How does WoM impact sequential social learning accuracy?
On Word-of-Mouth and Private-Prior Sequential Social Learning
This paper analyzes two models of social learning, "Private-Prior" (PP) and "Word-of-Mouth" (WoM), where networked agents estimate a dynamic value. In PP, agents combine private beliefs with noisy observations of predecessors' actions. In WoM, the last agent's belief becomes the shared prior for all. The study finds that WoM benefits later agents but harms earlier ones regarding estimation accuracy, a point relevant to hierarchical LLM agent systems where information flow resembles WoM. It highlights the risk of "data incest" or over-reliance on shared data in such systems, potentially degrading overall knowledge despite benefits for some agents. The analytical framework presented, although focusing on Kalman filter agents, offers a starting point for understanding information propagation and belief update dynamics within LLM-based multi-agent applications.