Reality-inspired voter models: A mini-review

Abstract This mini-review presents extensions of the voter model that incorporate various plausible features of real decision-making processes by individuals. Although these generalizations are not calibrated by empirical data, the resulting dynamics are suggestive of realistic collective social behaviors.

[1]  V. Eguíluz,et al.  Conservation laws for the voter model in complex networks , 2004, cond-mat/0408101.

[2]  P. Clifford,et al.  A model for spatial conflict , 1973 .

[3]  S. Galam,et al.  The role of inflexible minorities in the breaking of democratic opinion dynamics , 2007, physics/0703021.

[4]  Renaud Lambiotte,et al.  Unanimity rule on networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  K. N. Laland,et al.  The Biological Bases of Conformity , 2012, Front. Neurosci..

[6]  Sabrina Kruger,et al.  The Origin And Evolution Of Cultures , 2016 .

[7]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[8]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[9]  J. T. Cox,et al.  Coalescing Random Walks and Voter Model Consensus Times on the Torus in $\mathbb{Z}^d$ , 1989 .

[10]  M. A. Muñoz,et al.  Nonlinear q-voter model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[12]  C. List,et al.  Group decisions in humans and animals: a survey , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[13]  Krapivsky.  Kinetics of monomer-monomer surface catalytic reactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[14]  G. Owen,et al.  Thirteen theorems in search of the truth , 1983 .

[15]  R. Holley,et al.  Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model , 1975 .

[16]  Andrea Baronchelli,et al.  The emergence of consensus: a primer , 2017, Royal Society Open Science.

[17]  S. Redner,et al.  Heterogeneous voter models. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  K. Sznajd-Weron,et al.  Some new results on one-dimensional outflow dynamics , 2007, 0712.2035.

[19]  鈴木 増雄.  Time-Dependent Statistics of the Ising Model , 1965 .

[20]  F. Vazquez,et al.  Analytical solution of the voter model on uncorrelated networks , 2008, 0803.1686.

[21]  R. May,et al.  Nonlinear Aspects of Competition Between Three Species , 1975 .

[22]  S. Redner,et al.  Voter models on heterogeneous networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  R. Durrett,et al.  Graph fission in an evolving voter model , 2012, Proceedings of the National Academy of Sciences.

[24]  Ira B Schwartz,et al.  Enhanced vaccine control of epidemics in adaptive networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[26]  Alessandro Vespignani,et al.  Ordering phase transition in the one-dimensional Axelrod model , 2002 .

[27]  S. Redner,et al.  A Kinetic View of Statistical Physics , 2010 .

[28]  S. Redner,et al.  Dynamics of vacillating voters , 2007, 0710.0914.

[29]  R. Glauber.  Time‐Dependent Statistics of the Ising Model , 1963 .

[30]  Dietrich Stauffer.  Monte Carlo simulations of Sznajd models , 2002, J. Artif. Soc. Soc. Simul..

[31]  Andrew Whiten,et al.  Integrating the study of conformity and culture in humans and nonhuman animals. , 2012, Psychological bulletin.

[32]  R. Axelrod.  The Dissemination of Culture , 1997 .

[33]  A. Kolmogoroff.  Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung , 1931 .

[34]  S. Galam.  Minority opinion spreading in random geometry , 2002, cond-mat/0203553.

[35]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[37]  Nicolas de Condorcet.  Essai Sur L'Application de L'Analyse a la Probabilite Des Decisions Rendues a la Pluralite Des Voix , 2009 .

[38]  S Redner,et al.  Freezing in Ising ferromagnets. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  D. R. Taunt.  On A-groups , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[40]  S. Redner,et al.  Fate of zero-temperature Ising ferromagnets. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Krzysztof Suchecki,et al.  Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Guillaume Deffuant,et al.  Meet, discuss, and segregate! , 2002, Complex..

[43]  Raúl Toral,et al.  Nonequilibrium transitions in complex networks: a model of social interaction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Serge Moscovici,et al.  Toward A Theory of Conversion Behavior , 1980 .

