Quantifying Rational Belief
arXiv:0908.3212 · doi:10.1063/1.3275647
Abstract
Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there counterexamples to Cox? Rather than justifying Cox's choice of axioms we follow a different path and derive the sum and product rules of probability theory as the unique (up to regraduations) consistent representations of the Boolean AND and OR operations.
Presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA.) In version 2 one mistake and a few typos have been corrected
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