Power Indices in the Context of Social Learning Behaviour in Social Networks

This paper puts forward the concept of integrated power, synthetically measures the voters' ability to influence the results of decision-making by influencing others through social learning, considering the interactions between decision-makers in social networks, and offers a method for measuring integrated power. Based on the theory and model of social learning, we analyze the influence of social learning on the voting process and power indices from the perspective of individuals' professional level, position within the social network structure, relationship closeness, and learning efficiency. A measurement model of integrated power is constructed, and the variation in integrated power compared with that of the Banzhaf index is analyzed by numerical simulation. The results show that when the individual's professional level is higher and closeness with neighboring decision-makers is greater, then the integrated power index is higher. An individual's integrated power index may decrease when he/she changes from an isolated node to a nonisolated node, and then his/her integrated power will increase with the increases of neighbor nodes. Social learning efficiency can promote the integrated power of individuals with lower social impact and relationship closeness, but it is not beneficial for the core and influential members of the social network.