This paper proposes a probabilistic aggregation framework based on propositional probability logic. Unlike existing judgment aggregation approaches that focus on static rationality, this model addresses dynamic rationality by ensuring that collective beliefs are consistently updated in response to new information. We show that all consensual and independent aggregation rules for non-overlapping agendas are linear. Furthermore, we present sufficient conditions for a fair learning process, where individuals initially agree on a subset of propositions, called the common ground, and new information is constrained to this shared ground. This ensures that individual judgment updates via Bayesian conditionalization generate identical collective beliefs, whether performed before or after aggregation. A key feature of this framework is its ability to handle sequential decision-making, allowing for the gradual integration of new information across multiple stages while maintaining established common ground. We illustrate our findings with examples from political scenarios concerning health and immigration policies.
