[FoRK] Black Belt Bayesian vs. Authority, Fight!

Matt Jensen <mattj at newsblip.com> on Thu Aug 9 10:48:56 PDT 2007

Speaking of Bayesian statistics, run, don't walk, over to Amazon  
Canada.  For some reason Jayne's monumental "Probability Theory : The  
Logic of Science" is priced at $4 (versus $49 in U.S., $80 list).   
Maybe that's why it's currently at #3 on the overall bestseller list!   
I just bought my copy...


Matt Jensen

Quoting Jeff Bone <jbone at place.org>:

> BBB is quickly becoming one of my favorite blogs.  This post from
> earlier today is a perfect example, and a standalone gem.  Anything
> that begins with the lines "Tim is a famous geologist. Tom is a famous
> clown." --- is a keeper.  :-)  (Despite the bit of naming confusion
> that appears midway...)
> Cf.
>   http://www.acceleratingfuture.com/steven/?p=33
> --
> (This post will be a more in-depth explanation of something I was
> trying to get across in much of the Rapture of the Nerds essay.)
> Tim is a famous geologist. Tom is a famous clown. Tim gives us a theory
> about rocks. We judge it to be 90% probable. In a parallel universe,
> Tom gives us the same theory about rocks. We judge it to be 10%
> probable.
> Jim gives us a theory about fish and presents a full technical case   
> that is good — the facts all fit. In a parallel universe, Jom gives   
> us a theory about fish and presents a full technical case that is   
> bad — it needs coincidences or leaps of logic. We judge Jim’s theory  
>  to be 90% probable. We judge Jom’s theory to be 10% probable.
> These two situations might seem the same. In the first case, we used  
>  only indirect evidence — the theorist’s credentials — to assess   
> probabilities. In the second case, we used only direct evidence —   
> the known facts of the matter — to assess probabilities. Both are   
> useful kinds of evidence. But there is an important difference.
> Suppose we ask Tim and Tom to make a full technical case. Tim the   
> geologist gives us a full technical case that is, as expected, quite  
>  good. Tom the clown, in his own parallel universe, gives us the  
> same  full technical case — one much better than we expected from a  
> clown.  Since a full technical case relies in no way on authority,  
> we put  the same probabilities on Tim’s claim and Tom’s claim.  
> Anything else  would be unreasonable.
> Suppose we ask Jim and Jom about all of their credentials. It turns   
> out their credentials are exactly the same. Maybe they’re both   
> equally famous clowns, who both took a course in marine biology once  
>  — surprising in Jim’s case, given that his arguments are so good.  
> Or  maybe they’re both famous marine biologists of exactly equal  
> fame  and competence — surprising in Jom’s case, given that his  
> arguments  are so bad. None of this matters for our probabilities.  
> Again, we  already have a full technical case, and a full technical  
> case relies  in no way on authority. Jim’s theory is still 90%  
> probable, Jom’s  theory still 10% probable.
> So once we knew Tim and Tom’s full technical arguments, their   
> credentials no longer mattered. But once we knew Jim and Jom’s full   
> credentials, their technical arguments still mattered. Technical   
> arguments and credentials are useful types of information   
> individually, but when both types are available, one trumps the other.
> If I’m not mistaken (but I need to read up on this!), what I’ve been  
>  doing here is just repeating the definition of “screening off” from  
>  the theory of causal diagrams. If we have three variables (A, B,  
> C),  and A and C are independent conditional on the value of B, then  
> B  screens off A from C, and A and C do not cause each other. In the  
>  authority example of this post, you could see the causality running  
>  as follows. If a theory is true, that causes the technical case for  
>  it to be good. If people have good credentials, that causes them to  
>  adopt theories for which the technical cases are good. But  
> causality  does not run directly from truth to adoption by people  
> with good  credentials, or from adoption by people with good  
> credentials to  truth.
> Maybe this all sounds like a complicated way to make a simple point,  
>  but it matters, because people’s intuitions sometimes get it all   
> wrong. If an  idea is adopted by silly people, or is not adopted by   
> competent people, that is seen as a “bad point” that is weighed   
> against the “good point” of solid technical argumentation. But this   
> weighing makes no sense — to a rational thinker, the “bad point”   
> counts until the “good point” arrives, and is then annihilated. In   
> real life, everything interesting is a mix of things you’ll always   
> have to take on authority and things you can check for yourself, but  
>  you can still apply this insight.
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