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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (15 January 2024) | Viewed by 20940

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Dr. Francisco W. De Sousa Lima

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Department of Physics, Federal University of Piauí (UFPI), Teresina 64049550, Brazil
Interests: Monte Carlo simulation; networks; critical exponents; disorder and Ising models
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Dear Colleagues,

The study of sociophysics has greatly increased in the last two decades. The models used in sociophysics mainly envisage the study of the macroscopic dynamics of social systems or networks. Then, the statistical physics tools successfully applied in treating diverse systems in the physical world are used to find extensive applications in problems related to such topics. Stauffer, in 2012, stated an interesting and rather fundamental question: does sociophysics have any practical applications? The answer to this question came in 2017 from Galam with a model that uses local-majority-rule arguments and obeys threshold dynamics. Galam applied this model to predict Trump’s victory in the 2016 United States election. In fact, Galam is convinced that the dynamics of opinions obey discoverable universal quantitative laws and can be modeled in the same way that scientists model the physical world. As a consequence, opinion-dynamics models have become a mainstream of research in sociophysics. In these models, opinion entropy, based on Shannon entropy, is a useful tool to evaluate the uncertainty of opinions, that is, it is helpful for exploring the dynamics of opinion entropy and controlling the formation of public opinion.

Dr. Francisco W. De Sousa Lima
Guest Editor

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Keywords

opinion dynamics
vote
consensus
econophysics
network-based agents

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17 pages, 1913 KiB

Open AccessArticle

Chaos in Opinion-Driven Disease Dynamics

by Thomas Götz, Tyll Krüger, Karol Niedzielewski, Radomir Pestow, Moritz Schäfer and Jan Schneider

Entropy 2024, 26(4), 298; https://doi.org/10.3390/e26040298 - 28 Mar 2024

Cited by 1 | Viewed by 1489

Abstract

During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion–epidemic systems. The findings reveal either intricate periodic patterns or chaotic dynamics, leading to substantial fluctuations in opinion distribution and, consequently, significant variations in the total number of infections over time. Interestingly, the model exhibits a protective pattern. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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14 pages, 12048 KiB

Open AccessArticle

Decoding the News Media Diet of Disinformation Spreaders

by Anna Bertani, Valeria Mazzeo and Riccardo Gallotti

Entropy 2024, 26(3), 270; https://doi.org/10.3390/e26030270 - 19 Mar 2024

Cited by 1 | Viewed by 2057

Abstract

In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users’ habits within the digital ecosystem is a challenging task that requires, at the same time, large databases and accurate methodological approaches. This study contributes to this expanding research landscape by employing network science methodologies and entropic measures to analyze the behavioral patterns of social media users sharing news pieces and dig into the diverse news consumption habits within different online social media user groups. Our analyses reveal that users are more inclined to share news classified as fake when they have previously posted conspiracy or junk science content and vice versa, creating a series of “misinformation hot streaks”. To better understand these dynamics, we used three different measures of entropy to gain insights into the news media habits of each user, finding that the patterns of news consumption significantly differ among users when focusing on disinformation spreaders as opposed to accounts sharing reliable or low-risk content. Thanks to these entropic measures, we quantify the variety and the regularity of the news media diet, finding that those disseminating unreliable content exhibit a more varied and, at the same time, a more regular choice of web-domains. This quantitative insight into the nuances of news consumption behaviors exhibited by disinformation spreaders holds the potential to significantly inform the strategic formulation of more robust and adaptive social media moderation policies. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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33 pages, 1012 KiB

Open AccessArticle

Opinion Models, Election Data, and Political Theory

by Matthias Gsänger, Volker Hösel, Christoph Mohamad-Klotzbach and Johannes Müller

Entropy 2024, 26(3), 212; https://doi.org/10.3390/e26030212 - 28 Feb 2024

Cited by 2 | Viewed by 1466

Abstract

A unifying setup for opinion models originating in statistical physics and stochastic opinion dynamics are developed and used to analyze election data. The results are interpreted in the light of political theory. We investigate the connection between Potts (Curie–Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model, which is adapted by Lagrangian parameters. We also discuss weak and strong effects (also called extensive and nonextensive) continuum limits for the models. The results are used to compare the Curie–Weiss model, two q-voter models (weak and strong effects), and a reinforcement model (weak effects) in explaining electoral outcomes in four western democracies (United States, Great Britain, France, and Germany). We find that particularly the weak effects models are able to fit the data (Kolmogorov–Smirnov test) where the weak effects reinforcement model performs best (AIC). Additionally, we show how the institutional structure shapes the process of opinion formation. By focusing on the dynamics of opinion formation preceding the act of voting, the models discussed in this paper give insights both into the empirical explanation of elections as such, as well as important aspects of the theory of democracy. Therefore, this paper shows the usefulness of an interdisciplinary approach in studying real world political outcomes by using mathematical models. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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24 pages, 4692 KiB

