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Publication - Dr John Fennell

    Uncertainty plus prior equals rational bias: An intuitive Bayesian probability weighting function


    Fennell, J & Baddeley, R, 2012, ‘Uncertainty plus prior equals rational bias: An intuitive Bayesian probability weighting function’. Psychological Review, vol 119., pp. 878-887


    Empirical research has shown that, when making choices based on probabilistic options, people behave as if they overestimate small probabilities, underestimate large probabilities, and treat positive and negative outcomes differently. These distortions have been modelled using a non-linear probability weighting function, which is found in several non-expected utility theories, including rank-dependent models and prospect theory ; here we propose a Bayesian approach to the probability weighting function and with it, a psychological rationale. In the real world, uncertainty is ubiquitous and accordingly, the optimal strategy is to combine probability statements with prior information using Bayes’ rule. First we show that any reasonable prior on probabilities leads to two of the observed effects; over weighting of low probabilities and underweighting of high probabilities. We then investigate two plausible kinds of priors; informative priors based on previous experience and uninformative priors of ignorance. Employed individually, these priors potentially lead to large problems of bias and inefficiency respectively, however, when combined using Bayesian model comparison methods, both forms of prior can be employed adaptively, gaining the efficiency of empirical priors and the robustness of ignorance priors. We illustrate this for the simple case of generic good and bad options, using internet blogs to estimate the relevant priors of inference. Given this combined ignorant/informative prior, the Bayesian probability weighting function is not only robust and efficient, but matches all the major characteristics of the distortions found in empirical research.

    Full details in the University publications repository