From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sat Jun 14 2003 - 14:15:39 MDT
Harvey Newstrom wrote:
> Dehede011@aol.com wrote,
>
>> In a message dated 6/13/2003 7:33:59 AM Central Standard Time,
>> mail@HarveyNewstrom.com writes: Amara is assumed to be supportive if
>> she hasn't complained.
>>
>> No Harvey, Amara is assumed to not be terribly insulted or misquoted
>> if she doesn't complain.
>
> This sounds less extreme, but the logic error is still there. You
> cannot assume anything about anyone based on a lack of information from
> them.
The dog that doesn't bark is, in fact, valid Bayesian evidence. If a
positive indicator is informative, the negative indicator *must* be
informative in the opposite direction. However, the negative indicator
can be much weaker evidence than the positive indicator, if the positive
indicator is rare and the negative indicator is common. The structure of
Bayesian reasoning forces a law of Conservation of Evidence - rare strong
evidence in one direction must be counterbalanced by common weak evidence
in the opposite direction.
> There could be a million reasons why someone doesn't respond.
Right; rare strong evidence that only fits one explanation can be
counterbalanced by common weak evidence that can fit many possible
explanations. The rare positive indicator takes probability from a host
of now-disconfirmed little alternatives to add up to a big strong
probability flow to one definite hypothesis; the common negative indicator
takes a little probability from the same hypothesis and distributes it
among the many possible explanations, making the weak evidence even weaker
after it's been divided up. See Jaynes on "Multiple Hypothesis Testing":
http://bayes.wustl.edu/etj/science.pdf.html
> This tactic can never add information to a debate, while it can
> frequently lead to misunderstandings and accusations of
> misrepresentation. I maintain that this source of information is
> unsupportable and should not be used in a rational debate where the
> person in question is available for comment if they so choose.
I agree; but this is because negative evidence is weak and divided among
many possible explanations, not because taking the negative indicator as
evidence is a logic error.
-- Eliezer S. Yudkowsky http://singinst.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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