Opinion Formation by Voter Models in Social Networks

author: Hiroshi Motoda, Osaka University
published: Sept. 28, 2012,   recorded: September 2012,   views: 271
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Large scale social networking applications have made it possible for news, ideas, opinions and rumors to spread easily, which affects and changes our daily life style substantially. Massive data are constantly being produced and are made available to us, enabling the study of the spread of influence in social networks. Much of the work has treated information as one entity and nodes in the network are either active (influenced) or inactive (uninfluenced), i.e., there are only two states. In this work, we address a different type of information diffusion, which is ``opinion formation'', i.e., spread of opinions. This requires a model that handles multiple states. Since each opinion (what is said) has its own value and an opinion with a higher value propagates more easily/rapidly, we first extend the basic voter model to be able to handle multiple opinions, and incorporate the value for each opinion. We call this model the value-weighted voter (VwV) model. We learn the weight from a limited number of opinion propagation data and predict the future share. We further added a new component to the VwV model reflecting the fact that there are always people that do not agree with the majority, i.e. anti-majoritarians. The model is called the value-weighted mixture voter (VwMV) model which combines the VwV and the anti-voter models both with multiple opinions. We also learn the weight and the anti-majoritarian tendency from the data. Learning the anti-majoritarian tendency is much more difficult than learning the weight, but we show that both are learnable from the data. We carry out the mean field analysis to VwMV model to gain an insight into the average behavior of opinion share and find some interesting features. Finally, we address the problem of detecting the change in opinion share caused by an unknown external situation change under the VwV model with multiple opinions in a retrospective setting. This is the double loop learning problem and the brute force approach is infeasible. We show that the use of the first order derivative of the log likelihood results in much faster solution.

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