David_Gerard comments on Knowledge value = knowledge quality × domain importance - Less Wrong

8 Post author: John_Maxwell_IV 16 April 2012 08:40AM

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Comment author: David_Gerard 16 April 2012 04:33:51PM 0 points [-]

The human mind doesn't do 64-bit floating weights. It doesn't even do shorts.

BTW, has anyone ascertained what resolution it does do? (Is this even a coherent question?)

Comment author: gwern 16 April 2012 04:40:32PM *  5 points [-]

Well, it's a question which could be turned into a coherent question in a couple ways, so before getting an answer, you need to decide what question you're asking and what an answer ought to look like. For example:

  • You could ask whether people can distinguish between biased dice down to single percent level or smaller by rolling them a ton of times.
  • You could ask whether calibrated experts can be calibrated down to sub-percent levels without resorting to explicit models and calculation, or whether the inherent mental noise overwhelms differentials before then.
  • You could try to tie it to pulse-coding for utility/rewards (lukeprog covered in one of his neuroscience posts) which would imply something like nothing finer than 1/1000th or something. And so on.

I don't know the answers to any of these - my own impression is that people have fairly granular probabilities. I don't bother with single-percent differences in my own predictions on PredictionBook.com unless I'm in the 0-10/90-100% decile (where 0% is quite different from 1%).

Comment author: TheOtherDave 16 April 2012 05:25:59PM 1 point [-]

Hrm.

Rolling dice a ton of times starts running into problems with short-term memory buffer size and conflation with explicit strategies for managing that limit; it might be more useful to provide a histogram of the results of a hundred die rolls and ask whether it's a biased die or not.

Though, thinking about this... surely this isn't an absolute granularity? I mean, even supposing that it's constant at all. I would expect the minimum size of a detectable probability shift to be proportional to the magnitude of the original probability.

Comment author: David_Gerard 16 April 2012 05:04:35PM *  0 points [-]

This is a question I've thought of posting in discussion before, but I couldn't work out a coherent phrasing. Just how well can the untrained human mind resolve probabilities? Just how well can the trained human mind (e.g. say, a professional bookmaker) resolve probabilities? (Note I have no idea how individual bookmakers do things these days, for all I know they routinely use computers rather than estimating odds themselves. I know the chain ones do.)

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