevitably involves many simplifying assumptions or could just be wrong, and become more confident in our conclusions than we should. Based on your post (“you can pull out the equations to verify if you like” instead of “here’s my math, please help me check it for mistakes and bad assumptions”) I think this worry is justified.
I couldn’t figure out how to translate your English into math, or see how to do the math myself.
Based on your post (“you can pull out the equations to verify if you like” instead of “here’s my math, please help me check it for mistakes and bad assumptions”) I think this worry is justified.
Sorry. I had some math in there for the solder and submarine example, and I’ve got the math somewhere for the courage thing, but I decided that the math didn’t add much value. Should I leave the math in where it exists next time? Or put it back in now even?
If I get around to it, I’ll post some equations in the comments.
I can see how courage might be a bad example. The revealing skill level thing is potentially important. I probably missed some stuff too. Maybe I should break that into another post, because deriving that sort of thing from the equations is an interesting thing to do that could use a lot more scrutiny.
I do think it’s useful to look at actual specific mechanisms and actual math, but I worry it’s easy to forget that the mechanism we’re looking at is just one among many that exist in reality and the math inevitably involves many simplifying assumptions or could just be wrong, and become more confident in our conclusions than we should.
Good point. Simplifying assumptions could sink us, as could overconfidence. I reckon a good way to figure it out is to test it and see how often the quick scribbly math fails us. My particular approach been quite useful and generally accurate, but since I can’t yet see from first principles which bits of my habit are the important ones, all I can do is report my success, describe my procedure, and urge people to try it themselves, so that they’ll figure out the important bits too. (hence the “don’t take my word for it go look at the difference”, and the meta example at the end)
Anyways, I know of no procedure better than actually trying to comprehend the reason for things, when it exists. Not looking at the reasons seems like a bad idea (seems may be an understatement. I’ve seen lots of people fail or push in the wrong direction when a bit of From First Principles would have saved them).
Yes, please post your math, either in the comments here or in another post, depending on how involved it is.
I reckon a good way to figure it out is to test it and see how often the quick scribbly math fails us.
How would you test whether your math for “courage” failed you? (Presumably, if it’s wrong, then you’d fail to maximize expected utility, but how could you tell that?)
I’ve seen lots of people fail or push in the wrong direction when a bit of From First Principles would have saved them).
Do you have any examples of this in the sphere of interpersonal behavior?
Yes, please post your math, either in the comments here or in another post, depending on how involved it is.
will do later. Too busy to dig it up now.
How would you test whether your math for “courage” failed you? (Presumably, if it’s wrong, then you’d fail to maximize expected utility, but how could you tell that?)
Look at other people, and your past self I guess? Are you doing better than you would have? Does it look like it’s got to do with risk strategy? Not rigorous or anything, but you can get evidence. The courage thing is built on expected utility being measurable, so it shouldn’t be too hard. Won’t be easy either, though.
Do you have any examples of this in the sphere of interpersonal behavior?
Not off the top of my head. I don’t have a good solid set of equations or even rules for interpersonal stuff, so I wouldn’t expect to recognize it. Also the bottleneck in interpersonal stuff is usually something other than using models blindly.
I couldn’t figure out how to translate your English into math, or see how to do the math myself. For the reasons stated in Nick’s essay, I’m skeptical that it is feasible to fully “do the math” in problems like these. I suspect you may have done the math incorrectly, or applied simplifying assumptions that are not safe to make. My other top-level comment pointed out one important consideration that your math probably ignored.
I do think it’s useful to look at actual specific mechanisms and actual math, but I worry it’s easy to forget that the mechanism we’re looking at is just one among many that exist in reality and the math inevitably involves many simplifying assumptions or could just be wrong, and become more confident in our conclusions than we should. Based on your post (“you can pull out the equations to verify if you like” instead of “here’s my math, please help me check it for mistakes and bad assumptions”) I think this worry is justified.
Sorry. I had some math in there for the solder and submarine example, and I’ve got the math somewhere for the courage thing, but I decided that the math didn’t add much value. Should I leave the math in where it exists next time? Or put it back in now even?
If I get around to it, I’ll post some equations in the comments.
I can see how courage might be a bad example. The revealing skill level thing is potentially important. I probably missed some stuff too. Maybe I should break that into another post, because deriving that sort of thing from the equations is an interesting thing to do that could use a lot more scrutiny.
Good point. Simplifying assumptions could sink us, as could overconfidence. I reckon a good way to figure it out is to test it and see how often the quick scribbly math fails us. My particular approach been quite useful and generally accurate, but since I can’t yet see from first principles which bits of my habit are the important ones, all I can do is report my success, describe my procedure, and urge people to try it themselves, so that they’ll figure out the important bits too. (hence the “don’t take my word for it go look at the difference”, and the meta example at the end)
Anyways, I know of no procedure better than actually trying to comprehend the reason for things, when it exists. Not looking at the reasons seems like a bad idea (seems may be an understatement. I’ve seen lots of people fail or push in the wrong direction when a bit of From First Principles would have saved them).
Yes, please post your math, either in the comments here or in another post, depending on how involved it is.
How would you test whether your math for “courage” failed you? (Presumably, if it’s wrong, then you’d fail to maximize expected utility, but how could you tell that?)
Do you have any examples of this in the sphere of interpersonal behavior?
will do later. Too busy to dig it up now.
Look at other people, and your past self I guess? Are you doing better than you would have? Does it look like it’s got to do with risk strategy? Not rigorous or anything, but you can get evidence. The courage thing is built on expected utility being measurable, so it shouldn’t be too hard. Won’t be easy either, though.
Not off the top of my head. I don’t have a good solid set of equations or even rules for interpersonal stuff, so I wouldn’t expect to recognize it. Also the bottleneck in interpersonal stuff is usually something other than using models blindly.