A Study of Positive Exponential Consensus on DeGroot Model

In this paper, to reveal the influence of multilayer network structure on opinion diffusion in social networks, we study an opinion dynamics model based on DeGroot model on multilayer networks. We find that if the influence matrix integrating the information of connectedness for each layer and correlation between layers is strongly connected and aperiodic, all agents’ opinions will reach a consensus. However, if there are stubborn agents in the networks, regular agents’ opinions will finally be confined to the convex combinations of the stubborn agents’. Specifically, if all stubborn agents hold the same opinion, even if the agents only exist on a certain layer, their opinions will diffuse to the entire multilayer networks. This paper not only characterizes the influence of multilayer network topology and agent attribute on opinion diffusion in a holistic way, but also demonstrates the importance of coupling agents which play an indispensable role in some social and economic situations.

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TRUST MODELING: A PROBABILITY APPROACH

Bulletin of V. N. Karazin Kharkiv National University Economic Series ◽

10.26565/2311-2379-2021-100-10 ◽

2021 ◽

Keyword(s):

Social Group ◽

Interpersonal Trust ◽

Initial Vector ◽

Limit Value ◽

Economic Decisions ◽

Economic Decision Making ◽

Trust Modeling ◽

Group A ◽

Degroot Model ◽

Group Members

The work is devoted to describing an application of the DeGroot model in the following analysis: is it possible to establish a consensus of opinions of members in a social group (a society). This model describes the process of changing the agents’ opinion about a certain event or statement, factoring in the effect of interpersonal trust between agents, which is modelled by Markov chains. Agents’ opinions are represented by the probability of them showing their support to a given statement (event). The interpretation of the DeGroot model is quite broad. It includes, in particular, the study of economic decision-making, the influence of public opinion on people and the fact of achieving a consensus. The paper considers the conditions under which the process of updating the opinions of agents, belonging to a social group (network), converges to a certain limit value - a consensus, i.e. a case when all agents in a social group have the same opinion on a particular issue. We also show some generalizations of the DeGroot model, namely those that concern adding time dependency to the rules of updating the opinions of agents. To test the DeGroot model, we implemented the two-dimensional case as a dynamic Microsoft Excel workbook. The paper describes 2 types of problems related to reaching a consensus, solved with the model. The first kind of problem constitutes an analysis of possibilities of obtaining the desired consensus with a given matrix of trust (interpersonal trust of agents), whilst changing the initial group members’ opinions vector about an event (statement). We also discuss a solution of the inverse problem: find the trust matrix such that the iterative opinion update process converges to the desired consensus with a given initial vector of opinions. The results we obtained may be used for analyzing the process of managing public (collective) opinion concerning certain economic decisions in a social group (network).

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A two-step communication opinion dynamics model with self-persistence and influence index for social networks based on the DeGroot model

Information Sciences ◽

10.1016/j.ins.2020.01.052 ◽

2020 ◽

Vol 519 ◽

pp. 363-381 ◽

Cited By ~ 2

Author(s):

Qinyue Zhou ◽

Zhibin Wu ◽

Abdulrahman H. Altalhi ◽

Francisco Herrera

Keyword(s):

Social Networks ◽

Opinion Dynamics ◽

Dynamics Model ◽

Degroot Model

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Naïve Learning with Uninformed Agents

The American Economic Review ◽

10.1257/aer.20181151 ◽

2021 ◽

Vol 111 (11) ◽

pp. 3540-3574

Author(s):

Abhijit Banerjee ◽

Emily Breza ◽

Arun G. Chandrasekhar ◽

Markus Mobius

Keyword(s):

