Greetings,
In light of last spring's discussions of Cox, Jaynes, priors,
Bayesian exclusive rationality, etc., on this list, readers may be
interested in checking out the extended abstract described briefly below.
The postscript text may be downloaded _via_
http://www.cs.unh.edu/~paulsnow
Please note the tilde.
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The Reasonableness of Possibility from the Perspective of Cox
The possibility calculus is shown to be a reasonable belief representation
in Cox's sense, even though possibility is formally different from
probability. So-called "linear" possibility measures satisfy the equations
which appear in Cox's Theorem. General possibility measures encode sets of
linear measures, consistent with a method of belief representation based
on sets which Cox pioneered. Exploring the relationship between possibility
and Cox's belief measures provides an opportunity to discuss some of the
ways in which Cox dissented from Bayesian orthodoxy, especially in his
tolerance of partially ordered belief and his rejection of prior
probabilities for evidentiary inference which begins in ignorance.
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These results, of course, complement the already available logical
and default-reasoning translations between possibility and the class of
probabilities which solve "atomic bound systems." The new translation does
not rely on ABS probabilities, however, but uses instead a cute beastie
peculiar to Cox's equations.
Possibility illustrates that while Cox's Theorem is an excellent
justification of subjective probability, it confers no monopoly of
"reasonableness" upon orthodox Bayesian methods, as distinct from more
inclusive subjectivist approaches.
Best regards,
Paul
