Modelling Biased Judgement with Weighted Updating

The weighted updating model is a generalization of Bayesian updating that allows for biased beliefs by weighting the constituent functions of Bayes' rule with real exponents. In this paper I show that transforming a distribution by exponential weighting and normalization systematically affects the information entropy of the resulting distribution. Specifically, if the weight is greater then one then the resulting distribution has less information entropy than the original distribution (and vice versa). This result provides a useful interpretation of the model, since, for example a likelihood function with greater entropy translates to the associated data being treated with less information content. The result also justifies using the model as it has been used in the literature, i.e. to model biases in which individuals treat observations as being either more or less informative than they should.