Network Structure ◽

Real World ◽

Network Formation ◽

Single Agent ◽

Natural Extension ◽

Small World ◽

Information Aggregation ◽

Information Loss ◽

Degroot Model ◽

First Time

The DeGroot model has emerged as a credible alternative to the standard Bayesian model for studying learning on networks, offering a natural way to model naïve learning in a complex setting. One unattractive aspect of this model is the assumption that the process starts with every node in the network having a signal. We study a natural extension of the DeGroot model that can deal with sparse initial signals. We show that an agent’s social influence in this generalized DeGroot model is essentially proportional to the degree-weighted share of uninformed nodes who will hear about an event for the first time via this agent. This characterization result then allows us to relate network geometry to information aggregation. We show information aggregation preserves “wisdom” in the sense that initial signals are weighed approximately equally in a model of network formation that captures the sparsity, clustering, and small-world properties of real-world networks. We also identify an example of a network structure where essentially only the signal of a single agent is aggregated, which helps us pinpoint a condition on the network structure necessary for almost full aggregation. Simulating the modeled learning process on a set of real-world networks, we find that there is on average 22.4 percent information loss in these networks. We also explore how correlation in the location of seeds can exacerbate aggregation failure. Simulations with real-world network data show that with clustered seeding, information loss climbs to 34.4 percent. (JEL D83, D85, Z13)

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Are People Subject to Persuasion Bias? Test of Degroot Model

SSRN Electronic Journal ◽

10.2139/ssrn.3043655 ◽

2017 ◽

Author(s):

Tatiana Mayskaya ◽

Li Song

Keyword(s):

Degroot Model

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Nonlinear Convergence Algorithm: Structural Properties with Doubly Stochastic Quadratic Operators for Multi-Agent Systems

Journal of Artificial Intelligence and Soft Computing Research ◽

10.1515/jaiscr-2018-0003 ◽

2018 ◽

Vol 8 (1) ◽

pp. 49-61 ◽

Cited By ~ 8

Author(s):

Rawad Abdulghafor ◽

Sherzod Turaev ◽

Akram Zeki ◽

Adamu Abubaker

Keyword(s):

Nonlinear Operator ◽

Stochastic Matrices ◽

Multi Agent Systems ◽

Quadratic Operator ◽

Dimensional Simplex ◽

Agent Systems ◽

Doubly Stochastic ◽

Degroot Model ◽

Multi Agent ◽

Time Required

Abstract This paper proposes nonlinear operator of extreme doubly stochastic quadratic operator (EDSQO) for convergence algorithm aimed at solving consensus problem (CP) of discrete-time for multi-agent systems (MAS) on n-dimensional simplex. The first part undertakes systematic review of consensus problems. Convergence was generated via extreme doubly stochastic quadratic operators (EDSQOs) in the other part. However, this work was able to formulate convergence algorithms from doubly stochastic matrices, majorization theory, graph theory and stochastic analysis. We develop two algorithms: 1) the nonlinear algorithm of extreme doubly stochastic quadratic operator (NLAEDSQO) to generate all the convergent EDSQOs and 2) the nonlinear convergence algorithm (NLCA) of EDSQOs to investigate the optimal consensus for MAS. Experimental evaluation on convergent of EDSQOs yielded an optimal consensus for MAS. Comparative analysis with the convergence of EDSQOs and DeGroot model were carried out. The comparison was based on the complexity of operators, number of iterations to converge and the time required for convergences. This research proposed algorithm on convergence which is faster than the DeGroot linear model.

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Consensus reaching in social network DeGroot Model: The roles of the Self-confidence and node degree

Information Sciences ◽

10.1016/j.ins.2019.02.028 ◽

2019 ◽

Vol 486 ◽

pp. 62-72 ◽

Cited By ~ 15

Author(s):

Zhaogang Ding ◽

Xia Chen ◽

Yucheng Dong ◽

Francisco Herrera

Keyword(s):

Social Network ◽

The Self ◽

Node Degree ◽

Self Confidence ◽

Degroot Model ◽

Consensus Reaching

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A Survey on Nonstrategic Models of Opinion Dynamics

Games ◽

10.3390/g11040065 ◽

2020 ◽

Vol 11 (4) ◽

pp. 65

Author(s):

Michel Grabisch ◽

Agnieszka Rusinowska

Keyword(s):

Threshold Model ◽

Opinion Dynamics ◽

Time Varying ◽

Binary Variable ◽

Rule Model ◽

Bounded Confidence ◽

Degroot Model ◽

Voter Models ◽

Time Varying Models ◽

Continuous Opinions

The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models.

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