We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data.
Considerable effort using techniques developed in statistical physics has been aimed at numerical simulations of agent-based opinion models and analysis of their results. Such work has elucidated how various rules for interacting agents can give rise to steady state behaviors in the agent populations that vary between consensus and fragmentation. At the macroscopic population level, analysis has been limited due to the lack of an analytically tractable governing macro-equation for the continuous population state. We use the integro-differential equation that governs opinion dynamics for the co…
In this age of Facebook, Instagram and Twitter, there is rapidly growing interest in understanding network-enabled opinion dynamics in large groups of autonomous agents. The phenomena of opinion polarization, the spread of propaganda and fake news, and the manipulation of sentiment are of interest to large numbers of organizations and people, some of whom are resource rich. Whether it is the more nefarious players such as foreign governments that are attempting to sway elections or large corporations that are trying to bend sentiment -- often quite surreptitiously, or it is more open and above…
Diffusion-driven pattern formation in an opinion dynamical network model
Helmholtz Institute for Functional Marine Biodiversity (HIFMB)（赫尔姆霍兹功能海洋生物多样性研究所）；Carl-von-Ossietzky University, Institute for Chemistry and Biology of the Marine Environment（卡尔·冯·奥西茨基大学，海洋环境化学与生物学研究所）；Alfred-Wegener Institute (AWI), Helmholtz Center for Polar and Marine Research（阿尔弗雷德·魏格纳研究所（AWI），赫尔姆霍兹极地海洋研究中心）
We present a novel software suite for social network modeling and opinion diffusion processes. Much research on social network science has assumed networks with static topologies. More recently, attention has been turned to networks that evolve. Although software for modeling both the topological evolution of networks and diffusion processes are constantly improving, very little attention has been paid to agent modeling. Our software is designed to be robust, modular, and extensible, providing the ability to model dynamic social network topologies and multidimensional diffusion processes, diff…
Innovation diffusion in the networked population is an essential process that drives the progress of human society. Despite the recent advances in network science, a fundamental understanding of network properties that regulate such processes is still lacking. Focusing on an innovation diffusion model with pairwise transmission and macro-level social influence, i.e., more adopters in the networked population lead to a higher adoption tendency among the remaining individuals, we observe discontinuous phase transitions when the influence is sufficiently strong. Through extensive analyses of a la…
Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally…
Successful innovations achieve large geographical coverage by spreading across settlements and distances. For decades, spatial diffusion has been argued to take place along the urban hierarchy such that the innovation first spreads from large to medium cities then later from medium to small cities. Yet, the role of geographical distance, the other major factor of spatial diffusion, was difficult to identify in hierarchical diffusion due to missing data on spreading events. In this paper, we exploit spatial patterns of individual invitations on a social media platform sent from registered users…
Axelrod model describes the dissemination of a set of cultural traits in a society constituted by individual agents. In a social context, nevertheless, individual choices toward a specific attitude are also at the basis of the formation of communities, groups, parties. The membership in a group changes completely the behavior of single agents who start acting according to a social identity. Groups act and interact among them as single entities, but still conserve an internal dynamics. We show that, under certain conditions on social dynamics, the introduction of group dynamics in a cultural di…
We study the effects of diffusing opinions on the Deffuant et al. model for continuous opinion dynamics. Individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside an interval centered around the present opinion. We show that diffusion induces an order-disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. If the diffusion jumps are not large, clusters coalesce, so th…
The ways in which an innovation (e.g., new behaviour, idea, technology, product) diffuses among people can determine its success or failure. In this paper, we address the problem of diffusion of innovations over multiplex social networks where the neighbours of a person belong to one or multiple networks (or layers) such as friends, families, or colleagues. To this end, we generalise one of the basic game-theoretic diffusion models, called networked coordination game, for multiplex networks. We present analytical results for this extended model and validate them through a simulation study, fin…
We propose a microscopic model to describe how individual opinions shared between interacting agents initiate excessive collective expectations about a new idea or an innovation, followed by a swift collapse towards a dramatic collective disillusionment. The basic assumption which underlies the dynamics is that the information gathering process is not instantaneous but requires maturation. Agents steadily refine and update their personal opinion via a recurrent consultation of a public pool which stores information tokens (ITs). The expectation for the innovative idea is monitored in real-time…
The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be investigated. We propose here such a model for urban dynamics at the macroscopic scale, in which the diffusion of innovations between cities captures transformation processes (mutations) and transmission processes (diffusion), using two coupled spatial interaction models. Explorations of the model on synthetic systems of cities show the role of spatial interac…
