Consensus in Motion: A Case of Dynamic Rationality of Sequential Learning in Probability Aggregation

2025-04-20

AI Summary

This paper addresses the problem of dynamic irrationality in probabilistic aggregation—specifically, the failure of group beliefs to update coherently as new information arrives. Methodologically, it introduces a sequential aggregation framework grounded in propositional probability logic, formally embedding dynamic rationality by defining a “common basis” constraint and proving its equivalence to sequential Bayesian updating. Integrating non-nested agenda modeling, the paper derives that any consensus-compatible and independent aggregation rule must be linear. It further establishes sufficient conditions for fair learning. Theoretically, this work provides the first formal foundation for dynamically rational probabilistic aggregation. Empirically, the framework is validated on real-world political policy datasets, demonstrating both its theoretical soundness and practical applicability in sustaining consistent, adaptive collective belief revision under evolving evidence.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Multiagent Systems: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Dynamic rationality in probability aggregation with new information
• Linear aggregation rules for non-nested agendas
• Sequential decision-making maintaining common ground consistency

Innovation

• Dynamic rationality in probability aggregation
• Linear consensus-compatible aggregation rules
• Sequential Bayesian updating with common ground