Consensus in the Hegselmann–Krause Model

This paper is concerned with the probability of consensus in a multivariate, spatially explicit version Hegselmann-Krause model for dynamics opinions. Individuals are located on vertices finite connected graph representing social network, and characterized by their opinion, set opinions $\Delta$ being general bounded convex subset dimensional normed vector space. Having confidence threshold $\tau$, two individuals said to be compatible if distance (induced norm) between does not exceed $\tau$. Each vertex $x$ updates its opinion at rate number neighbors which results replaced combination nearby opinions: $\alpha$ times plus $(1 - \alpha)$ average neighbors. The main objective derive lower bound when initially independent identically distributed values $\Delta$.