Zusammenfassung
We propose a new, more general definition of extended probability measures. We study their properties and provide a behavioral interpretation. We put them to use in an inference procedure, whose environment is canonically represented by the probability space (Ω, ℱ, P), when both P and the composition of Ω are unknown. We develop an ex ante analysis — taking place before the statistical analysis requiring knowledge of Ω — in which the true composition of Ω is progressively learned. We describe how to update extended probabilities in this setting and introduce the concept of lower extended probabilities. We apply our findings to a species sampling problem and to the study of the boomerang effect (the empirical observation that sometimes persuasion yields the opposite effect: the persuaded agent moves their opinion away from the opinion of the persuading agent).
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