[extropy-chat] what is probability?"

Jef Allbright jef at jefallbright.net
Thu Jan 11 20:48:07 UTC 2007

gts wrote:

> --- Jef Allbright <jef at jefallbright.net> wrote:
> > I suspect we're using the term "subjective"
> differently.  
> So that you know, I mean something very precise by that term 
> in the context of this question about probability theory:
> A subjective probabilist is one who has no theoretical 
> problem with two individuals using different bayesian priors 
> about the same situation, provided only that those priors are 
> coherent. 

Well, to use your "very precise" terminology.  I "have no theoretical
problem" with what you've stated below. 

It seems as simple and obvious as the principle of indeterminacy and is
really just a restatement of that principle in the context of optimum
decision-making under uncertainty.

- Jef

> "coherent" means here that no so-called "dutch books"
> may be made against the agent by a clever adversary in a 
> betting arrangement in which the agent places multiple bets 
> on an outcome consistent with his subjective degrees of 
> belief. A "dutch book" is a sort of arbitrage situation in 
> which the agent would lose no matter the outcome because of 
> the incoherency of his bets.
> This is how the subjective theory was elucidated by both 
> Frank Ramsey and Bruno de Finetti, each of whom discovered 
> the theory independently of one another.
> More accurately they discovered that the simple coherency 
> constraint on bets as described above was sufficient to 
> satisfy the axioms of probability, with no need for 
> logical/rational constraints and the problems they entail, 
> which I think is very interesting... 
> -gts
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