Compromise and Synchronization in Opinion Dynamics
Alessandro Pluchino, Vito Latora, Andrea Rapisarda
备注：
Talk presented at the international conference Next05 Sigma Phi, 13-18 august 2005, Kolymbari, Crete. EPJ B (2006) in press. Typos corrected, refs added
We discuss two models of opinion dynamics. First wepresent a brief review of the Hegselmann and Krause (HK) compromise model in two dimensions, showing that it is possible to simulate the dynamics in the limit of an infinite number of agents by solving numerically a rate equation for a continuum distribution of opinions. Then, we discuss the Opinion Changing Rate (OCR) model, which allows to study under which conditions a group of agents with a different natural tendency (rate) to change opinion can find the agreement. In the context of the this model, consensus is viewed as a synchronization process.
A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ more than a tolerance parameter. In pairwise interactions, one of the pair, randomly selected, converts to the opinion of the other. The model can be used to simulate cases where no compromise is possible, such as choices of substitute goods, or other exclusive choices. The homogeneous case with maximum tolerance is equivalent to the Gambler's Ruin problem. A homogeneous system always ends up in an absorbing state, which can have one or mor…
Some political strategies to win elections over the last years were based heavily on fomenting general distrust in information institutions and favoring distrustful sources. The misinformation pandemic has the straightforward consequence that people do not believe any information unless it is compatible with their own beliefs. We present a simple model to study the emergence of consensus in opinion pools of uncertain agents that trust (couple to) their neighbors (information sources) with strength K. We focus the studies on regular lattices and linear coupling. Depending on the coupling consta…
In this paper we discuss opinion dynamics in the Opinion Changing Rate (OCR) model, recently proposed (A.Pluchino, V.Latora and A.Rapisarda Int. J. Mod. Phys. C, 16, No.4, 515-531 (2005)). The OCR model allows to study whether and how a group of social agents, with a different intrinsic tendency rate to change opinion, finds agreement. In particular, we implement the OCR model on a small graph describing the topology of a real social system. The nodes of the graph are scientists partecipating to the Tepoztlan conference, celebrating Alberto Robledo's 60th birthday, and the links are based on c…
We consider a nonlinear kinetic equation of Boltzmann type which takes into account the influence of conviction during the formation of opinion in a system of agents which interact through the binary exchanges introduced in [G. Toscani, Commun. Math. Sci. 4, 481 (2006)]. The original exchange mechanism, which is based on the human tendency to compromise and change of opinion through self-thinking, is here modified in the parameters of the compromise and diffusion terms, which now are assumed to depend on the personal degree of conviction. The numerical simulations show that the presence of con…
Hierarchical Synchronization and Distortion Scaling in Social Media Networks: A Fractal-Like Topology Theory
School of Information Science and Technology, Fudan University（复旦大学信息科学与技术学院）；School of Physics and Electronic Science, East China Normal University（华东师范大学物理与电子科学学院）
We study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearest-neighbor interactions on a two-dimensional square lattice. Each agent can hold either a positive or a negative opinion orientation, and can have two levels of intensity --moderate and extremist. When two interacting agents have the same orientation become extremists with persuasion probability $p$, while if they have opposite orientations become moderate with compromise probability $q$. These updating rules lead to the formation of same-opinion domains with …
We study the Deffuant et al. model for continuous--opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending of a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce an order-disorder transition. In the di…
In the compromise model of continuous opinions proposed by Deffuant et al, the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance $ε$. In directed networks, if agent i is a neighbor of agent j, j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions $<F>$ and their distribution as a function of $ε$ and of the network structural disorder. In directed networks $<F>$ exhibits a rich structure, being lar…
We study the continuum opinion dynamics of the compromise model of Krause and Hegselmann for a community of mutually interacting agents, by solving numerically a rate equation. The opinions are here represented by bidimensional vectors with real-valued components. We study the situation starting from a uniform probability distribution for the opinion configuration and for different shapes of the confidence range. In all cases, we find that the thresholds for consensus and cluster merging either coincide with their one-dimensional counterparts, or are very close to them. The symmetry of the fin…
