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The voter model and the Axelrod model are two of the main stochasticprocesses that describe the spread of opinions on networks. The former includessocial influence, the tendency of individuals to become more similar when theyinteract, while the latter also accounts for homophily, the tendency tointeract more frequently with individuals which are more similar. The Axelrodmodel has been extensively studied during the past ten years based on numericalsimulations. In contrast, we give rigorous analytical results for ageneralization of the voter model that is closely related to the Axelrod modelas it combines social influence and confidence threshold, which is modeledsomewhat similarly to homophily. Each vertex of the network, represented by afinite connected graph, is characterized by an opinion and may interact withits adjacent vertices. Like the voter model, an interaction results in anagreement between both interacting vertices -- social influence -- but unlikethe voter model, an interaction takes place if and only if the vertices'opinions are within a certain distance -- confidence threshold. In adeterministic static approach, we first give lower and upper bounds for themaximum number of opinions that can be supported by the network as a functionof the confidence threshold and various characteristics of the graph. Thenumber of opinions coexisting at equilibrium is then investigated in aprobabilistic dynamic approach for the stochastic process starting from arandom configuration ...

Opinion dynamics with confidence threshold: an alternative to the Axelrod model