Modelling Biased Judgement with Weighted Updating

I study the weighted updating model, a generalization of Bayesian updating that allows for biased beliefs by weighting the functions that constitute Bayes ’ rule with real exponents. I show that weighting a distribution affects the information entropy of the resulting distribution, suggesting that weighted updating can model biases in which individuals misperceive the information content of data. I augment the base model in two ways, allowing weighted updating to account for additional biases. The first expansion involves discrimination between data. The second allows the weights to vary over time. I also find sufficient conditions for the uniqueness of a maximum of the weighted updating model and that log-concavity plays a key role. As an applied example, I detail how the model can show that self attribution bias can lead to optimism bias.