[extropy-chat] what is probability?

[gts]

On Mon, 15 Jan 2007 11:16:20 -0500, Russell Wallace  
<russell.wallace at gmail.com> wrote:

> Seriously, that's why I said _practical_ example. If it matters, there
> should be real world cases that can serve as such. If it doesn't matter,
> well then it doesn't matter.

Not sure what you're getting at here, but assume you are political  
pollster commissioned by a politician wanting to know the political  
make-up of some newly districted congressional district about which there  
is no reliable prior data, and at a time in which the entire country is in  
political turmoil such that not even national statistics can be relied  
upon for priors. Assume also that you don't care about third parties.

In that situation, if you are using bayesian methods, you might use the PI  
and set your prior judgemental probability to .5 of finding, among those  
voters in the district who say they belong to one of the two major  
parties, someone who professes to be a democrat. You would then update  
your judgemental probability as you condition on new evidence (new  
interviews), just as in the urn example in which you would draw new  
marbles, with the idea that your posterior judgemental probability will  
converge in the limit with the objective chance of a person in that group  
professing to be a democrat.

Now, as I indicated in my last message, our original prior above rests on  
some shaky reasoning (the PI).

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.

-gts