Divisible Updating

Résumé

A characterisation is provided of the belief updating processes that are independent of how an individual chooses to divide up/partition the statistical information they use in their updating. These \divisible" updating processes are in general not Bayesian, but can be interpreted as a re-parameterisation of Bayesian updating. This class of rules incorporates over- and under-reaction to new information in the updating and other biases. We also show that a martingale property is, then, sufficient the updating process to be Bayesian.