Opinion influence and evolution in social networks: A Markovian agents model

Abstract

In this paper, the effect on collective opinions of filtering algorithms managed by social network platforms is modeled and investigated. A stochastic multi-agent model for opinion dynamics is proposed, that accounts for a centralized tuning of the strength of interaction between individuals. The evolution of each individual opinion is described by a Markov chain, whose transition rates are affected by the opinions of the neighbors through influence parameters. The properties of this model are studied in a general setting as well as in interesting special cases. A general result is that the overall model of the social network behaves like a high-dimensional Markov chain, which is viable to Monte Carlo simulation. Under the assumption of identical agents and unbiased influence, it is shown that the influence intensity affects the variance, but not the expectation, of the number of individuals sharing a certain opinion. Moreover, a detailed analysis is carried out for the so-called Peer Assembly, which describes the evolution of binary opinions in a completely connected graph of identical agents. It is shown that the Peer Assembly can be lumped into a birth-death chain that can be given a complete analytical characterization. Both analytical results and simulation experiments are used to highlight the emergence of particular collective behaviours, e.g. consensus and herding, depending on the centralized tuning of the influence parameters.

Data-driven model reduction of agent-based systems using the Koopman generator

“…Another way is to represent the agents as a system of ordinary or stochastic (partial) differential equations (ODEs, meanfield ODEs, SDEs, or SPDEs), see, for instance, [13][14][15][16]. Assuming that the population of homogeneous agents that interact with each other (e.g., via a complete network) is sufficiently large, this system can be modeled as a Markov jump process (see also [10,11]), which in turn can be approximated using ordinary or stochastic differential equations [8,17]. This does not hold for all ABMs (consider, e.g., network-free or off-lattice models).…”

“…Agent-based models provide an easily explainable and accessible framework for studying the dynamical behavior of interacting agents without requiring an extensive mathematical background. Models range from (highly detailed) microscopic stochastic descriptions following spatial movement and neighbor interactions [ 9 ] and individual-based stochastic descriptions in a network without movement [ 10 ] to Markov chain approaches for collective population dynamics [ 11 ]. Most agent-based models have in common that they are hard to analyze due to their high-dimensionality.…”

Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading

“…in Stangor (2015). There have been recent advances in simulating the process in which members of a society change their opinions; see, e.g., Banisch et al (2011), Klimek et al (2007), Misra (2012), Li et al (2012), Nardini et al (2008), Böhme and Gross (2012), Bolzern et al (2017) and the review articles Anderson and Ye (2019), Xia et al (2011), Castellano et al (2009), Sîrbu et al (2017). This is in part due to increasing computing power which enables to carry out agent-based models that simulate behaviour of members of a synthetic population, such as members of a society, on the microscale by emulating the decision-making rules.…”

Information Diffusion Model in Twitter: A Systematic Literature Review

“…The largest use of social media data comes from microblogs, as much as 46% [1]. Twitter data can be used in a remarkably diverse number of research studies, such as sentiment analyses [3,4], text analyses [5][6][7][8], opinion analyses [9,10], as well as analyses of influence or information diffusion [11][12][13][14].…”