2018/11/08 by Mackin, Erika, Patterson, Stacy · 1 citation
#FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Social and Information Networks (cs.SI) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1811.03706
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.