[extropy-chat] three coins in a fountain, part 3: the test

[Eliezer S. Yudkowsky]

spike wrote:
> 
> The game then would be to see how a contestant
> would distribute the confidence levels.  The
> head-prole test maker must assign probability
> levels to each possible answer, then multiply
> the responses probability distribution by the
> pre-decided distribution, then normalize the
> score to 1.  We want a perfect score on this
> kind of test to be 1.

No no no.  You multiply the logarithm of the response's probability by 
the pre-decided distribution.  You *must* do it that way for reasons 
explained in http://yudkowsky.net/bayes/technical.html.  Otherwise 
you're just doing weird things with no mathematical interpretation, like 
adding up the temperature of all the stars in the sky.

-- 
Eliezer S. Yudkowsky                          http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence