Echoes of Disagreement: Measuring Disparity in Social Consensus

Public discourse and opinions stem from multiple social groups. Each group has beliefs about a topic (such as vaccination, abortion, gay marriage, etc.), and opinions are exchanged and blended to produce consensus. A particular measure of interest corresponds to measuring the influence of each group on the consensus and the disparity between groups on the extent to which they influence the consensus. In this paper, we study and give provable algorithms for optimizing the disparity under the DeGroot or the Friedkin-Johnsen models of opinion dynamics. Our findings provide simple poly-time algorithms to optimize disparity for most cases, fully characterize the instances that optimize disparity, and show how simple interventions such as contracting vertices or adding links affect disparity. Finally, we test our developed algorithms in a variety of real-world datasets.