The emergence of “fifty–fifty” probability judgments through Bayesian updating under ambiguity

This paper explains the empirical phenomenon of persistent “fifty–fifty” probability judgments through a model of Bayesian updating under ambiguity. To this purpose I characterize an announced probability judgment as a Bayesian estimate given as the solution to a Choquet expected utility maximization problem with respect to a neo-additive capacity that has been updated in accordance with the Generalized Bayesian update rule. Only for the non-generic case, in which this capacity degenerates to an additive probability measure, the agent will learn the eventʹs true probability if the number of i.i.d. data observations gets large. In contrast, for the generic case in which the capacity is not additive, the agentʹs announced probability judgment becomes a persistent “fifty–fifty” probability judgment after finitely many observations.