Lee Corbin wrote:
>
> Choose at random? Here, I suspect, is where Bayesianism comes in.
> The B statisticians are happy to assume certain priors when there
> is no evidence for them. Now, I've always liked that, and feel
> that in many cases it is justified, because it enables them to
> give answers to questions that others shy away from (complaining
> of insufficient data, etc.).
>
> But in some cases, like this, they start reading into situations
> protocols that aren't needed to answer the question. In this case,
> as you say, they demand a "do" (and then have to conjure up what
> could reasonably cause the "do"). Staying with *could*, on the
> other hand---which mathematicians apparently are more prone to
> do---obviates further assumptions. One simply considers sets
> and subsets, and so on, and defines probability accordingly.
Which is all fine and good except when it gives you the WRONG ANSWER. In
this case, "could" may be more convenient (why?) but it is still the wrong
way to define the mathematical problem given the word problem. Our entire
real world consists of "did", not "could". "Could" is the rational
construct; "did" is the observed reality. If you want to pose a
mathematical problem, you should use a pure mathematical language, or a
word problem with no flexibility in the priors. To put it another way,
Bayesian probabilities automatically govern all problems that are posed in
real-world language, and if you want to pose a purely mathematical
question in that language, you need to eliminate any Bayesian
ambiguities. If you don't, then somebody who gives a "common-sense but
wrong answer" that is actually correct gets to gloat over you instead of
vice versa.
-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
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