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

Jeff Bone <jbone at place.org> on Thu Aug 9 09:23:13 PDT 2007

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...)




(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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