Majority Rule for Belief Evolution in Social Networks
This addresses the problem of understanding belief dynamics in social networks for researchers in social science and network theory, but it is incremental as it builds on existing frameworks.
The paper tackles the problem of belief evolution in social networks, focusing on the majority rule where an agent updates belief based on neighbors' majority, and finds that while convergence is not guaranteed in general, it occurs under random asynchronous updates.
In this paper, we study how an agent's belief is affected by her neighbors in a social network. We first introduce a general framework, where every agent has an initial belief on a statement, and updates her belief according to her and her neighbors' current beliefs under some belief evolution functions, which, arguably, should satisfy some basic properties. Then, we focus on the majority rule belief evolution function, that is, an agent will (dis)believe the statement iff more than half of her neighbors (dis)believe it. We consider some fundamental issues about majority rule belief evolution, for instance, whether the belief evolution process will eventually converge. The answer is no in general. However, for random asynchronous belief evolution, this is indeed the case.