Abstract
Within this paper we explore the idea of a critical value representing the proportion of majority members within a group that affects dramatic changes in influence targets’ conformity. We consider the threshold q-voter model when the responses of the Willis-Nail model, a well-established two-dimensional model of social response, are used as a foundation. Specifically, we study a generalized threshold q-voter model when all basic types of social response described by Willis-Nail model are considered, i.e. conformity, anticonformity, independence, and uniformity/congruence. These responses occur in our model with complementary probabilities. We introduce independently two thresholds: one needed for conformity, as well as a second one for anticonformity. In the case of conformity, at least r individuals among q neighbors have to share the same opinion in order to persuade a voter to follow majority’s opinion, whereas in the case of anticonformity, at least w individuals among q neighbors have to share the same opinion in order to influence voters to take an opinion that goes against that of their own reference group. We solve the model on a complete graph and show that the threshold for conformity significantly influences the results. For example, there is a critical threshold for conformity above which the system behaves as in the case of unanimity, i.e. displays continuous and discontinuous phase transitions. On the other hand, the threshold for anticonformity is almost irrelevant. We discuss our results from the perspective of theories of social psychology, as well as the philosophy of agent-based modeling.
Highlights
In 2008 Nolan et al reported a series of very interesting social experiments on energy conservation [1]
The agent-based model (ABM) we propose here takes its roots in the Sznajd model [18, 19], in which the idea of unanimity for conformity has been introduced
In the q-voter model with conformity and only one type of nonconformity, i.e. for either z = 1 or z = 0, two types of steady states are possible depending on the model’s parameters. This means that, as a result of competition between conformity and nonconformity, an order-disorder phase transition is observed for a critical value of p = p, which depends on q and the type of nonconformity
Summary
In 2008 Nolan et al reported a series of very interesting social experiments on energy conservation [1] In one of their studies they examined different potential influence sources related to either self-interest (viz., saving money) or social responsibility (viz., protecting the environment) in hopes of changing individual’s behavior regarding using less electricity. Neither of these sources worked as well as a simple message/ a descriptive norm saying: “In a recent survey of households in your community, researchers at Cal State San Marcos found. These findings indicate that what the majority is doing, or at least what one thinks the majority is doing, can be more influential in changing behavior than inherent rewards from either financial incentives or from safeguarding the environment
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