  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.
