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A Formal Model for Polarization under Confirmation Bias in Social Networks
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Abstract
We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of agents with dissimilar views. We show that even under this bias polarization eventually vanishes (converges to zero) if the influence graph is strongly-connected. If the influence graph is a regular symmetric circulation, we determine the unique belief value to which all agents converge. Our more insightful result establishes that, under some natural assumptions, if polarization does not eventually vanish then either there is a disconnected subgroup of agents, or some agent influences others more than she is influenced. We also prove that polarization does not necessarily vanish in weakly-connected graphs under confirmation bias. Furthermore, we show how our model relates to the classic DeGroot model for social learning. We illustrate our model with several simulations of a running example about polarization over vaccines and of other case studies. The theoretical results and simulations will provide insight into the phenomenon of polarization.
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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 polarization and cascade dynamics, and accounts for the aforementioned tradeoff between confirmation bias and social connectivity through analytic results. We investigate the model’s predictions empirically using US county-level data on the impact of Internet access on the formation of beliefs about global warming. We conclude by discussing policy implications of our model, highlighting the downsides of debunking and suggesting alternative strategies to contrast misinformation.
Despite the initial promise of social media platforms as a means of facilitating discourse on matters of civic discourse, in practice it has turned out to impair fruitful conversation on civic issues by a number of means. From self-isolation into echo chambers, to algorithmically supported filter bubbles, to widespread failure to engage politically owing to psychological phenomena like the ‘spiral of silence’, a variety of factors have been blamed. I argue that extant accounts overlook the importance of interpersonal relationships to sustaining quality civic discourse on social media. Drawing on an Aristotelian account of friendship with an emphasis on the value of interpersonal difference plus the influence of interactions on individual character, I argue that a common scapegoat for the failure of civic discourse online—the variety of “unfriend” disconnection tools offered on various platforms—actually show promise at promoting better-quality civic conversation and overcoming the obstacles present on social media platforms.
This paper provides a model to investigate information spreading over cyber-social network of agents communicating with each other. The cyber-social network considered here comprises individuals and news agencies. Each individual holds a belief represented by a scalar. Individuals receive information from news agencies that are closer to their belief, confirmation bias is explicitly incorporated into the model. The proposed dynamics of cyber-social networks is adopted from DeGroot-Friedkin model, where the individual's opinion update mechanism is a convex combination of his innate opinion, his neighbors' opinions at the previous time step (obtained from the social network), and the opinions passed along by news agencies from cyber layer which he follows. The characteristics of the interdependent social and cyber networks are radically different here: the social network relies on trust and hence static while the news agencies are highly dynamic since they are weighted as a function of the distance between an individual state and the state of news agency to account for confirmation bias. The conditions for convergence of the aforementioned dynamics to a unique equilibrium are characterized. The estimation and exact computation of the steady-state values under non-linear and linear state-dependent weight functions are provided. Finally, the impact of polarization in the opinions of news agencies on the public opinion evolution is numerically analyzed in the context of the well-known Krackhardt's advice network.
Most of the distributed protocols for multi-agent consensus assume that the
agents are mutually cooperative and "trustful," and so the couplings among the
agents bring the values of their states closer. Opinion dynamics in social
groups, however, require beyond these conventional models due to ubiquitous
competition and distrust between some pairs of agents, which are usually
characterized by repulsive couplings and may lead to clustering of the
opinions. A simple yet insightful model of opinion dynamics with both
attractive and repulsive couplings was proposed recently by C. Altafini, who
examined first-order consensus algorithms over static signed graphs. This
protocol establishes modulus consensus, where the opinions become the same in
modulus but may differ in signs. In this paper, we extend the modulus consensus
model to the case where the network topology is an arbitrary time-varying
signed graph and prove reaching modulus consensus under mild sufficient
conditions of uniform connectivity of the graph. For cut-balanced graphs, not
only sufficient, but also necessary conditions for modulus consensus are given.
