  We define a new class of Bayesian point estimators, which we refer to as risk
averse. Using this definition, we formulate axioms that provide natural
requirements for inference, e.g. in a scientific setting, and show that for
well-behaved estimation problems the axioms uniquely characterise an estimator.
Namely, for estimation problems in which some parameter values have a positive
posterior probability (such as, e.g., problems with a discrete hypothesis
space), the axioms characterise Maximum A Posteriori (MAP) estimation, whereas
elsewhere (such as in continuous estimation) they characterise the
Wallace-Freeman estimator.
  Our results provide a novel justification for the Wallace-Freeman estimator,
which previously was derived only as an approximation to the
information-theoretic Strict Minimum Message Length estimator. By contrast, our
derivation requires neither approximations nor coding.
