The noisy voter model under the influence of contrarians

The influence of contrarians on the noisy voter model is studied at the mean-field level. The noisy voter model is a variant of the voter model where agents can adopt two opinions, optimistic or pessimistic, and can change them by means of an imitation (herding) and an intrinsic (noise) mechanisms. An ensemble of noisy voters undergoes a finite-size phase transition, upon increasing the relative importance of the noise to the herding, form a bimodal phase where most of the agents shear the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states. By the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents (anti-herding). We first consider the case of only contrarians and show that the only possible steady state is the unimodal one. More generally, when voters and contrarians are present, we show that the bimodal-unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four, and their characteristic rates are small enough. For the number of contrarians bigger or equal to four, the voters and the contrarians can be seen only in the unimodal phase. Moreover, if the number of voters and contrarians, as well as the noise and herding rates, are of the same order, then the probability functions of the steady state are very well approximated by the Gaussian distribution

The role of homophily in opinion formation among mobile agents

Understanding the evolution and spread of opinions within social groups gives important insight into areas such as public elections and marketing. We are specifically interested in how psychological theories of interpersonal influence may affect how individuals change their opinion through interactions with their peers, and apply Agent-Based Modelling to explore the factors that may affect the emergence of consensus. We investigate the co-evolution of opinion and location by extending the Deffuant–Weisbuch bounded confidence opinion model to include mobility inspired by the psychological theories of homophily and dissonance, where agents are attracted or repelled by their neighbours based on the agreement of their opinions. Based on wide experimentation, we characterize the time it takes to converge to a steady state and the local diversity of opinions that results, finding that homophily leads to drastic differences in the nature of consensus. We further extend our mobility model and add noise in order to check the model's robustness, finding that a number of opinion clusters survive even with high levels of noise

Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias

We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with three other random agents and takes the majority opinion among the agents with probability (Formula presented.) (majority behavior) or the opposite opinion with probability (Formula presented.) (contrarian behavior). The probability of following the majority rule (Formula presented.) varies with the temperature T and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as T is varied. A transition temperature (Formula presented.) separates a bimodal oscillatory regime for (Formula presented.), where the population’s mean opinion m oscillates around a positive or a negative value from a unimodal oscillatory regime for (Formula presented.) in which m oscillates around zero. These regimes are characterized by the distribution of residence times that exhibit a unique peak for a resonance temperature (Formula presented.), where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that (Formula presented.) and (Formula presented.) are closely related.Fil: Gimenez, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Reinaudi, Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Cs.químicas. Departamento de Química Teórica y Computacional; ArgentinaFil: Galam, Serge. Centre National de la Recherche Scientifique; FranciaFil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentin

Heterogeneity in evolutionary games: an analysis of the risk perception

In this study, we analyse the relationship between heterogeneity and cooperation. Previous investigations suggest that this relation is non-trivial, as some authors found that heterogeneity sustains cooperation, while others obtained different results. Among the possible forms of heterogeneity, we focus on the individual perception of risks and rewards related to a generic event, which can appear in a number of social and biological systems. The modelling approach is based on the framework of evolutionary game theory. To represent this kind of heterogeneity, we implement small and local perturbations on the pay-off matrix of simple two-strategy games, such as the Prisoner’s Dilemma. So, while usually the pay-off is considered to be a global and time-invariant structure, i.e. it is the same for all individuals of a population at any time, in our model its value is continuously affected by small variations, in both time and space (i.e. position on a lattice). We found that such perturbations can be beneficial or detrimental to cooperation, depending on their setting. Notably, cooperation is strongly supported when perturbations act on the main diagonal of the pay-off matrix, whereas when they act on the off-diagonal the resulting effect is more difficult to quantify. To conclude, the proposed model shows a rich spectrum of possible equilibria, whose interpretation might offer insights and enrich the description of several systems

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

Opinion formation among mobile agents

The evolution of public opinion has been widely studied to understand how atomic interactions between individuals cause opinions to evolve. However, while many studies have paid attention to the influence and interaction mechanisms, the vast majority of the literature assumes a static representation of immobile agents, ignoring the effect that physical proximity and mobility has on interactions, as observed in real-life. Mobility provides humans with the opportunity to meet and locally interact with a diverse range of people, which can heavily influence opinion spread in human societies. Considering both opinion and location dynamics on widely used opinion models, such as the Bounded Confidence model, can therefore result in more realistic understanding of the drivers that cause agreement and diversity. This thesis investigates both directed and random mobility, inspired by two fundamental concepts from psychology: homophily and cognitive dissonance. These theories can drive the response behaviours to agreement and disagreement in humans. We translate these as attraction and repulsion forces in our mobility model. Through incorporating these phenomena, we quantify the different outcomes that arise and propose new evaluation metrics for analysis in this context that capture the formation of opinions and communities, reflecting the self-organisation among the populations. Extensive simulation results demonstrate the impact of the random and directed mobility. The main findings show that opinion formation is highly insensitive to random mobility, showing similarity in behaviour to static modelling. This is a very important result because the literature usually applies this approach. Furthermore, we find that alternative psychological theories, as incorporated into mobility, impact differently on both the opinion and spatial organisation of the agents. As these parameters are varied, we find a distinct transition in behaviour. Finally, by combining and analysing all the results, we propose a novel classification approach for different outcomes of self-organisation in opinion models

Role of inflexible minorities in the evolution of alcohol consumption

In this work we study a simple mathematical model for drinking behavior evolution. For this purpose, we considered three compartments, namely Susceptible individuals $S$ (nonconsumers), Moderated drinkers $M$ and Risk drinkers $R$. Inside the $S$ and $R$ compartments, we considered the presence of inflexible or zealot agents, i.e., individuals that never change their behavior (never drink or always drink a lot). These inflexible agents are described by fixed densities $s_I$ and $r_I$, for nonconsumer inflexible and risk drinking inflexible individuals, respectively. We analyze the impact of the presence of such special agents in the evolution of drinking behavior in the population. Specifically, since the presence of inflexible agents are similar to the introduction of quenched disorder in the model, we are interested in the impact of such disorder in the critical behavior of the system. Our analytical and numerical results indicate that the presence of only one class of inflexible agents, $s_I$ or $r_I$, destroys one of the two possible absorbing phases that are observed in the model without such inflexibles, i.e., for $s_i=r_I=0$. In the presence of the both kinds of inflexible agents simultaneously, there are no absorbing states anymore. Since absorbing states are collective macroscopic states with the presence of only one kind of individuals in the population, nonconsumers or risk drinkers, we argue that the inclusion of inflexible agents in the population makes the model more realistic. In addition, the work makes a contribution to studies on the impact of quenched disorder in nonequilibrium phase transitions, that are a subject of interest for Nonequilibrium Statistical Physics.Comment: 19 pages, 7 figures, submitted for publicatio

Econophysics, Statistical Mechanics Approach to

This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.Comment: 24 pages, 11 figures, 151 citations. V.2: one reference added. V.3: many minor corrections, some references added. V.4: many minor stylistic corrections incorporated after receiving the proof