[extropy-chat] what is probability?"

[gts]

--- Jef Allbright <jef at jefallbright.net> wrote:
 
> 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.

Sorry, I think you missed my point. 

The principle of "indeterminacy" (of "indifference", I
think you meant, as this is the principle we'd been
discussing) is one of the logical/rational constraints
*not* required in the subjective theory of Ramsey and
De Finetti.

Subjective Bayesians are free to set their prior
probabilities in any way they please, *no matter how
irrational*, provided only that they are consistent
such that if they were betting on their subjective
probabilities a clever betting adversary could not
force them to lose money no matter the outcome.

For example a subjective bayesian might set the prior
probability of intelligent life on the moon at .99999,
near certainty. Any rational, scientifically informed
person would call him crazy, and tell him very bluntly
that he needs to take a course in "optimum
decision-making under uncertainty" among other things.

But it matters only for the purposes of the subjective
theory that his hypothetical bets about life on the
moon be coherent, such that no one could exploit his
position such as to *force* him to lose money no
matter whether his crazy theory is correct or
incorrect.

That is what distinguishes subjective bayesianism from
the objective/logical bayesianism that you have
wittingly or unwittingly defended here and in the
"Paradox? What Paradox?" thread. 

The remarkable thing is that the subjective theory so
defined still satisfies the axioms of probability. 

-gts