Symmetric conformity functions make decision-making processes independent of the distribution of learning strategies

Two main procedures characterize the way in which social actors evaluate the qualities of the options in decision-making processes: they either seek to evaluate their intrinsic qualities (individual learners) or they rely on the opinion of the others (social learners). For the latter, social experiments have suggested that the mathematical form of the probability of adopting an option, called the conformity function, is symmetric in the adoption rate. However, the literature on decision making includes models where social learners employ either symmetric and non-symmetric conformity functions. Here, we generalize previous models and show analytically that when symmetric conformity functions are considered, the form of the probability distribution of the individual strategies (behaving as a social or an individual learner) does not matter: only the expected value of this distribution influences the determination of the steady state. Moreover, we show that a dynamics that considers strategies as idiosyncratic properties of the agents and another that allows them to change in time lead to the same result in the case of symmetric conformity functions, while the results differ in the case of non-symmetric ones. This fact can inspire experiments that could shed light on the debate about this point.Comment: 17 pages, 6 figures, links to the source code repositor

Statistical Physics Of Opinion Formation: is it a SPOOF?

We present a short review based on the nonlinear $q$-voter model about problems and methods raised within statistical physics of opinion formation (SPOOF). We describe relations between models of opinion formation, developed by physicists, and theoretical models of social response, known in social psychology. We draw attention to issues that are interesting for social psychologists and physicists. We show examples of studies directly inspired by social psychology like: "independence vs. anticonformity" or "personality vs. situation". We summarize the results that have been already obtained and point out what else can be done, also with respect to other models in SPOOF. Finally, we demonstrate several analytical methods useful in SPOOF, such as the concept of effective force and potential, Landau's approach to phase transitions, or mean-field and pair approximations.Comment: 29 pages, 4 figures, new section 6 slightly extended, figures of higher quality, corrected typos, extended references, other minor improvements throughout the tex

Think then act or act then think?

We introduce a new agent-based model of opinion dynamics in which binary opinions (yes/no) of each agent can be measured and described regarding both pre- and post-influence at both of two levels, public and private, vis-\`a-vis the influence source. The model combines ideas introduced within the $q$-voter model with noise, proposed by physicists, with the descriptive, four-dimensional model of social response, formulated by social psychologists. We investigate two versions of the same model that differ only by the updating order: an opinion on the public level is updated before an opinion on the private level or vice versa. We show how the results on the macroscopic scale depend on this order. The main finding of this paper is that both models produce the same outcome if one looks only at such a macroscopic variable as the total number of the individuals with positive opinions. However, if also the level of internal harmony (viz., dissonance) is measured, then significant, qualitative differences are seen between these two versions of the model. All results were obtained simultaneously within Monte Carlo simulations and analytical calculations. We discuss the importance of our studies and findings from three points of view: the theory of phase transitions, agent-based modeling of social systems, and social psychology.Comment: 24 pages, 5 figures, corrected typos and the algorithm description, extended Methods and results section, replaced Fig. 1., added supporting materials with derivations, layout issues solve