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(Non-)Commutative Aggregation

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  • Yuzhao Yang

Abstract

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.

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  • Yuzhao Yang, 2024. "(Non-)Commutative Aggregation," Papers 2407.14959, arXiv.org.
    • Handle: RePEc:arx:papers:2407.14959
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    File URL: http://arxiv.org/pdf/2407.14959
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