Open AccessArticle

Opinion Formation in the World Trade Network

by Célestin Coquidé, José Lages and Dima L. Shepelyansky

Entropy 2024, 26(2), 141; https://doi.org/10.3390/e26020141 - 5 Feb 2024

Cited by 2 | Viewed by 3459

Abstract

We extend the opinion formation approach to probe the world influence of economical organizations. Our opinion formation model mimics a battle between currencies within the international trade network. Based on the United Nations Comtrade database, we construct the world trade network for the years of the last decade from 2010 to 2020. We consider different core groups constituted by countries preferring to trade in a specific currency. We will consider principally two core groups, namely, five Anglo-Saxon countries that prefer to trade in US dollar and the 11 BRICS+ that prefer to trade in a hypothetical currency, hereafter called BRI, pegged to their economies. We determine the trade currency preference of the other countries via a Monte Carlo process depending on the direct transactions between the countries. The results obtained in the frame of this mathematical model show that starting from the year 2014, the majority of the world countries would have preferred to trade in BRI than USD. The Monte Carlo process reaches a steady state with three distinct groups: two groups of countries preferring to trade in whatever is the initial distribution of the trade currency preferences, one in BRI and the other in USD, and a third group of countries swinging as a whole between USD and BRI depending on the initial distribution of the trade currency preferences. We also analyze the battle between three currencies: on one hand, we consider USD, BRI and EUR, the latter currency being pegged by the core group of nine EU countries. We show that the countries preferring EUR are mainly the swing countries obtained in the frame of the two currencies model. On the other hand, we consider USD, CNY (Chinese yuan), OPE, the latter currency being pegged to the major OPEC+ economies for which we try to probe the effective economical influence within international trade. Finally, we present the reduced Google matrix description of the trade relations between the Anglo-Saxon countries and the BRICS+. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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13 pages, 2878 KiB

Open AccessArticle

Modeling Misinformation Spread in a Bounded Confidence Model: A Simulation Study

by Yujia Wu and Peng Guo

Entropy 2024, 26(2), 99; https://doi.org/10.3390/e26020099 - 23 Jan 2024

Cited by 1 | Viewed by 1399

Abstract

Misinformation has posed significant threats to all aspects of people’s lives. One of the most active areas of research in misinformation examines how individuals are misinformed. In this paper, we study how and to what extent agents are misinformed in an extended bounded confidence model, which consists of three parts: (i) online selective neighbors whose opinions differ from their own but not by more than a certain confidence level; (ii) offline neighbors, in a Watts–Strogatz small-world network, whom an agent has to communicate with even though their opinions are far different from their own; and (iii) a Bayesian analysis. Furthermore, we introduce two types of epistemically irresponsible agents: agents who hide their honest opinions and focus on disseminating misinformation and agents who ignore the messages received and follow the crowd mindlessly. Simulations show that, in an environment with only online selective neighbors, the misinforming is more successful with broader confidence intervals. Having offline neighbors contributes to being cautious of misinformation, while employing a Bayesian analysis helps in discovering the truth. Moreover, the agents who are only willing to listen to the majority, regardless of the truth, unwittingly help to bring about the success of misinformation attempts, and they themselves are, of course, misled to a greater extent. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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23 pages, 1111 KiB

Open AccessArticle

Students’ Learning Behaviour in Programming Education Analysis: Insights from Entropy and Community Detection

by Tai Tan Mai, Martin Crane and Marija Bezbradica

Entropy 2023, 25(8), 1225; https://doi.org/10.3390/e25081225 - 17 Aug 2023

Cited by 3 | Viewed by 2444

Abstract

The high dropout rates in programming courses emphasise the need for monitoring and understanding student engagement, enabling early interventions. This activity can be supported by insights into students’ learning behaviours and their relationship with academic performance, derived from student learning log data in learning management systems. However, the high dimensionality of such data, along with their numerous features, pose challenges to their analysis and interpretability. In this study, we introduce entropy-based metrics as a novel manner to represent students’ learning behaviours. Employing these metrics, in conjunction with a proven community detection method, we undertake an analysis of learning behaviours across higher- and lower-performing student communities. Furthermore, we examine the impact of the COVID-19 pandemic on these behaviours. The study is grounded in the analysis of empirical data from 391 Software Engineering students over three academic years. Our findings reveal that students in higher-performing communities typically tend to have lower volatility in entropy values and reach stable learning states earlier than their lower-performing counterparts. Importantly, this study provides evidence of the use of entropy as a simple yet insightful metric for educators to monitor study progress, enhance understanding of student engagement, and enable timely interventions. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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14 pages, 718 KiB