[45]  Luke Rendell,et al.  Social Learning Strategies: Bridge-Building between Fields , 2018, Trends in Cognitive Sciences.

[46]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[47]  Mirta Galesic,et al.  Statistical physics models of belief dynamics: Theory and empirical tests , 2017, Physica A: Statistical Mechanics and its Applications.

[48]  S. Redner,et al.  Non-monotonicity and divergent time scale in Axelrod model dynamics , 2007 .

[49]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[50]  H. Stanley,et al.  Phase Transitions and Critical Phenomena , 2008 .

[51]  R. Axelrod.  The Complexity of Cooperation , 2011 .

[52]  A. N. Shiryayev,et al.  On Analytical Methods In Probability Theory , 1992 .

[53]  Boleslaw K. Szymanski,et al.  Social consensus through the influence of committed minorities , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  P. Richerson,et al.  The Origin and Evolution of Cultures , 2005 .

[55]  Raúl Toral,et al.  Global culture: a noise-induced transition in finite systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  A. Bray.  Theory of phase-ordering kinetics , 1994, cond-mat/9501089.

[57]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[58]  Ira B Schwartz,et al.  Fluctuating epidemics on adaptive networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Robert L. Axtell,et al.  Aligning simulation models: A case study and results , 1996, Comput. Math. Organ. Theory.

[60]  Marsili,et al.  Nonequilibrium phase transition in a model for social influence , 2000, Physical review letters.

[61]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.

[62]  M. Newman,et al.  Nonequilibrium phase transition in the coevolution of networks and opinions. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  Thilo Gross,et al.  Consensus time and conformity in the adaptive voter model. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[64]  S. Galam.  Application of statistical physics to politics , 1999, cond-mat/0004306.

[65]  S Redner,et al.  Majority versus minority dynamics: phase transition in an interacting two-state spin system. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[66]  J. Stoyanov.  A Guide to First‐passage Processes , 2003 .

[67]  S. Redner,et al.  Dynamics of majority rule in two-state interacting spin systems. , 2003, Physical review letters.

[68]  Katarzyna Sznajd-Weron,et al.  Statistical Physics Of Opinion Formation: Is it a SPOOF? , 2019, Comptes Rendus Physique.

[69]  P. Zweifel.  Advanced Mathematical Methods for Scientists and Engineers , 1980 .

[70]  J. Angus.  The Asymptotic Theory of Extreme Order Statistics , 1990 .

[71]  S. Redner,et al.  Ultimate fate of constrained voters , 2004, cond-mat/0405652.

[72]  S Redner,et al.  Evolutionary dynamics on degree-heterogeneous graphs. , 2006, Physical review letters.

[73]  Peter Sheridan Dodds,et al.  Universal behavior in a generalized model of contagion. , 2004, Physical review letters.

[74]  Serge Moscovici,et al.  Perspectives on minority influence: Innovation and minority influence , 1985 .

[75]  S Redner,et al.  Majority rule dynamics in finite dimensions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[77]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[78]  D. Parisi,et al.  Comparison of voter and Glauber ordering dynamics on networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[79]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[80]  S. Redner,et al.  Dynamics of non-conservative voters , 2007, 0712.0364.

[81]  P Mishra.  Семантические особенности английского глагола meet , 2012 .

[82]  A. Barrat,et al.  Consensus formation on adaptive networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[83]  S. Redner,et al.  Dynamics of confident voting , 2011, 1111.3883.

[84]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

[85]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[86]  E. Ben-Naim,et al.  Bifurcations and patterns in compromise processes , 2002, cond-mat/0212313.

[87]  Krapivsky,et al.  Exact results for kinetics of catalytic reactions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[88]  H. Hinrichsen,et al.  Critical coarsening without surface tension: the universality class of the voter model. , 2001, Physical review letters.

[89]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

[90]  Thilo Gross,et al.  Epidemic dynamics on an adaptive network. , 2005, Physical review letters.