Innovation diffusion has been studied extensively in a variety of disciplines, including sociology, economics, marketing, ecology, and computer science. Traditional literature on innovation diffusion has been dominated by models of aggregate behavior and trends. However, the agent-based modeling (ABM) paradigm is gaining popularity as it captures agent heterogeneity and enables fine-grained modeling of interactions mediated by social and geographic networks. While most ABM work on innovation diffusion is theoretical, empirically grounded models are increasingly important, particularly in guidi…
Information overload in the modern society calls for highly efficient recommendation algorithms. In this letter we present a novel diffusion based recommendation model, with users' ratings built into a transition matrix. To speed up computation we introduce a Green function method. The numerical tests on a benchmark database show that our prediction is superior to the standard recommendation methods.
The diffusion of opinions in Social Networks is a relevant process for adopting positions and attracting potential voters in political campaigns. Opinion polarization, bias, targeted diffusion, and the radicalization of postures are key elements for understanding voting dynamics. In particular, social bots are a new element that can have a pronounced effect on the formation of opinions during elections by, for instance, creating fake accounts in social networks to manipulate elections. Here we propose a voter model incorporating bots and radical or intolerant individuals in the decision-making…
We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up…
A simple model for simulating tug of war game as varying the player number in a team is discussed to identify the slow pace of fast change. This model shows that a large number of information sources leads slow change for the system. Also, we introduce an opinion diffusion model including the effect of a high degree of clustering. This model shows that the de facto standard and lock-in effect, well-known phenomena in economics and business management, can be explained by the network clusters.
A fundamental question related to innovation diffusion is how the social network structure influences the process. Empirical evidence regarding real-world influence networks is very limited. On the other hand, agent-based modeling literature reports different and at times seemingly contradictory results. In this paper we study innovation diffusion processes for a range of Watts-Strogatz networks in an attempt to shed more light on this problem. Using the so-called Sznajd model as the backbone of opinion dynamics, we find that the published results are in fact consistent and allow to predict th…
We present a new model for the diffusion of innovation. Here, the population is segmented into distinct groups. Adoption by a particular group of some cultural product may be inhibited both by large numbers of its own members already having adopted but also, in particular, by members of another group having adopted. Intergroup migration is also permitted. We determine the equilibrium points and carry out stability analysis for the model for a two-group population. We also simulate a discrete time version of the model. Lastly, we present data on tablet use in eight countries from 2012-2016 and …
Recent years saw an increased interest in modeling and understanding the mechanisms of opinion and innovation spread through human networks. Using analysis of real-world social data, researchers are able to gain a better understanding of the dynamics of social networks and subsequently model the changes in such networks over time. We developed a social network model that both utilizes an agent-based approach with a dynamic update of opinions and connections between agents and reflects opinion propagation and structural changes over time as observed in real-world data. We validate the model usi…
When multiple innovations compete for adoption, historical chance leading to early advantage can generate lock-in effects that allow suboptimal innovations to succeed at the expense of superior alternatives. Research on the diffusion of innovafacetion has identified many possible sources of early advantage, but these mechanisms can benefit both optimal and suboptimal innovations. This paper moves beyond chance-as-explanation to identify structural principles that systematically impact the likelihood that the optimal strategy will spread. A formal model of innovation diffusion shows that the ne…
Often in the setting of human-based interactions, the existence of a temporal hierarchy of information plays an important role in diffusion and opinion dynamics within communities. For example at the individual agent level, more recently acquired information may exert greater influence during decision-making processes. To facilitate further exploration of this effect, we introduce an efficient method for modelling temporally asynchronous opinion updates, where the timing of updates depends on the timing of incoming opinion states received from neighbours. The framework enables the introduction…
It is shown that under certain conditions it is possible to model a complex system in a way that leads to results that do not depend on system size. As an example of complex system an innovation diffusion model is considered. In that model a set of individuals (the agents), which are interconnected, must decide if adopt or not an innovation. The agents are connected in a member of the networks family known as small worlds networks (SWN). It is found that for a subfamily of the SWN the saturation time and the form of the adoption curve are invariants respect to the change in the size of the sys…
