[extropy-chat] what is probability?"

[gts]

--- 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. 

"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