Statistical Physics Of Opinion Formation: Is it a SPOOF?

Abstract

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.

Is Independence Necessary for a Discontinuous Phase Transition within the q-Voter Model?

“…. (40) We see that within the Landau approach we have obtained exactly the same value as previously in Equation (14). The transition is continuous as long as B > 0 and for B < 0 it is discontinuous, so we obtain the tricritical point from the condition:…”

“…Results obtained here has encouraged us to design a laboratory experiment, based on the idea introduced in [41], to check how the size of the influence group impacts the level of anticonformity. However, it is too soon to provide more details of this project, as reported in [14].…”

“…However, it has occurred that discontinuous phase transitions are not that typical in models of opinion dynamics, especially if we consider models belonging to the class of the binary-state dynamics [13,14] such as the voter model [15], the majority-vote model [15][16][17], the Galam model [18], the Sznajd model [19], the threshold model [6,20], the q-voter model [21] or the threshold q-voter model [22,23]. This is not very surprising, taking into account claims that the nonequilibrium spin systems with up-down symmetry fall in the universality class of the equilibrium Ising model, at least on regular lattices [1,17,24].…”

Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

“…Because all binary models, mentioned above, have been extensively investigated for years, many modifications and extensions of their original formulations have been proposed; a short review on modifications of the majorityvote model can be found in [29], on the Watts threshold model in [30], on the q-voter model in [31] and on the Galam model comprehensive review has been written by the author of the model [32,33]. Among many extensions, going into different directions, the introduction of an additional type of the social response was particularly interesting from the point of view of social/psychological sciences, as well as the theory of non-equilibrium phase transitions.…”

Compartmental voter model

“…Most well-known models of opinion dynamics seem to imply that a stable fixed state, either consensus or polarization, is inevitable [1][2][3][4][5][6][7]. However, local and spatial heterogeneity and ongoing exchange of opinions and cultural traits is a characterizing feature of social systems.…”