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.
The majority rule evolution function is named from the same well known approach in voting system @cite_10 . Generally speaking, belief evolution can be considered as voting in a social network for two opposite candidates. However, in belief evolution, the majority rule voting is performed locally, individually, distributedly and iteratively, while in voting system, it is performed globally, wholly, contralizedly and only once.
@cite_10
1590250213
GLOSSARY OF MAJOR CONCEPTS 1. Introduction 2. Arrow's Impossibility Result 3. Majority Decision Under Restricted Domains 4. Individual Rights 5. Manipulability 6. Espacing Impossibilities: Social Choice Rules 7. Distributive Justice: Rawlsian and Utilitarian Rules 8. Cooperative Bargaining 9. Empirical Social Choice 10. A Few Steps Beyond