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%).
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.
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.)
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%).
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.
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.)