Confirmation bias and peer pressure both have substantial impacts on the formation of collective decisions. Nevertheless, few attempts have been made to study how the interplay between these two mechanisms affects public opinion evolution. Here we propose an agent-based model of opinion dynamics which incorporates the conjugate effect of confirmation bias (characterized by the population identity scope and individual stubbornness) and peer pressure (described by a susceptibility threshold). We show that the number of opinion fragments first increases and then decreases to one as population identity scope becomes larger in a homogeneous population. Further, in heterogeneous situations, we find that even a small fraction of impressionable individuals who are sensitive to peer pressure could help eliminate public polarization when population identity scope is relatively large. Intriguingly, we highlight the emergence of 'impressionable moderates' who are easily influenced, hold wavering opinions, and are of vital significance in competitive campaigns.
We propose a collective opinion formation model with a so-called confirmation bias. The confirmation bias is a psychological effect with which, in the context of opinion formation, an individual in favor of an opinion is prone to misperceive new incoming information as supporting the current belief of the individual. Our model modifies a Bayesian decision-making model for single individuals [M. Rabin and J. L. Schrag, Q. J. Econ. 114, 37 (1999)] for the case of a well-mixed population of interacting individuals in the absence of the external input. We numerically simulate the model to show tha…
Background: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical research of this phenomenon has mainly focused on its economic implications possibly missing its potential connections with broader notions of cognitive science. Methodology/Principal Findings: We formulate a (non-Bayesian) model for revising subjective probabilistic opinion of a confirmationally-biased agent in the light of a persuasive opinion. The revision …
Probabilistic neighbors' selection competes with confirmation bias in a bounded confidence model
CNRS, Complex Systems Institute of Paris Île-de-France (ISC-PIF)（法国国家科学研究中心，巴黎法兰西岛复杂系统研究所）；Laboratoire de Physique Théorique et Modélisation, CNRS-CY Cergy Paris Université（理论与建模物理实验室，CNRS-CY塞尔吉巴黎大学）；EHESS, Centre d’Analyse et de Mathématique Sociales (CAMS)（高等社会科学学院，社会分析与数学中心）；Cergy Paris Université（塞尔吉巴黎大学）
With the advent of online networks, societies are substantially more connected with individual members able to easily modify and maintain their own social links. Here, we show that active network maintenance exposes agents to confirmation bias, the tendency to confirm one's beliefs, and we explore how this affects collective opinion formation. We introduce a model of binary opinion dynamics on a complex network with fast, stochastic rewiring and show that confirmation bias induces a segregation of individuals with different opinions. We use the dynamics of global opinion to generally categoriz…
In this study, I present a theoretical social learning model to investigate how confirmation bias affects opinions when agents exchange information over a social network. Hence, besides exchanging opinions with friends, agents observe a public sequence of potentially ambiguous signals and interpret it according to a rule that includes confirmation bias. First, this study shows that regardless of level of ambiguity both for people or networked society, only two types of opinions can be formed, and both are biased. However, one opinion type is less biased than the other depending on the state of…
In this paper, the influence of the social media on the opinion formation process is modeled during an election campaign. In the proposed model, peer- to-peer interactions and targeted online propaganda messages are assumed to be the driving forces of the opinion formation dynamics. The conviction power of the targeted messages is based on the collected and processed private information. In this work, the model is based on an artificial society, initially evenly divided between two parties. The bounded confidence model governs peer-to-peer interactions with a value of confidence parameter whic…
In this paper, we study a model of opinion dynamics in a social network in the presence increasing interpersonal influence, i.e., increasing peer pressure. Each agent in the social network has a distinct social stress function given by a weighted sum of internal and external behavioral pressures. We assume a weighted average update rule and prove conditions under which a connected group of agents converge to a fixed opinion distribution, and under which conditions the group reaches consensus. We show that the update rule is a gradient descent and explain its transient and asymptotic convergenc…
Topological heterogeneities of social networks have a strong impact on the individuals embedded in those networks. One of the interesting phenomena driven by such heterogeneities is the friendship paradox (FP), stating that the mean degree of one's neighbors is larger than the degree of oneself. Alternatively, one can use the median degree of neighbors as well as the fraction of neighbors having a higher degree than oneself. Each of these reflects on how people perceive their neighborhoods, i.e., their perception models, hence how they feel peer pressure. In our paper, we study the impact of p…
We introduce and analyse a three-body consensus model (3CM) for non-linear consensus dynamics on hypergraphs. Our model incorporates reinforcing group effects, which can cause shifts in the average state of the system even in if the underlying graph is complete (corresponding to a mean-field interaction), a phenomena that may be interpreted as a type of peer pressure. We further demonstrate that for systems with two clustered groups, already a small asymmetry in our dynamics can lead to the opinion of one group becoming clearly dominant. We show that the nonlinearity in the model is the essent…
