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Nair S, Ng KW, Iamnitchi A, Skvoretz J. Diffusion of social conventions across polarized communities: an empirical study. SOCIAL NETWORK ANALYSIS AND MINING 2021. [DOI: 10.1007/s13278-021-00726-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Braha D, de Aguiar MAM. Voting contagion: Modeling and analysis of a century of U.S. presidential elections. PLoS One 2017; 12:e0177970. [PMID: 28542409 PMCID: PMC5436881 DOI: 10.1371/journal.pone.0177970] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2017] [Accepted: 05/04/2017] [Indexed: 11/19/2022] Open
Abstract
Social influence plays an important role in human behavior and decisions. Sources of influence can be divided as external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science—elections and voting behavior. We provide an analytical expression of the county vote-share distribution, which is in excellent agreement with almost a century of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt phase transition from low to high levels of social contagion, and robust differences among regions. These results suggest that social contagion effects are becoming more instrumental in shaping large-scale collective political behavior, with implications on democratic electoral processes and policies.
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Affiliation(s)
- Dan Braha
- New England Complex Systems Institute, Cambridge, Massachusetts, United States of America
- University of Massachusetts, Dartmouth, Massachusetts, United States of America
- * E-mail:
| | - Marcus A. M. de Aguiar
- New England Complex Systems Institute, Cambridge, Massachusetts, United States of America
- Universidade Estadual de Campinas, Campinas, São Paulo, Brazil
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3
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The impact of variable commitment in the Naming Game on consensus formation. Sci Rep 2017; 7:41750. [PMID: 28150714 PMCID: PMC5288711 DOI: 10.1038/srep41750] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Accepted: 12/22/2016] [Indexed: 11/11/2022] Open
Abstract
The Naming Game has proven to be an important model of opinion dynamics in complex networks. It is significantly enriched by the introduction of nodes committed to a single opinion. The resulting model is still simple but captures core concepts of opinion dynamics in networks. This model limitation is rigid commitment which never changes. Here we study the effect that making commitment variable has on the dynamics of the system. Committed nodes are assigned a commitment strength, w, defining their willingness to lose (in waning), gain (for increasing) or both (in variable) commitment to an opinion. Such model has committed nodes that can stick to a single opinion for some time without losing their flexibility to change it in the long run. The traditional Naming Game corresponds to setting w at infinity. A change in commitment strength impacts the critical fraction of population necessary for a minority consensus. Increasing w lowers critical fraction for waning commitment but increases this fraction for increasing commitment. Further, we show that if different nodes have different values of w, higher standard deviation of w increases the critical fraction for waning commitment and decrease this fraction for increasing commitment.
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Sîrbu A, Loreto V, Servedio VDP, Tria F. Opinion Dynamics: Models, Extensions and External Effects. UNDERSTANDING COMPLEX SYSTEMS 2017. [DOI: 10.1007/978-3-319-25658-0_17] [Citation(s) in RCA: 53] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
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Singh P, Sreenivasan S, Szymanski BK, Korniss G. Competing effects of social balance and influence. Phys Rev E 2016; 93:042306. [PMID: 27176311 DOI: 10.1103/physreve.93.042306] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 11/07/2022]
Abstract
We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field p_{c} such that for a weak external field (p<p_{c}), the system exhibits a metastable fixed point and a saddle point in addition to a stable fixed point. However, if the strength of the external field is sufficiently large (p>p_{c}), there is only one (stable) fixed point, which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasistationary distribution and is found to be in agreement with the results obtained by numerical simulations.
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Affiliation(s)
- P Singh
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.,Social Cognitive Networks Academic Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA
| | - S Sreenivasan
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.,Social Cognitive Networks Academic Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.,Department of Computer Science, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA
| | - B K Szymanski
- Social Cognitive Networks Academic Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.,Department of Computer Science, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.,Faculty of Computer Science and Management, Wroclaw University of Technology, 50-370 Wroclaw, Poland
| | - G Korniss
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.,Social Cognitive Networks Academic Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA
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Svenkeson A, Swami A. Reaching Consensus by Allowing Moments of Indecision. Sci Rep 2015; 5:14839. [PMID: 26439503 PMCID: PMC4594304 DOI: 10.1038/srep14839] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2015] [Accepted: 07/24/2015] [Indexed: 11/17/2022] Open
Abstract
Group decision-making processes often turn into a drawn out and costly battle between two opposing subgroups. Using analytical arguments based on a master equation description of the opinion dynamics occurring in a three-state model of cooperatively interacting units, we show how the capability of a social group to reach consensus can be enhanced when there is an intermediate state for indecisive individuals to pass through. The time spent in the intermediate state must be relatively short compared to that of the two polar states in order to create the beneficial effect. Furthermore, the cooperation between individuals must not be too low, as the benefit to consensus is possible only when the cooperation level exceeds a specific threshold. We also discuss how zealots, agents that remain in one state forever, can affect the consensus among the rest of the population by counteracting the benefit of the intermediate state or making it virtually impossible for an opposition to form.
