2021/11/01 by Michele Caprio, Sayan Mukherjee, Caprio, Michele +1 · 1 citation
Physics and Astronomy · Social Sciences · #60A05 #62A01 #FOS: Mathematics #Misinformation and Its Impacts #Opinion Dynamics and Social Influence #Probability (math.PR) #Statistical Mechanics and Entropy #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2111.01050
openalex publication_date 2021/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).