Voter model with non-Poissonian interevent intervals

Abstract

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.

18 pages, 8 figures

References in corpus (14)

• Statistical physics of social dynamics
• Dynamics of person-to-person interactions from distributed RFID sensor networks
• What's in a crowd? Analysis of face-to-face behavioral networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Uncovering individual and collective human dynamics from mobile phone records
• A Poissonian explanation for heavy-tails in e-mail communication
• Voter Models on Heterogeneous Networks
• A message passing approach for general epidemic models
• Conservation laws for the voter model in complex networks
• Analytical Solution of the Voter Model on Disordered Networks
• Decelerating microdynamics can accelerate macrodynamics in the voter model
• Spreading Dynamics Following Bursty Human Activity Patterns
• Scaling in the Inter-Event Time of Random and Seasonal Systems
• Update rules and interevent time distributions: Slow ordering vs. no ordering in the Voter Model

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• A consensus opinion model based on the evolutionary game
• Small inter-event times govern epidemic spreading on temporal networks
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• Opinion percolation in structured population
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• Competition in the presence of aging: order, disorder, and synchronized collective behavior
• Non-Markovian Majority-Vote model
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• Flow Motifs Reveal Limitations of the Static Framework to Represent Human interactions
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• Accelerating coordination in temporal networks by engineering the link order
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