Not sure how much sense it makes to take the arithmetic mean of probabilities when the odds vary over many orders of magnitude. If the average is, say, 30%, then it hardly matters whether someone answers 1% or .000001%. Also, it hardly matters whether someone answers 99% or 99.99999%.
I guess the natural way to deal with this would be to average (i.e., take the arithmetic mean of) the order of magnitude of the odds (i.e., log[p/(1-p)], p someone’s answer). Using this method, it would make a difference whether someone is “pretty certain” or “extremely certain” that a certain statement is true or false.
Does anyone know what the standard way for dealing with this issue is?
Yeah, log odds sounds like a good way to do it. Aggregating estimates is hard because peoples’ estimates aren’t independent, but averaging log odds will at least do better than averaging probabilities.
Not sure how much sense it makes to take the arithmetic mean of probabilities when the odds vary over many orders of magnitude. If the average is, say, 30%, then it hardly matters whether someone answers 1% or .000001%. Also, it hardly matters whether someone answers 99% or 99.99999%.
I guess the natural way to deal with this would be to average (i.e., take the arithmetic mean of) the order of magnitude of the odds (i.e., log[p/(1-p)], p someone’s answer). Using this method, it would make a difference whether someone is “pretty certain” or “extremely certain” that a certain statement is true or false.
Does anyone know what the standard way for dealing with this issue is?
Yeah, log odds sounds like a good way to do it. Aggregating estimates is hard because peoples’ estimates aren’t independent, but averaging log odds will at least do better than averaging probabilities.
Use medians and percentiles instead of means and standard deviations.