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Engaging with dissenting views, fostering productive disagreements or strategic anticonformity can benefit organizations as it challenges the status quo. The question arises, however, whether such strategic anticonformity ultimately leads to social polarization, which is not a desirable phenomenon. We address this question within an agent-based model of discrete choices. Using the way of modeling social responses in continuous opinion models, we propose a three-state $q$-voter model with anticonformity and bounded confidence. We analyze the model on a complete graph using the mean-field approach and Monte Carlo simulations. We show that strong polarization appears only for a small probability of anticonformity, which means that conformity combined with homophily enhances polarization. Our findings agree with results obtained previously in the group discussion experiment and within various continuous opinion models., Comment: 27 pages, 10 figures

We study an asymmetric version of the threshold model with anticonformity under asynchronous update mode that mimics continuous time. We study this model on a complete graph using three different approaches: mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The latter approach yields analytical results for arbitrarily small systems, in contrast to the mean-field approach, which is strictly correct only for an infinite system. We show that for sufficiently large systems, all three approaches produce the same results, as expected. We consider two cases: (1) homogeneous, in which all agents have the same tolerance threshold, and (2) heterogeneous, in which the thresholds are given by a beta distribution parametrized by two positive shape parameters $\alpha$ and $\beta$. The heterogeneous case can be treated as a generalized model that reduces to a homogeneous model in special cases. We show that particularly interesting behaviors, including social hysteresis and critical mass, arise only for values of $\alpha$ and $\beta$ that yield the shape of the distribution observed in real social systems., Comment: 10 pages, 5 figures

Using two models of opinion dynamics, the $q$-voter model with independence and the $q$-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. To derive phase diagrams on networks, we develop the pair approximation for the quenched versions of the models. This formalism can be also applied to other quenched dynamics of similar kind. The results indicate that such a change of disorder eliminates all discontinuous phase transitions and broadens ordered phases. We show that although the annealed and quenched types of disorder lead to the same result in the $q$-voter model with anticonformity at the mean-field level, they do lead to distinct phase diagrams on networks. These phase diagrams shift towards each other as the average node degree of a network increases, and eventually, they coincide in the mean-field limit. In contrast, for the $q$-voter model with independence, the phase diagrams move towards the same direction regardless of the disorder type, and they do not coincide even in the mean-field limit. To validate our results, we carry out Monte Carlo simulations on random regular graphs and Barab\'{a}si-Albert networks. Although the pair approximation may incorrectly predict the type of phase transitions for the annealed models, we have not observed such errors for their quenched counterparts., Comment: 13 pages, 6 figures, extended section II and appendix B, visually modified Fig. 4, added descriptions of notation in figure captions, other minor improvements throughout the text, corrected typos