[extropy-chat] A New Year's gift for Bayesians

[Robin Hanson]

I responded to Eliezer S. Yudkowsky
>>Laplace takes every event in your life, and every probability you 
>>assigned to each event, and multiplies all the probabilities together. 
>>This is your Final Judgment - the probability you assigned to your life. ...
>
>Saint Laplace should instead extrapolate your probabilities and assign 
>them to all events that happen, regardless of whether you learn about 
>them.  Then you won't want to commit suicide, etc.

Hara Ra responded to me:
>How Newtonian. 1 ml of air has 10^19 molecules, and all we know are a few 
>statistical values..... When you start with quantum theory and then recall 
>the sensitvities in chaos, knowing probablities as described is obviously 
>unknowable. Only a saint would think otherwise..... (Saint Laputa?)

On reflection, all we really need is for Saint Laplace to extrapolate what 
probability you would have assigned to all the events you could possibly 
have observed during your lifetime.  This is of course still unreasonably 
large.

Eliezer responded:
>All events that actually happen, everywhere in the (any?) universe... 
>hm.  That sounds fair.  But what about conditional probabilities?  In what 
>order is the Judged soul's judgment over all events extrapolated? In a 
>single life, the linear ordering is obvious, even when we evaluate the 
>conditional likelihood of other possible outcomes for any single 
>branch.  If we are to evaluate all events in the universe, how do we 
>compute the joint probability of all those events together?

Good question.  .... (think) .... OK, how about this.  Saint Laplace could 
randomly pick some different set of key choices that you might have made in 
your life, and then extrapolate your actual probability assigning style 
from your actual life to this other set of choices.  You'd be judged by 
this alternate probability.  Or perhaps he could sample a thousand such 
alternative lives, and give you an average score over them, reducing your 
risk at the cost of more computation.

If these key choices include the choices that you might have made to 
manipulate your final score, by limiting the amount of data you get, then 
it avoids that problem.  But if these key choices include when you actually 
choose your probability assigning style, it wouldn't give you an incentive 
to make that choice well.  So it comes down to whether Saint Laplace can 
distinguish probability assigning style choices from choices about how much 
data to get.

By the way, I've been reading this related edited volume:
Foundations of Bayesianism, ed. D. Cornfield and Jon Williamson, Kluwer, 2001.



Robin Hanson  rhanson at gmu.edu  http://hanson.gmu.edu
Assistant Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326  FAX: 703-993-2323