On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?

Abstract

In this paper, we investigate the so-called ``Sznajd Model'' (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatio-temporal evolution of the opinion distribution $L(t)$, the evolution of magnetization $m(t)$, the distribution of decision times $P(\tau )$ and relaxation times $P(\mu )$. In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear VM, where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the second-nearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow your second-nearest neighbor''. The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of $L(t)$, $m(t)$, $P(\tau )$, $P(\mu )$, and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter $\sigma$, to bias between anti- and ferromagnetic decisions in the case of frustration. We show that $\sigma$ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. Compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.

22 pages, 20 figures. For related publications see http://www.ais.fraunhofer.de/~frank

References in corpus (5)

• Opinion evolution in closed community
• Dynamics of Majority Rule
• A simple model of price formation
• On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?
• How to convince others ? Monte Carlo simulations of the Sznajd model

Cited by in corpus (24)

• Statistical physics of social dynamics
• Individualization as driving force of clustering phenomena in humans
• Nonlinear Voter Models: The Transition from Invasion to Coexistence
• On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?
• Public debates driven by incomplete scientific data: the cases of evolution theory, global warming and H1N1 pandemic influenza
• The drastic outcomes from voting alliances in three-party bottom-up democratic voting (1990 $\to$ 2013)
• Tipping points in opinion dynamics: a universal formula in five dimensions
• Exit probability in a one-dimensional nonlinear q-voter model
• Irrelevance of information outflow in opinion dynamics models
• Inflow versus outflow zero-temperature dynamics in one dimension
• Opinion Dynamics and Unifying Principles: A Global Unifying Frame
• Outward-inward information flux in an opinion formation model on different topologies
• Relaxation under outflow dynamics with random sequential updating
• Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry and fluctuation
• Mapping the $q$-voter model: From a single chain to complex networks
• Dynamical phase transitions in Hegselmann-Krause model of opinion dynamics and consensus
• Dynamical and Topological Aspects of Consensus Formation in Complex Networks
• Neighborhood approximations for non-linear voter models
• Rise of the centrist: from binary to continuous opinion dynamics
• Sociophysics and the Forming of Public Opinion: Threshold versus Non Threshold Dynamics
• From modeling of political opinion formation to two-spin statistical physics model
• Consensus from group interactions: An adaptive voter model on hypergraphs
• Collective beliefs and individual stubbornness in the dynamics of public debates
• Consensus formation: The case of using cell phones while driving