Homogeneous symmetrical threshold model with nonconformity: independence vs. anticonformity

Abstract

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and posses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, such as the majority-vote and the q-voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q-voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean-field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed, if the threshold r = 0.5, which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r > 0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.

12 pages, 4 figures, accepted to Complexity

References in corpus (24)

• Statistical physics of social dynamics
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Sociophysics: A review of Galam models
• The non-linear q-voter model
• Opinion dynamics: models, extensions and external effects
• Binary-state dynamics on complex networks: pair approximation and beyond
• Phase transitions in the q-voter model with two types of stochastic driving
• Statistical Physics Of Opinion Formation: is it a SPOOF?
• Nonlinear $q$-voter model with inflexible zealots
• Pair approximation for the q-voter model with independence on complex networks
• Analytical and numerical study of the non-linear noisy voter model on complex networks
• Phase transitions in the q-voter model with noise on a duplex clique
• The Trump phenomenon, an explanation from sociophysics
• Phase transitions in the majority-vote model with two types of noises
• Threshold $q$-voter model
• Conformity, anticonformity and polarization of opinions: insights from a mathematical model of opinion dynamics
• Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear $q$-Voter Model with Zealotry
• The drastic outcomes from voting alliances in three-party bottom-up democratic voting (1990 $\to$ 2013)
• Impact of memory on opinion dynamics
• Opinion dynamics as a movement in a bistable potential
• A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry
• Fundamental ingredients for the emergence of discontinuous phase transitions in the majority vote model
• Majority vote model with ancillary noise in complex networks
• Complex Contagions with Timers

Cited by in corpus (13)

• Fake news and rumors: a trigger for proliferation or fading away
• Hysteresis and disorder-induced order in continuous kinetic-like opinion dynamics in complex networks
• Threshold cascade dynamics on signed random networks
• Binary-state dynamics on complex networks: Stochastic pair approximation and beyond
• Multi-choice opinion dynamics model based on Latane theory
• Will Trump win again in the 2020 election? An answer from a sociophysics model
• In search for the social hysteresis -- the symmetrical threshold model with independence on Watts-Strogatz graphs
• Dynamical Phase Transitions in Graph Cellular Automata
• Nonlinear $q$-voter model from the quenched perspective
• Phase transition and universality of the majority-rule model on complex networks
• The threshold model with anticonformity under random sequential updating
• Ferromagnetic and spin-glass like transition in the $q$-neighbor Ising model on random graphs
• When Does Population Diversity Matter? A Unified Framework for Binary-Choice Dynamics