We consider a variation of the Deffuant-Weisbuch model introduced by Deffuant et al. in 2000, to provide new analytical insights on the opinion dynamics in a social group. We model the trust that may exist between like-minded agents through a trust function, which is a discontinuous (hard-interaction) non-increasing function of the opinion distance. In this model, agents exchange their opinions with their neighbors and move their opinions closer to each other if they are like-minded (that is, the distance between opinions is smaller than a threshold). We first study the dynamics of opinion formation under random interactions with a fixed rate of communication between pairs of agents. Our goal is to analyze the convergence properties of the opinion dynamics and explore the underlying characteristics that mark the phase transition from opinion polarization to consensus. Furthermore, we extend the hard-interaction model to a strategic interaction model by considering a time-varying rate of interaction. In this model, social agents themselves decide the time and energy that should be expended on interacting each of their neighbors, based on their utility functions. The aim is to understand how and under what conditions clustering patterns emerge in opinion space. Extensive simulations are provided to validate the analytical results of both the hard-interaction model and the strategic interaction model. We also offer evidence that suggests the validity of the proposed model, using the location and monthly survey data collected in the Social Evolution experiment over a period of nine months.
This paper presents a two-dimensional modal logic for reasoning about the
changing patterns of knowledge and social relationships in networks organised
on the basis of a symmetric 'friendship' relation, providing a precise language
for exploring 'logic in the community' [11]. Agents are placed in the model,
allowing us to express such indexical facts as 'I am your friend' and 'You, my
friends, are in danger'.
The technical framework for this work is general dynamic dynamic logic (GDDL)
[4], which provides a general method for extending modal logics with dynamic
operators for reasoning about a wide range of model-transformations, starting
with those definable in propositional dynamic logic (PDL) and extended to allow
for the more subtle operators involved in, for example, private communication,
as represented in dynamic epistemic logic (DEL) and related systems. We provide
a hands-on introduction to GDDL, introducing elements of the formalism as we
go, but leave the reader to consult [4] for technical details.
Instead, the purpose of this paper is to investigate a number of conceptual
issues that arise when considering communication between agents in such
networks, both from one agent to another, and broadcasts to socially-defined
groups of agents, such as the group of my friends.
Online information intermediaries such as Facebook and Google are slowly replacing traditional media channels thereby partly becoming the gatekeepers of our society. To deal with the growing amount of information on the social web and the burden it brings on the average user, these gatekeepers recently started to introduce personalization features, algorithms that filter information per individual. In this paper we show that these online services that filter information are not merely algorithms. Humans not only affect the design of the algorithms, but they also can manually influence the filtering process even when the algorithm is operational. We further analyze filtering processes in detail, show how personalization connects to other filtering techniques, and show that both human and technical biases are present in today’s emergent gatekeepers. We use the existing literature on gatekeeping and search engine bias and provide a model of algorithmic gatekeeping.
We study learning in a setting where agents receive independent noisy signals about the true value of a variable and then communicate in a network. They naïvely update beliefs by repeatedly taking weighted averages of neighbors' opinions. We show that all opinions in a large society converge to the truth if and only if the influence of the most influential agent vanishes as the society grows. We also identify obstructions to this, including prominent groups, and provide structural conditions on the network ensuring efficient learning. Whether agents converge to the truth is unrelated to how quickly consensus is approached. (JEL D83, D85, Z13)
We propose a boundedly rational model of opinion formation in which individuals are subject to persuasion bias; that is, they fail to account for possible repetition in the information they receive. We show that persuasion bias implies the phenomenon of social influence, whereby one's influence on group opinions depends not only on accuracy, but also on how well-connected one is in the social network that determines communication. Persuasion bias also implies the phenomenon of unidimensional opinions; that is, individuals' opinions over a multidimensional set of issues converge to a single "left-right" spectrum. We explore the implications of our model in several natural settings, including political science and marketing, and we obtain a number of novel empirical implications. © 2001 the President and Fellows of Harvard College and the Massachusetts Institute of Technology
When does opinion formation within an interacting group lead to consensus, polarization or fragmentation? The article investigates various models for the dynamics of continuous opinions by analytical methods as well as by computer simulations. Section 2 develops within a unified framework the classical model of consensus formation, the variant of this model due to Friedkin and Johnsen, a time-dependent version and a nonlinear version with bounded confidence of the agents. Section 3 presents for all these models major analytical results. Section 4 gives an extensive exploration of the nonlinear model with bounded confidence by a series of computer simulations. An appendix supplies needed mathematical definitions, tools, and theorems.
Suppose that the authors are interested in the distribution of a set of characteristics over a population. They study a precise sense in which this distribution can be said to be polarized and provide a theory of measurement. Polarization, as conceptualized here, is closely related to the generation of social tensions, to the possibilities of revolution and revolt, and to the existence of social unrest in general. The authors take special care to distinguish their theory from the theory of inequality measurement. They derive measures of polarization that are easily applicable to distributions of characteristics such as income and wealth. Copyright 1994 by The Econometric Society.
