Opinion dynamics with similarity-based random neighbors

A typical assumption made in the existing opinion formation models is that two individuals can communicate with each other only if the distance between their opinions is less than a threshold called bound of confidence. However, in the real world it is quite possible that people may also have a few friends with quite different opinions. To model this situation, we propose a bounded confidence plus random selection model, in which each agent has several long-range neighbors outside the bound who are selected according to a similarity-based probability rule. We find that the opinions of all agents can reach a consensus in bounded time. We further consider the situation when agents ignore the bound of confidence and select all their neighbors randomly according to the similarity-based probability rule. We prove that in this scenario the whole group could also reach a consensus but in the probability sense.