An Axiomatic Framework for Belief Updates
  In the 1940's, a physicist named Cox provided the first formal justification
for the axioms of probability based on the subjective or Bayesian
interpretation. He showed that if a measure of belief satisfies several
fundamental properties, then the measure must be some monotonic transformation
of a probability. In this paper, measures of change in belief or belief updates
are examined. In the spirit of Cox, properties for a measure of change in
belief are enumerated. It is shown that if a measure satisfies these
properties, it must satisfy other restrictive conditions. For example, it is
shown that belief updates in a probabilistic context must be equal to some
monotonic transformation of a likelihood ratio. It is hoped that this formal
explication of the belief update paradigm will facilitate critical discussion
and useful extensions of the approach.
