提出动态理性概率聚合框架，确保集体信念随新信息一致更新
Consensus in Motion: A Case of Dynamic Rationality of Sequential Learning in Probability Aggregation
- 基于命题概率逻辑构建动态更新的聚合模型
- 共识兼容且独立的规则必为线性，保障一致性
- 适合需逐步决策的群体共识场景，如政策讨论
我们提出一种基于命题概率逻辑的概率聚合框架。与传统关注静态理性的判断聚合不同，该模型强调动态理性，确保集体信念能随新信息一致更新。我们证明：在非嵌套议程上，任何与共识兼容且独立的聚合规则必然为线性规则。此外，我们给出公平学习过程的充分条件：个体初始在特定命题子集（即共同基础）上达成一致，新信息仅限于该共享基础。这保证了无论先聚合还是先贝叶斯更新，最终的集体信念相同。本框架的独特之处在于对序列决策的处理，允许通过多个阶段逐步引入新信息，同时保持既定的共同基础。我们在一个涉及医疗与移民政策的政治情景中展示了该理论的应用。
原文摘要 · Abstract (English)
We propose a framework for probability aggregation based on propositional probability logic. Unlike conventional judgment aggregation, which focuses on static rationality, our model addresses dynamic rationality by ensuring that collective beliefs update consistently with new information. We show that any consensus-compatible and independent aggregation rule on a non-nested agenda is necessarily linear. Furthermore, we provide sufficient conditions for a fair learning process, where individuals initially agree on a specified subset of propositions known as the common ground, and new information is restricted to this shared foundation. This guarantees that updating individual judgments via Bayesian conditioning-whether performed before or after aggregation-yields the same collective belief. A distinctive feature of our framework is its treatment of sequential decision-making, which allows new information to be incorporated progressively through multiple stages while maintaining the established common ground. We illustrate our findings with a running example in a political scenario concerning healthcare and immigration policies.
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