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Affiliation(s)
- A Svenkeson
- Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA
| | - A Swami
- Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA
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Diakonova M, Eguíluz VM, San Miguel M. Noise in coevolving networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032803. [PMID: 26465524 DOI: 10.1103/physreve.92.032803] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2014] [Indexed: 06/05/2023]
Abstract
Coupling dynamics of the states of the nodes of a network to the dynamics of the network topology leads to generic absorbing and fragmentation transitions. The coevolving voter model is a typical system that exhibits such transitions at some critical rewiring. We study the robustness of these transitions under two distinct ways of introducing noise. Noise affecting all the nodes destroys the absorbing-fragmentation transition, giving rise in finite-size systems to two regimes: bimodal magnetization and dynamic fragmentation. Noise targeting a fraction of nodes preserves the transitions but introduces shattered fragmentation with its characteristic fraction of isolated nodes and one or two giant components. Both the lack of absorbing state for homogeneous noise and the shift in the absorbing transition to higher rewiring for targeted noise are supported by analytical approximations.
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Affiliation(s)
- Marina Diakonova
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), E07122 Palma de Mallorca, Spain
| | - Víctor M Eguíluz
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), E07122 Palma de Mallorca, Spain
| | - Maxi San Miguel
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), E07122 Palma de Mallorca, Spain
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Zhang H, Gao M, Wang W, Liu Z. Evolutionary prisoner's dilemma game on graphs and social networks with external constraint. J Theor Biol 2014; 358:122-31. [PMID: 24909494 DOI: 10.1016/j.jtbi.2014.05.038] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2013] [Revised: 05/23/2014] [Accepted: 05/27/2014] [Indexed: 11/19/2022]
Abstract
A game-theoretical model is constructed to capture the effect of external constraint on the evolution of cooperation. External constraint describes the case where individuals are forced to cooperate with a given probability in a society. Mathematical analyses are conducted via pair approximation and diffusion approximation methods. The results show that the condition for cooperation to be favored on graphs with constraint is b¯/c¯>k/A¯ (A¯=1+kp/(1-p)), where b¯ and c¯ represent the altruistic benefit and cost, respectively, k is the average degree of the graph and p is the probability of compulsory cooperation by external enforcement. Moreover, numerical simulations are also performed on a repeated game with three strategies, always defect (ALLD), tit-for-tat (TFT) and always cooperate (ALLC). These simulations demonstrate that a slight enforcement of ALLC can only promote cooperation when there is weak network reciprocity, while the catalyst effect of TFT on cooperation is verified. In addition, the interesting phenomenon of stable coexistence of the three strategies can be observed. Our model can represent evolutionary dynamics on a network structure which is disturbed by a specified external constraint.
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Affiliation(s)
- Hui Zhang
- Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi׳an, Shaanxi 710027, China.
| | - Meng Gao
- Yantai Institute of Coastal Zone Research, CAS, Yantai 264003, China
| | - Wenting Wang
- School of Mathematics and Computer Science Institute, Northwest University for Nationalities, Lanzhou, Gansu 730000, China
| | - Zhiguang Liu
- School of Mathematics and Information Sciences, Henan University, Kaifeng, Henan 475001, China
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Chen DB, Xiao R, Zeng A. Predicting the evolution of spreading on complex networks. Sci Rep 2014; 4:6108. [PMID: 25130862 PMCID: PMC4135329 DOI: 10.1038/srep06108] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2014] [Accepted: 07/30/2014] [Indexed: 11/10/2022] Open
Abstract
Due to the wide applications, spreading processes on complex networks have been intensively studied. However, one of the most fundamental problems has not yet been well addressed: predicting the evolution of spreading based on a given snapshot of the propagation on networks. With this problem solved, one can accelerate or slow down the spreading in advance if the predicted propagation result is narrower or wider than expected. In this paper, we propose an iterative algorithm to estimate the infection probability of the spreading process and then apply it to a mean-field approach to predict the spreading coverage. The validation of the method is performed in both artificial and real networks. The results show that our method is accurate in both infection probability estimation and spreading coverage prediction.
