We study the problem of maximizing opinion diversity in a social network that includes opinion leaders with binary opposing opinions. The members of the network who are not leaders form their opinions using the French-DeGroot model of opinion dynamics. To quantify the diversity of such a system, we adapt two diversity measures from ecology to our setting, the Simpson Diversity Index and the Shannon Index. Using these two measures, we formalize the problem of how to place a single leader with opinion 1, given a network with a leader with opinion 0, so as to maximize the opinion diversity. We give analytical solutions to these problems for paths, cycles, and trees, and we highlight our results through a numerical example.
REF studied the diversity of opinions in the network characterized by entropy of the distribution of opinions in the network, while the analysis is restricted to special families of graphs.
Maximizing Diversity of Opinion in Social Networks
2019 American Control Conference (ACC)
2019 American Control Conference (ACC)
Mathematics Computer Science