[extropy-chat] what is probability?

gts gts_2000 at yahoo.com
Mon Jan 15 15:34:08 UTC 2007

On Sun, 14 Jan 2007 21:36:50 -0500, Russell Wallace  
<russell.wallace at gmail.com> wrote:

> I'm inclined to think that issue would be best discussed in the context  
> of a practical example - do you have one to hand?


An urn contains 100 green and/or red marbles in unknown proportion. We  
want to know pr(green) (the probability of drawing a green marble).

For better or worse, the principle of indifference (PI) tells us that  
given no evidence to prefer either green or red, we should assign them  
equal probabilities. So pr(green) = 0.5.

We set .5 as the prior probability in bayes' theorem, then begin  
performing experiments (drawing marbles with replacement), updating our  
judgmental probability along the way according to the theorem (bayesian  

After we've conditioned on enough evidence our judgmental probability  
should match, in the limit, the true objective chance of drawing a green  
marble from the urn (assuming we believe in such things as objective  

This is I think not a totally unreasonable process, even though our  
initial prior probability judgment was based on what you and I agree is  
shaky reasoning.

Opposing the PI is the idea that given no evidence, we should assign no  
probability at all, i.e., that we should accumulate some empirical  
evidence *before* we start estimating probabilities. But this idea makes  
some bayesians very uncomfortable.


More information about the extropy-chat mailing list