Detecting Anti-majority Opinionists Using Value-Weighted Mixture Voter Model

We address the problem of detecting anti-majority opinionists using the value-weighted mixture voter (VwMV) model. This problem is motivated by the fact that some people have a tendency to disagree with any opinion expressed by the majority. We extend the value-weighted voter model to include this phenomenon with the anti-majoritarian tendency of each node as a new parameter, and learn this parameter as well as the value of each opinion from a sequence of observed opinion data over a social network. We experimentally show that it is possible to learn the anti-majoritarian tendency of each node correctly as well as the opinion values, whereas a naive approach which is based on a simple counting heuristic fails. We also show theoretically that, in a situation where the local opinion share can be approximated by the average opinion share, it is not necessarily the case that the opinion with the highest value prevails and wins when the opinion values are non-uniform, whereas the opinion share prediction problem becomes ill-defined and any opinion can win when the opinion values are uniform. The simulation results support that this holds for typical real world social networks.