We develop a model for timed, reactive computation by extending
the asynchronous, untimed concurrent constraint programming model in a
simple and uniform way. In the spirit of process algebras, we develop
some combinators expressible in this model, and reconcile their
operational, logical and denotational character. We show how programs
may be compiled into finite-state machines with loop-free computations
at each state, thus guaranteeing bounded response time
The tcc model is a formalism for reactive concurrent constraint programming. We present a model of temporal concurrent constraint programming which adds to tcc the capability of modeling asynchronous and nondeterministic timed behavior. We call this tcc extension the ntcc calculus. We also give a denotational semantics for the strongestpostcondition of ntcc processes and, based on this semantics, we develop a proof system for linear-temporal properties of these processes. The expressiveness of ntcc is illustrated by modeling cells, timed systems such as RCX controllers, multi-agent systems such as the Predator/Prey game, and musical applications such as generation of rhythms patterns and controlled improvisation.
In this paper we look at different ways of modally defining properties related to the concept of balance in signed social networks where relations can be either positive or negative. The motivation is to be able to formally reason about the social phenomenon of group polarization, for which balance theory forms a network-theoretical underpinning. The starting point is a recently developed basic modal logic that axiomatizes the class of social networks that are balanced up to a certain degree. This property is not modally definable but can be captured using a deduction rule. In this paper we examine different possibilities for extending this basic language, in order to, first, be able to define frame properties such as balance and related properties such as non-overlapping positive and negative relations and collective connectedness as axioms, and, second, be able to define the property of full balance rather than balanced-up-to-a-degree. We consider extensions with both static modalities such as the universal and the difference modality, the intersection modality, and nominals known from hybrid logic, as well as dynamic global bridge modalities known from sabotage logic. Along the way we provide axioms for weak balance. Finally, to explore measures of how far a network is from polarization, we consider and compare variations of distance measures between models in relation to balance.
Echo chamber is a widely used term describing a situation where certain information is reinforced within a closed network. To reason about echo chambers, we introduce a two-sorted hybrid logic of strong and weak ties based on a logic of positive and negative relations known from the literature. We show that some classical property definitions can be formalized and that a known claim from social network analysis is a validity. We also prove that the logic is axiomatizable, sound and strongly complete. We combine our results with research on homophily and social group formation to represent relations between similar agents. Lastly, we add a knowledge modality and dynamic operators to analyze change in these networks.
In this paper we explore the relationship between norms of belief revi-
sion that may be adopted by members of a community and the resulting dynamic
properties of the distribution of beliefs across that community. We show that at a
qualitative level many aspects of social belief change can be obtained from a very
simple model, which we call `threshold in
uence'. In particular, we focus on the
question of what makes the beliefs of a community stable under various dynamical
situations. We also consider re�nements and alternatives to the `threshold' model,
the most signi�cant of which is to consider changes to plausibility judgements
rather than mere beliefs. We show �rst that some such change is mandated by
di�cult problems with belief-based dynamics related to the need to decide on an
order in which di�erent beliefs are considered. Secondly, we show that the result-
ing plausibility-based account results in a deterministic dynamical system that is
non-deterministic at the level of beliefs.
Experiments exploring the effects of group discussion on attitudes, jury decisions, ethical decisions, judgments, person perceptions, negotiations, and risk taking (other than the choice-dilemmas task) are generally consistent with a "group polarization" hypothesis, derived from the risky-shift literature. Recent attempts to explain the phenomenon fall mostly into 1 of 3 theoretical approaches: (a) group decision rules, especially majority rule (which is contradicted by available data); (b) interpersonal comparisons (for which there is mixed support); and (c) informational influence (for which there is strong support). A conceptual scheme is presented which integrates the latter 2 viewpoints and suggests how attitudes develop in a social context. (41/2 p ref)
Consider a group of individuals who must act together as a team or committee, and suppose that each individual in the group has his own subjective probability distribution for the unknown value of some parameter. A model is presented which describes how the group might reach agreement on a common subjective probability distribution for the parameter by pooling their individual opinions. The process leading to the consensus is explicitly described and the common distribution that is reached is explicitly determined. The model can also be applied to problems of reaching a consensus when the opinion of each member of the group is represented simply as a point estimate of the parameter rather than as a probability distribution.