Online users tend to select claims that adhere to their system of beliefs and to ignore dissenting information. Confirmation bias, indeed, plays a pivotal role in viral phenomena. Furthermore, the wide availability of content on the web fosters the aggregation of likeminded people where debates tend to enforce group polarization. Such a configuration might alter the public debate and thus the formation of the public opinion. In this paper we provide a mathematical model to study online social debates and the related polarization dynamics. We assume the basic updating rule of the Bounded Confid…
Social media has emerged as a significant source of information for people. As agents interact with each other through social media platforms, they create numerous complex social networks. Within these networks, information spread among agents and their opinions may be altered by their neighbors' influence. This paper explores opinion dynamics on social networks, which are influenced by complex network structure, confirmation bias, and specific issues discussed. We propose a novel model based on previous models to simulate how public opinion evolves from consensus to radicalization and to pola…
Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainab…
Since the information available is fundamental for our perceptions and opinions, we are interested in understanding the conditions allowing for a good information to be disseminated. This paper explores opinion dynamics by means of multi-agent based simulations when agents get informed by different sources of information. The scenario implemented includes three main streams of information acquisition, differing in both the contents and the perceived reliability of the messages spread. Agents' internal opinion is updated either by accessing one of the information sources, namely media and exper…
In many instances of election, the electorate appears to be a composite of partisan and independent voters. Given that partisans are not likely to convert to a different party, a main goal for a party could be to mobilize independent voters toward the party with the help of strong leadership, mass media, partisans, and effects of peer-to-peer influence. Based on the exact solution of the classical voter model dynamics in the presence of perfectly partisan voters (i.e., zealots), we propose a computational method to maximize the share of the party in a social network of independent voters by pi…
Messages conveyed by media act as a major drive in shaping attitudes and inducing opinion shift. On the other hand, individuals are strongly affected by peer pressure while forming their own judgment. We solve a general model of opinion dynamics where individuals either hold one of two alternative opinions or are undecided and interact pairwise while exposed to an external influence. As media pressure increases, the system moves from pluralism to global consensus; four distinct classes of collective behavior emerge, crucially depending on the outcome of direct interactions among individuals ho…
By incorporating a multilayer network and time-decaying memory into the original voter model, the coupled effects of spatial and temporal cumulation of peer pressure on consensus are investigated. Heterogeneity in peer pressure and time-decaying mechanism are both found to be detrimental to consensus. The transition points, below which a consensus can always be reached and above which two opposed opinions are more likely to coexist, are found. A mean-field analysis indicates that the phase transitions in the present model are governed by the cumulative influence of peer pressure and the updati…
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…
We investigate an agent-based model of opinion dynamics with two types of social response: conformity and independence. Conformity is introduced to the model analogously as in the Sznajd model or $q$-voter model, which means that only unanimous group exerts peer pressure on individuals. The novelty, in relation to previous versions of the $q$-voter model, is memory possessed by each agent and external noise $T$, which plays the role of social temperature. Each agent has its own memories of past experiences related to the social costs and benefits of being independent or conformist. If an agent…
While the number and variety of models to explain opinion exchange dynamics is huge, attempts to justify the model results using empirical data are relatively rare. As linking to real data is essential for establishing model credibility, this Letter develops a empirical confirmation experiment by which an opinion model is related to real election data. The model is based on a representation of opinions as a vector of $k$ bits. Individuals interact according to the principle that similarity leads to interaction and interaction leads to still more similarity. In the comparison to real data we co…
What is the effect of the combined direct and indirect social influences-peer pressure (PP)-on a social groups collective decisions? We present a model that captures PP as a function of the socio-cultural distance between individuals in a social group. Using this model and empirical data from 15 real-world social networks we found that the PP level determines how fast a social group reaches consensus. More importantly, the levels of PP determine the leaders who can achieve full control of their social groups. PP can overcome barriers imposed upon a consensus by the existence of tightly connect…
Online social networks provide users with unprecedented opportunities to engage with diverse opinions. At the same time, they enable confirmation bias on large scales by empowering individuals to self-select narratives they want to be exposed to. A precise understanding of such tradeoffs is still largely missing. We introduce a social learning model where most participants in a network update their beliefs unbiasedly based on new information, while a minority of participants reject information that is incongruent with their preexisting beliefs. This simple mechanism generates permanent opinion…
We present an introduction to a novel model of an individual and group opinion dynamics, taking into account different ways in which different sources of information are filtered due to cognitive biases. The agent based model, using Bayesian updating of the individual belief distribution, is based on the recent psychology work by Dan Kahan. Open nature of the model allows to study the effects of both static and time-dependent biases and information processing filters. In particular, the paper compares the effects of two important psychological mechanisms: the confirmation bias and the politica…
