The emergence of "fifty-fifty" probability judgements in a conditional Savage world

Abstract

This paper models the empirical phenomenon of persistent fififty-fififty probability judgements within a dynamic non-additive Savage framework. To this purpose I construct a model of Bayesian learning such that an agents probability judgement is characterized as the solution to a Choquet expected utility maximization problem with respect to a conditional neo-additive capacity. Only for the non-generic case in which this capacity degenerates to an additive probability measure, the agent's probability judgement coincides with the familiar estimate of a Bayesian statistician who minimizes a quadratic (squared error) loss function with respect to an additive posterior distribution. In contrast, for the generic case in which the capacity is non-additive, the agent's probability judgements converge through Bayesian learning to the unique fuzzy probability measure that assigns a 0:5 probability to any uncertain event.

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