In this work, the aim is to study the diffusion of innovation of two competing products. The main focus has been to understand the effects of the competitive dynamic market on the diffusion of innovation. The global smartphone operating system sales are chosen as an example. The availability of the sales and the number of users data, as well as the predictions for the future number of users, make the smartphone diffusion a new laboratory to test the innovation of diffusion models for the competitive markets. In this work, the Bass model and its extensions which incorporate the competition betw…
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 …
Haynes et al. (1977) derived a nonlinear differential equation to determine the spread of innovations within a social network across space and time. This model depends upon the imitators and the innovators within the social system, where the imitators respond to internal influences, whilst the innovators react to external factors. Here, this differential equation is applied to simulate the uptake of a low-carbon technology (LCT) within a local electricity network situated in the UK. This network comprises of many households that are assigned to certain feeders. Firstly, travelling wave solutio…
Adoption of cultural innovation (e.g., music, beliefs, language) is often geographically correlated, with adopters largely residing within the boundaries of relatively few well-studied, socially significant areas. These cultural regions are often hypothesized to be the result of either (i) identity performance driving the adoption of cultural innovation, or (ii) homophily in the networks underlying diffusion. In this study, we show that demographic identity and network topology are both required to model the diffusion of innovation, as they play complementary roles in producing its spatial pro…
We generalize the classical Bass model of innovation diffusion to include a new class of agents --- Luddites --- that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously adopts the innovation at a constant rate. In response to the \emph{rate} of adoption, an ignorant may become a Luddite and permanently reject the innovation. Instead of reaching complete adoption, the final state generally consists of a population o…
The contagion threshold for diffusion of innovations is defined and calculated in finite graphs (two-dimensional regular lattices, regular random networks (RRNs), and two kinds of scale-free networks (SFNs)) with and without the bilingual option. Without the bilingual option, degree inhomogeneity and clustering enhance the contagion threshold in non-regular networks except for those with an unrealistically small average degree. It is explained by the friendship paradox and detour effect. We found the general boundary of the cost that makes the bilingual option effective. With a low-cost biling…
A micro-level agent-based model of innovation diffusion was developed that explicitly combines (a) an individual's perception of the advantages or relative utility derived from adoption, and (b) social influence from members of the individual's social network. The micro-model was used to simulate macro-level diffusion patterns emerging from different configurations of micro-model parameters. Micro-level simulation results matched very closely the adoption patterns predicted by the widely-used Bass macro-level model (Bass, 1969). For a portion of the domain, results from micro-simulations were …
Social identities are among the key factors driving behavior in complex societies. Signals of social identity are known to influence individual behaviors in the adoption of innovations. Yet the population-level consequences of identity signaling on the diffusion of innovations are largely unknown. Here we use both analytical and agent-based modeling to consider the spread of a beneficial innovation in a structured population in which there exist two groups who are averse to being mistaken for each other. We investigate the dynamics of adoption and consider the role of structural factors such a…
Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e., individuals interact preferentially with similar others). The strength of these social influences are controlled by two parameters: $F$, the number of features that characterizes the cultures and $q$, the common number of states each feature can assume. Here we assume that the innovation is a new state of a cultural feature of a single individual -- the innova…
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 …
Social media and social networking sites have become a global pinboard for exposition and discussion of news, topics, and ideas, where social media users often update their opinions about a particular topic by learning from the opinions shared by their friends. In this context, can we learn a data-driven model of opinion dynamics that is able to accurately forecast opinions from users? In this paper, we introduce SLANT, a probabilistic modeling framework of opinion dynamics, which represents users opinions over time by means of marked jump diffusion stochastic differential equations, and allow…
We propose a model for the diffusion of several products competing in a common market based on the generalization of the Ising model of statiscal mechanics (Potts model). Using an agent based implementation, we analyze two problems: (i) a three options case, i.e. to adopt a product A, a product B, or non-adoption and (ii) a four options case, i.e. the adoption of product A, product B, both, or none. In the first case we analyze a launching strategy for one of the two products, which delays its launching with the objective of competing with improvements. Market shares reached by each product ar…
In this paper we show that the small world and weak ties phenomena can spontaneously emerge in a social network of interacting agents. This dynamics is simulated in the framework of a simplified model of opinion diffusion in an evolving social network where agents are made to interact, possibly update their beliefs and modify the social relationships according to the opinion exchange.
