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April 01, 2007

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The astounding notion is that human beings are unbiased estimators of beans in a jar, having no significant directional error on the problem, yet with large variance. It implies that we tend to get the answer wrong but there's no systematic reason why. It requires that there be lots of errors that vary from individual to individual - and this is reliably true, enough so to keep most individuals from guessing the jar correctly. And yet there are no directional errors that everyone makes, or if there are, they cancel out very precisely in the average case, despite the large individual variations. Which is just plain odd. I find myself somewhat suspicious of the claim, and wonder whether other experiments that found less amazing accuracy were not as popularly reported.

This is precisely what I find disquieting about wisdom-of-crowds arguments - they require that our errors are nondirectional and normally distributed, but we know they aren't. We have cognitive biases!

I have a somewhat related question - and openly admit to being a neophyte

my question is this
traditional variance weights positive and negative outcomes equally

how can one compute a variance that reflects a persons bias (risk aversion) toward a directional outcome
as in business assume an ill favored outcome is worth 0.5x and a preferred outcome is worth 1.5x

would a person compute 2 variances by creating 2 sub populations illfavored/preferred and apply the
formula var (bx) = b^2times sigma^2 to each population and sum the final products?

am I wrong in this line of thinking?
is there another approach?
its been quite some time since my university stats days - so please be gentle with my ignorance

appreciate your thoughts and if you ping my email to let me know
miroslodki (at) yahoo (dot) ca

btw - fascinating site and discussion regarding crowd wisdom - fwiw I share your viewpoints/concerns
you've found a new reader
cheers
Miro


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