On linear aggregation of infinitely many finitely additive probability measures

  • Michael NielsenEmail author


We discuss Herzberg’s (Theory Decis 78(2):319–337, 2015) treatment of linear aggregation for profiles of infinitely many finitely additive probabilities and suggest a natural alternative to his definition of linear continuous aggregation functions. We then prove generalizations of well-known characterization results due to (J Am Stat Assoc 76(374):410–414, 1981). We also characterize linear aggregation of probabilities in terms of a Pareto condition, de Finetti’s notion of coherence, and convexity.


Probability aggregation Linear aggregation Finitely additive probability Coherence Integral representations 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Columbia UniversityNew YorkUSA

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