'Rich get richer' rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered in many papers, where the asymptotic behavior was proven to exhibit a.s. synchronization. We consider in this paper models where, even if interaction among agents is present, absence of synchronization may happen due to the choice of an individual…
We study opinion dynamics over multiplex networks where agents interact with bounded confidence. Namely, two neighbouring individuals exchange opinions and compromise if their opinions do not differ by more than a given threshold. In literature, agents are generally assumed to have a homogeneous confidence bound. Here, we study analytically and numerically opinion evolution over structured networks characterised by multiple layers with respective confidence thresholds and general initial opinion distributions. Through rigorous probability analysis, we show analytically the critical thresholds …
How do movements and coalitions which engage with multiple social issues succeed in cross-issue solidarity, and when do they instead become fragmented? To address this, the mechanisms of cross-issue interaction have to be understood. Prior work on opinion dynamics and political disagreement has focused on single-issue consensus and polarization. Inspired by practices of cross-issue movement building, we have developed a general model of multi-issue opinion dynamics where agreement on one issue can promote greater inclusivity in discussing other issues, thereby avoiding the pitfalls of exclusiv…
We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number $k$ that expresses its level of agreement on a given issue, from totally against $k=-M$ to totally in favor $k=M$. Same-orientation agents persuade each other with probability $p$, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability $q$. The population initially evolves to (a) a polarized state for $r=p/q>1$, where opinions' distr…
We propose new Degroot-type social learning models with feedback in a continuous time, to investigate the effect of a noisy information source on consensus formation in a social network. Unlike the standard Degroot framework, noisy information models destroy consensus formation. On the other hand, the noisy opinion dynamics converge to the equilibrium distribution that encapsulates correlations among agents' opinions. Interestingly, such an equilibrium distribution is also a non-equilibrium steady state (NESS) with a non-zero probabilistic current loop. Thus, noisy information source leads to …
In this paper we study the impact of active participation -- or deliberately seeking out other agents with an aim to convince them -- on the dynamics of consensus formation. For this purpose, we propose an adaptive network model in which two processes shape opinion dynamics at interwoven time-scales: (i) agents adapt their opinions subject to influence from social network neighbours who hold opinions within a tolerance interval $δ$ and (ii) agents rewire network connections with an aim to maximize their own influence on overall system opinion. We study this system in both an endogenous setting…
In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a consensus, and how long it takes a consensus to form. This idea has been studied heavily both in physics and in other disciplines, and the answer depends strongly on both the model for opinions and for the network structure on which the opinions evolve. One model that was created to study consensus formation quantitatively is the Deffuant model, in which the opinion distribution of a population evolves via sequentia…
We study the dynamics of the naming game as an opinion formation model on time-varying social networks. This agent-based model captures the essential features of the agreement dynamics by means of a memory-based negotiation process. Our study focuses on the impact of time-varying properties of the social network of the agents on the naming game dynamics. In particular, we perform a computational exploration of this model using simulations on top of real networks. We investigate the outcomes of the dynamics on two different types of time-varying data - (i) the networks vary on a day-to-day basi…
We present three models used to describe the recruitment of the undecided population by pro-vax and no-vax factions. Starting from real-world data of Facebook pages, we compare three opinion dynamics models that catch different behaviours of the undecided population. The first one is a variation of the SIS model, where undecided position is considered indifferent. Neutrals can be "infected" by one of the two extreme factions, joining their side, and they "recover" when they lose interest in the debate and go back to neutrality. The second model is a three parties Voters model: neutral pages re…
Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a flock, or the measurement of a sensor within a sensor network. This value is updated, at each iteration, to a weighted average of itself and of the values of the adjacent agents. It is well known that, under natural assumptions on the network's graph connectivity, thi…
