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<p>Geometric belief aggregation has four serious drawbacks. First, on uncountably infinite spaces, its standard definition has a major domain restriction: it requires all beliefs to be absolutely continuous with respect to a common “reference measure”. Second, the standard definition cannot be applied to beliefs defined on abstract Boolean algebras, without specifying the underlying state space. Third, it can only be applied to profiles that are <i>coherent</i>, meaning that the beliefs of the agents have overlapping support. Finally, geometric aggregation does not satisfy the <i>marginalization</i> property. So it is sensitive to the way that one individuates states in the state space. This paper defines and axiomatically characterizes versions of geometric aggregation that resolve the first three problems, and mitigate the fourth one.</p>

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General geometric belief aggregation

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Marcus Pivato

摘要

Geometric belief aggregation has four serious drawbacks. First, on uncountably infinite spaces, its standard definition has a major domain restriction: it requires all beliefs to be absolutely continuous with respect to a common “reference measure”. Second, the standard definition cannot be applied to beliefs defined on abstract Boolean algebras, without specifying the underlying state space. Third, it can only be applied to profiles that are coherent, meaning that the beliefs of the agents have overlapping support. Finally, geometric aggregation does not satisfy the marginalization property. So it is sensitive to the way that one individuates states in the state space. This paper defines and axiomatically characterizes versions of geometric aggregation that resolve the first three problems, and mitigate the fourth one.