On linear aggregation of infinitely many finitely additive probability measures

Abstract

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.