2024/07/20 by Yuzhao Yang, Yang, Yuzhao
Economics, Econometrics and Finance · #FOS: Economics and business #Game Theory and Voting Systems #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2407.14959
openalex publication_date 2024/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Commutativity is a normative criterion of aggregation and updating stating that the aggregation of expert posteriors should be identical to the update of the aggregated priors. I propose a thought experiment that raises questions about the normative appeal of Commutativity. I propose a weakened version of Commutativity and show how that assumption plays central roles in the characterization of linear belief aggregation, multiple-weight aggregation, and an aggregation rule which can be viewed as the outcome of a game played by "dual-selves," Pessimism and Optimism. Under suitable conditions, I establish equivalences between various relaxations of Commutativity and classic axioms for decision-making under uncertainty, including Independence, C-Independence, and Ambiguity Aversion.