Supportive interactions in the noisy voter model

Latane social impact theory predicts recruitment and supportive interactions being responsible for opinion formation. So far only recruitment interactions were considered in the voter models. Here we consider a noisy voter model with supportive interactions, which make voters less likely to change their opinions. This is similar to the voter models with freezing, but instead of interacting with their past selves voters get the support from their peers. We examine two different ways in which the support could be implemented: support deterring imitation as well as independence, support deterring imitation only. Both assumptions introduce strong drift into the model, which almost always overcomes the diffusion caused by the imitative behavior. The first assumption introduces strong attraction to a full consensus state, unless the support becomes too strong. The latter assumption promotes partial consensus, with surviving minority group.