Generalization of Krasnoshchekov’s Model for the Case of a Decomposable Matrix of Social Interactions

摘要

In this work, Krasnoshchekov’s model, which describes the behavior of people in a community under social and informational influences, is generalized to include the case of a system with a sophisticated structure of social interaction. In particular, the situation when an isolated group of people is formed who are not familiar with the rest of the community, which corresponds to a decomposable matrix of social interactions, is studied. The conditions for the solution of the system of equations describing the behavior of such a community to exist and be unique are considered. The problem of finding the relation between Krasnoshchekov’s and De Groot’s models is solved. The way this matrix of social interactions and the social independence of individuals affect the structure of the solution of this system, which describes in particularl how beliefs spread among people, is studied.