Maximizing Diversity of Opinion in Social Networks

Abstract

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.

The impact of noise and topology on opinion dynamics in social networks

“…the lack of global consensus) in a social network, though several measures have been proposed for different contexts. Mackin & Patterson [ 13 ] put forth a diversity index measure inspired by ecology and based on calculating probabilities that random individuals belong to a particular group. Their measure relies on setting a predefined threshold to distinguish boundaries between groups.…”

“…There is a growing body of literature looking at conflict within social networks, the bulk of which treats the topic as an optimization problem. Mackin & Patterson [ 13 ], for instance, propose a method for optimal leader placement, while Musco et al [ 14 ], suggest an algorithm that optimizes the weights in a network as a means to minimize polarization. The results of such optimization methods can be valuable to network administrators, especially for ‘social planning’ purposes, such as making link recommendations.…”

Maximizing Influence of Leaders in Social Networks

“…Many existing studies also pay attention to variants of the De-Groot model by selecting 1-leaders in the presence of competing 0-leaders, which are formulated for optimizing different objectives such as minimizing disagreement and polarization [41], maximizing the diversity [30] and the total opinion [29,31,42]. Similar opinion maximization problem was also studied for the FJ model by using different strategies, including identifying a given number of 1-leaders [20], as well as modifying individual's internal opinions [39] or susceptibility to persuasion [1,9].…”

“…In this section, we formulate the problem for optimizing the opinion influence of leaders in a social network described by a graph G( , ), where nodes represent individuals or agents, and edges represent interactions among agents. We adopt the discrete-time leader-follower DeGroot model [29,30,42] for opinion dynamics to achieve our goal.…”

“…We consider a variant of the DeGroot model [29,30,42] for opinion dynamics on a social network with nodes and edges, where nodes represent individuals, and edges denote interactions among individuals. In this extended DeGroot model, the individuals are classified two classes and : includes a small number ≪ of leader nodes, while the remaining − nodes in are followers.…”