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Affiliation(s)
- Duan-Bing Chen
- 1] Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, P.R. China [2] Department of Physics, University of Fribourg, Fribourg CH1700, Switzerland
| | - Rui Xiao
- Department of Physics, University of Fribourg, Fribourg CH1700, Switzerland
| | - An Zeng
- 1] Department of Physics, University of Fribourg, Fribourg CH1700, Switzerland [2] School of Systems Science, Beijing Normal University - Beijing 100875, P. R. China
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Abstract
We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation of the strategy selected by the zealots is a trivial outcome. We study fixation time in this scenario. We show that the fixation time is divided into three main regimes, in one of which the fixation time is short, and in the other two the fixation time is exponentially long in terms of the population size. Different from the case without zealots, there is a threshold selection intensity below which the fixation is fast for an arbitrary payoff matrix. We illustrate our results with examples of various social dilemma games.
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Abstract
The surprising social phenomena of the Arab Spring and the Occupy Wall Street movement posit the question of whether the active role of committed groups may produce political changes of significant importance. Under what conditions are the convictions of a minority going to dominate the future direction of a society? We address this question with the help of a Cooperative Decision Making model (CDMM) which has been shown to generate consensus through a phase-transition process. We observe that in a system of a finite size the global consensus state is not permanent and times of crisis occur when there is an ambiguity concerning a given social issue. The correlation function within the cooperative system becomes similarly extended as it is observed at criticality. This combination of independence (free will) and long-range correlation makes it possible for very small but committed minorities to produce substantial changes in social consensus.
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Singh P, Sreenivasan S, Szymanski BK, Korniss G. Threshold-limited spreading in social networks with multiple initiators. Sci Rep 2013; 3:2330. [PMID: 23900230 PMCID: PMC3728590 DOI: 10.1038/srep02330] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2013] [Accepted: 07/15/2013] [Indexed: 11/17/2022] Open
Abstract
A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple initiators trigger the cascade, and where all nodes possess the same adoption threshold ϕ. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction p. We find that even for arbitrarily high value of ϕ, there exists a critical initiator fraction pc(ϕ) beyond which the cascade becomes global. Network structure, in particular clustering, plays a significant role in this scenario. Similarly to the case of single-node or single-clique initiators studied previously, we observe that community structure within the network facilitates opinion spread to a larger extent than a homogeneous random network. Finally, we study the efficacy of different initiator selection strategies on the size of the cascade and the cascade window.
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Affiliation(s)
- P Singh
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180-3590 USA.
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Liu XT, Wu ZX, Zhang L. Impact of committed individuals on vaccination behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:051132. [PMID: 23214763 DOI: 10.1103/physreve.86.051132] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2012] [Indexed: 06/01/2023]
Abstract
We study how the presence of committed vaccinators, a small fraction of individuals who consistently hold the vaccinating strategy and are immune to influence, impact the vaccination dynamics in well-mixed and spatially structured populations. For this purpose, we develop an epidemiological game-theoretic model of a flu-like vaccination by integrating an epidemiological process into a simple agent-based model of adaptive learning, where individuals (except for those committed ones) use anecdotal evidence to estimate costs and benefits of vaccination. We show that the committed vaccinators, acting as "steadfast role models" in the populations, can efficiently avoid the clustering of susceptible individuals and stimulate other imitators to take vaccination, hence contributing to the promotion of vaccine uptake. We substantiate our findings by making comparative studies of our model on a full lattice and on a randomly diluted one. Our work is expected to provide valuable information for decision-making and design more effective disease-control strategy.
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Affiliation(s)
- Xiao-Tao Liu
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou 730000, China
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Masuda N. Evolution of cooperation driven by zealots. Sci Rep 2012; 2:646. [PMID: 22966421 PMCID: PMC3437515 DOI: 10.1038/srep00646] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2012] [Accepted: 08/28/2012] [Indexed: 11/24/2022] Open
Abstract
Recent experimental results with humans involved in social dilemma games suggest that cooperation may be a contagious phenomenon and that the selection pressure operating on evolutionary dynamics (i.e., mimicry) is relatively weak. I propose an evolutionary dynamics model that links these experimental findings and evolution of cooperation. By assuming a small fraction of (imperfect) zealous cooperators, I show that a large fraction of cooperation emerges in evolutionary dynamics of social dilemma games. Even if defection is more lucrative than cooperation for most individuals, they often mimic cooperation of fellows unless the selection pressure is very strong. Then, zealous cooperators can transform the population to be even fully cooperative under standard evolutionary dynamics.
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Affiliation(s)
- Naoki Masuda
- Department of Mathematical Informatics, The University of Tokyo , 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan.
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