Open AccessFeature PaperArticle

Opinion Dynamics Explain Price Formation in Prediction Markets

by Valerio Restocchi, Frank McGroarty, Enrico Gerding and Markus Brede

Entropy 2023, 25(8), 1152; https://doi.org/10.3390/e25081152 - 1 Aug 2023

Cited by 1 | Viewed by 1600

Abstract

Prediction markets are heralded as powerful forecasting tools, but models that describe them often fail to capture the full complexity of the underlying mechanisms that drive price dynamics. To address this issue, we propose a model in which agents belong to a social network, have an opinion about the probability of a particular event to occur, and bet on the prediction market accordingly. Agents update their opinions about the event by interacting with their neighbours in the network, following the Deffuant model of opinion dynamics. Our results suggest that a simple market model that takes into account opinion formation dynamics is capable of replicating the empirical properties of historical prediction market time series, including volatility clustering and fat-tailed distribution of returns. Interestingly, the best results are obtained when there is the right level of variance in the opinions of agents. Moreover, this paper provides a new way to indirectly validate opinion dynamics models against real data by using historical data obtained from PredictIt, which is an exchange platform whose data have never been used before to validate models of opinion diffusion. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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15 pages, 786 KiB

Open AccessArticle

Unanimity, Coexistence, and Rigidity: Three Sides of Polarization

by Serge Galam

Entropy 2023, 25(4), 622; https://doi.org/10.3390/e25040622 - 6 Apr 2023

Cited by 10 | Viewed by 1942

Abstract

Political polarization is perceived as a threat to democracies. Using the Galam model of opinion dynamics deployed in a five-dimensional parameter space, I show that polarization is the byproduct of an essential hallmark of a vibrant democratic society, namely open and informal discussions among agents. Indeed, within a homogeneous social community with floaters, the dynamics lead gradually toward unanimity (zero entropy). Polarization can eventually appear as the juxtaposition of non-mixing social groups sharing different prejudices about the issue at stake. On the other hand, the inclusion of contrarian agents produces a polarization within a community that mixes when their proportion x is beyond a critical value

x_{c} = \frac{1}{6} \approx 0.167

for discussing groups of size three and four. Similarly, the presence of stubborn agents also produces a polarization of a community that mixes when the proportion of stubborn agents is greater than some critical value. For equal proportions of stubborn agents a along each opinion,

a_{c} = \frac{2}{9} \approx 0.22

for group size four against

a_{c} = \frac{1}{4} = 0.25

for group size three. However, the evaluation of the proportion of individual opinion shifts at the attractor

\frac{1}{2}

and indicates that the polarization produced by contrarians is fluid with a good deal of agents who keep shifting between the two opposed blocks (high entropy). That favors a coexistence of opposite opinions in a divided community. In contrast, the polarization created by stubborn agents is found to be frozen with very few individuals shifting opinion between the two opinions (low entropy). That yields a basis for the emergence of hate between the frozen opposed blocks. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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10 pages, 562 KiB

Open AccessArticle

Opinion Dynamics Systems on Barabási–Albert Networks: Biswas–Chatterjee–Sen Model

by David S. M. Alencar, Tayroni F. A. Alves, Gladstone A. Alves, Antonio Macedo-Filho, Ronan S. Ferreira, F. Welington S. Lima and Joao A. Plascak

Entropy 2023, 25(2), 183; https://doi.org/10.3390/e25020183 - 17 Jan 2023

Cited by 4 | Viewed by 1591

Abstract

A discrete version of opinion dynamics systems, based on the Biswas–Chatterjee–Sen (BChS) model, has been studied on Barabási–Albert networks (BANs). In this model, depending on a pre-defined noise parameter, the mutual affinities can assign either positive or negative values. By employing extensive computer simulations with Monte Carlo algorithms, allied with finite-size scaling hypothesis, second-order phase transitions have been observed. The corresponding critical noise and the usual ratios of the critical exponents have been computed, in the thermodynamic limit, as a function of the average connectivity. The effective dimension of the system, defined through a hyper-scaling relation, is close to one, and it turns out to be connectivity-independent. The results also indicate that the discrete BChS model has a similar behavior on directed Barabási–Albert networks (DBANs), as well as on Erdös–Rènyi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs). However, unlike the model on ERRGs and DERRGs, which has the same critical behavior for the average connectivity going to infinity, the model on BANs is in a different universality class to its DBANs counterpart in the whole range of the studied connectivities. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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Review

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36 pages, 1976 KiB

Open AccessFeature PaperReview

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

by Suchismita Banerjee, Soumyajyoti Biswas, Bikas K. Chakrabarti, Asim Ghosh and Manipushpak Mitra

Entropy 2023, 25(5), 735; https://doi.org/10.3390/e25050735 - 28 Apr 2023

Cited by 5 | Viewed by 2148

Abstract

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini (g) index and the Kolkata (k) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as k, indicates the proportion of the ‘wealth’ owned by

(1 - k)

fraction of the ‘people’. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around

g = k \approx 0.87

, starting from the point of perfect equality, where

g = 0

and

k = 0.5

) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto’s 80/20 law (

k = 0.80

), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the g and k indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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