Communities consist of individuals bounds together by social
relationships and roles. Within communities, individuals reason about
each other's beliefs, knowledge and preferences. Knowledge, belief,
preferences and even the social relationships are constantly changing,
and yet our ability to keep track of these changes is an important part
of what it means to belong to a community.
We study a simple but compelling model of network of agents interacting via time-dependent communication links. The model finds application in a variety of fields including synchronization, swarming and distributed decision making. In the model, each agent updates his current state based upon the current information received from neighboring agents. Necessary and/or sufficient conditions for the convergence of the individual agents' states to a common value are presented, thereby extending recent results reported in the literature. The stability analysis is based upon a blend of graph-theoretic and system-theoretic tools with the notion of convexity playing a central role. The analysis is integrated within a formal framework of set-valued Lyapunov theory, which may be of independent interest. Among others, it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence, even for the simple models discussed in the present paper.
and Frank Valencia. A Multi-agent Model for Polarization Under Confirmation Bias in Social Networks
- S Mário
- Bernardo Alvim
- Sophia Amorim
- Santiago Knight
- Quintero
Mário S. Alvim, Bernardo Amorim, Sophia Knight, Santiago Quintero, and Frank Valencia. A Multi-agent Model for Polarization Under Confirmation Bias in Social Networks. In
FORTE 2021 -41st International Conference on Formal Techniques for Distributed Objects,
Components, and Systems, Valletta, Malta, June 2021. Accepted.
Toward a formal model for group polarization in social networks
- S Mário
- Sophia Alvim
- Frank Knight
- Valencia
Mário S. Alvim, Sophia Knight, and Frank Valencia. Toward a formal model for group
polarization in social networks. In The Art of Modelling Computational Systems, volume 11760
of Lecture Notes in Computer Science, pages 419-441. Springer, 2019.
- Elliot Aronson
- Timothy Wilson
- Robin Akert
Elliot Aronson, Timothy Wilson, and Robin Akert. Social Psychology. Upper Saddle River,
NJ : Prentice Hall, 7 edition, 2010.
Dynamic logics of networks: information flow and the spread of opinion
- Zoé Christoff
Zoé Christoff et al. Dynamic logics of networks: information flow and the spread of opinion.
PhD thesis, PhD Thesis, Institute for Logic, Language and Computation, University of
Amsterdam, 2016.
A measure of polarization on social media networks based on community boundaries
- P H Guerra
- Wagner Meira
- Claire Cardie
- R Kleinberg
P.H. Calais Guerra, Wagner Meira Jr, Claire Cardie, and R Kleinberg. A measure of polarization
on social media networks based on community boundaries. Proceedings of the 7th International
Conference on Weblogs and Social Media, ICWSM 2013, pages 215-224, 01 2013.
[CVCL + 20]
Robust Opinion Aggregation and its Dynamics
- Simone Cerreia
- Vioglio
- Roberto Corrao
- Giacomo Lanzani
Simone Cerreia-Vioglio, Roberto Corrao, Giacomo Lanzani, et al. Robust Opinion Aggregation
and its Dynamics. IGIER, Università Bocconi, 2020.
The role of homophily in the emergence of opinion controversies
- Floriana Gargiulo
- Yerali Gandica
Floriana Gargiulo and Yerali Gandica. The role of homophily in the emergence of opinion
controversies. arXiv preprint arXiv:1612.05483, 2016.
Reasoning about trust and belief change on a social network: A formal approach
- Aaron Hunter
Aaron Hunter. Reasoning about trust and belief change on a social network: A formal approach.
In International Conference on Information Security Practice and Experience, pages 783-801.
The city getting rich from fake news. BBC News Documentary
- E J Kirby
E.J. Kirby. The city getting rich from fake news. BBC News Documentary, 05 2017.
https://www.bbc.com/news/magazine-38168281.
Polarization and echo chambers: A logical analysis of balance and triadic closure in social networks
- Mina Young Pedersen
Mina Young Pedersen. Polarization and echo chambers: A logical analysis of balance and
triadic closure in social networks.
Algorithmic bias amplifies opinion polarization: A bounded confidence model
- Alina Sîrbu
- Dino Pedreschi
- Fosca Giannotti
- János Kertész
Alina Sîrbu, Dino Pedreschi, Fosca Giannotti, and János Kertész. Algorithmic bias amplifies
opinion polarization: A bounded confidence model. arXiv preprint arXiv:1803.02111, 2018.