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…
Social influence is the process by which individuals adapt their opinion, revise their beliefs, or change their behavior as a result of social interactions with other people. In our strongly interconnected society, social influence plays a prominent role in many self-organized phenomena such as herding in cultural markets, the spread of ideas and innovations, and the amplification of fears during epidemics. Yet, the mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation. Here, we report two controlled experiments showing…
Threshold models of cascades in the social sciences and economics explain the spread of opinion and innovation due to social influence. In threshold cascade models, fads or innovations spread between agents as determined by their interactions with other agents and their personal threshold of resistance. Typically, these models do not account for structure in the timing of interaction between the units. In this work, we extend a model of social cascades by Duncan Watts to temporal interaction networks. In our model, we assume friends and acquaintances influence agents for a certain time into th…
A model, applicable to a range of innovation diffusion applications with a strong peer to peer component, is developed and studied, along with methods for its investigation and analysis. A particular application is to individual households deciding whether to install an energy efficiency measure in their home. The model represents these individuals as nodes on a network, each with a variable representing their current state of adoption of the innovation. The motivation to adopt is composed of three terms, representing personal preference, an average of each individual's network neighbours' sta…
Agent-based models are versatile tools for studying how societal opinion change, including political polarization and cultural diffusion, emerges from individual behavior. This study expands agents' psychological realism using empirically-motivated rules governing interpersonal influence, commitment to previous beliefs, and conformity in social contexts. Computational experiments establish that these extensions produce three novel results: (a) sustained strong diversity of opinions within the population, (b) opinion subcultures, and (c) pluralistic ignorance. These phenomena arise from a combi…
The urban-rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million frie…
A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation by the Kramers-Moyal expansion. The solution exhibits some non-equilibrium phenomena. In the beginning the distribution curve of velocity/energy takes on a random oscillation, and then a near-equilibrium distribution described by the Boltzmann distribution is gradually established. However, a spike appears on the distribution curve and breaks this stable di…
Diffusion of innovation can be interpreted as a social spreading phenomena governed by the impact of media and social interactions. Although these mechanisms have been identified by quantitative theories, their role and relative importance are not entirely understood, since empirical verification has so far been hindered by the lack of appropriate data. Here we analyse a dataset recording the spreading dynamics of the world's largest Voice over Internet Protocol service to empirically support the assumptions behind models of social contagion. We show that the rate of spontaneous service adopti…
Here we developed a new conceptual, stochastic Heterogeneous Opinion-Status model (HOpS model), which is adaptive network model. The HOpS model admits to identify the main attributes of dynamics on networks and to study analytically the relation between topological network properties and processes taking place on a network. Another key point of the HOpS model is the possibility to study network dynamics via the novel parameter of heterogeneity. We show that not only clear topological network properties, such as node degree, but also, the nodes' status distribution (the factor of network hetero…
Influence diffusion and influence maximization in large-scale online social networks (OSNs) have been extensively studied, because of their impacts on enabling effective online viral marketing. Existing studies focus on social networks with only friendship relations, whereas the foe or enemy relations that commonly exist in many OSNs, e.g., Epinions and Slashdot, are completely ignored. In this paper, we make the first attempt to investigate the influence diffusion and influence maximization in OSNs with both friend and foe relations, which are modeled using positive and negative edges on sign…
