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We study an extension of the DeGroot model where part of the players may berebels. The updating rule for rebels is quite different with that of normalplayers (which are referred to as conformists): at each step a rebel firsttakes the opposite value of the weighted average of her neighbors' opinions,i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual),and then updates her opinion by taking another weighted average between thatvalue and her own opinion in the last round. We find that the effect of rebelsis rather significant: as long as there is at least one rebel in every closedand strongly connected group, under very weak conditions, the opinion of eachplayer in the whole society will eventually tend to 0.5.

Rebels Lead to the Doctrine of the Mean: Opinion Dynamic in a Heterogeneous DeGroot Model