Opinion dynamics have attracted the interest of researchers from different fields. Local interactions among individuals create interesting dynamics for the system as a whole. Such dynamics are important from a variety of perspectives. Group decision making, successful marketing, and constructing networks (in which consensus can be reached or prevented) are a few examples of existing or potential applications. The invention of the Internet has made the opinion fusion faster, unilateral, and on a whole different scale. Spread of fake news, propaganda, and election interferences have made it clea…
We investigate the impact of noise and topology on opinion diversity in social networks. We do so by extending well-established models of opinion dynamics to a stochastic setting where agents are subject both to assimilative forces by their local social interactions, as well as to idiosyncratic factors preventing their population from reaching consensus. We model the latter to account for both scenarios where noise is entirely exogenous to peer influence and cases where it is instead endogenous, arising from the agents' desire to maintain some uniqueness in their opinions. We derive a general …
Traditional models of opinion dynamics provide a simple approach to understanding human behavior in basic social scenarios. However, when it comes to issues such as polarization and extremism, we require a more nuanced understanding of human biases and cognitive tendencies. In this paper, we propose an approach to modeling opinion dynamics by integrating mental models and assumptions of individuals agents using Bayesian-inspired methods. By exploring the relationship between human rationality and Bayesian theory, we demonstrate the efficacy of these methods in describing how opinions evolve. O…
The dynamic behavior of a multiagent system in which the agent size $s_{i}$ is variable it is studied along a Lotka-Volterra approach. The agent size has hereby for meaning the fraction of a given market that an agent is able to capture (market share). A Lotka-Volterra system of equations for prey-predator problems is considered, the competition factor being related to the difference in size between the agents in a one-on-one competition. This mechanism introduces a natural self-organized dynamic competition among agents. In the competition factor, a parameter $σ$ is introduced for scaling the…
Human behavior often exhibit a scheme in which individuals adopt indifferent, neutral, or radical positions on a given topic. The mechanisms leading to community formation are strongly related with social pressure and the topology of the contact network. Here, we discuss an approach to model social behavior which accounts for the protection by alike peers proportional to their relative abundance in the closest neighborhood. We explore the ensuing non-linear dynamics emphasizing the role of the specific structure of the social network, modeled by scale-free graphs. We find that both coexistence…
Opinion polls mediated through a social network can give us, in addition to usual demographics data like age, gender and geographic location, a friendship structure between voters and the temporal dynamics of their activity during the voting process. Using a Facebook application we collected friendship relationships, demographics and votes of over ten thousand users on the referendum on the definition of marriage in Croatia held on 1st of December 2013. We also collected data on online news articles mentioning our application. Publication of these articles align closely with large peaks of vot…
In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective pairwise node interactions, regardless of the initially underlying multi-way interaction structure. We thus focus on dynamics based on a certain class of non-linear interaction functions, which can model different sociological phenomena such as peer pressure and stubbornness. Unlike for linear consensus dynamics on networks, we show how our nonlinear model dyn…
The flow of information reaching us via the online media platforms is optimized not by the information content or relevance but by popularity and proximity to the target. This is typically performed in order to maximise platform usage. As a side effect, this introduces an algorithmic bias that is believed to enhance polarization of the societal debate. To study this phenomenon, we modify the well-known continuous opinion dynamics model of bounded confidence in order to account for the algorithmic bias and investigate its consequences. In the simplest version of the original model the pairs of …
This work consists of an epidemic model with vaccination coupled with an opinion dynamics. Our objective was to study how disease risk perception can influence opinions about vaccination and therefore the spreading of the disease. Differently from previous works we have considered continuous opinions. The epidemic spreading is governed by a SIS-like model with an extra vaccinated state. In our model individuals vaccinate with a probability proportional to their opinions. The opinions change due to peer influence in pairwise interactions. The epidemic feedback to the opinion dynamics acts as an…
Quantum Modeling of Filter Bubbles Based on Kubo-Matsubara Form Green's Functions Considering Remote and Proximity Interactions:Ultraviolet Divergence to Indefinite Ghosting, Consideration of Cut Surfaces
Echo chambers are defined by the simultaneous presence of opinion polarization with respect to a controversial topic and homophily, i.e. the preference of individuals to interact with like-minded peers. While recent efforts have been devoted to detecting the presence of echo chambers in polarized debates on online social media, the dynamics leading to the emergence of these phenomena remain unclear. Here, we contribute to this endeavor by proposing novel metrics to single out the effect of the network dynamics from the opinion polarization. By using a Twitter data set collected during a contro…
Discerning media bias within a network of political allies: an analytic condition for disruption by partisans
University of Melbourne（墨尔本大学）；Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), University of Melbourne（澳大利亚研究委员会引力波发现卓越中心（OzGrav），墨尔本大学）
