Woolcock, Anthony, Connaughton, Colm, Merali, Yasmin and Vazquez, Federico (2017) Fitness voter model : damped oscillations and anomalous consensus. Physical Review E, 96 (3). 032313. doi:10.1103/PhysRevE.96.032313 ISSN 1539-3755.

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Abstract

We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter k ≥ 0, in addition to its + or − opinion state. The evolution of the distribution of k–values and the opinion dynamics are coupled together, so as to allow the system to dynamically develop heterogeneity and memory in a simple way. When two agents with different opinions interact, their k–values are compared and, with probability p the agent with the lower value adopts the opinion of the one with the higher value, while with probability 1 − p the opposite happens. The winning agent then increments its k–value by one. We study the dynamics of the system in the entire 0 ≤ p ≤ 1 range and compare with the case p = 1/2, in which opinions are decoupled from the k–values and the dynamics is equivalent to that of the standard voter model. When 0 ≤ p < 1/2, agents with higher k–values are less persuasive, and the system approaches exponentially fast to the consensus state of the initial majority opinion. The mean consensus time τ appears to grow logarithmically with the number of agents N, and it is greatly decreased relative to the linear behavior τ ∼ N found in the standard voter model. When 1/2 < p ≤ 1, agents with higher k–values are more persuasive, and the system initially relaxes to a state with an even coexistence of opinions, but eventually reaches consensus by finite-size fluctuations. The approach to the coexistence state is monotonic for 1/2 < p < po ' 0.8, while for po ≤ p ≤ 1 there are damped oscillations around the coexistence value. The final approach
to coexistence is approximately a power law t−b(p) in both regimes, where the exponent b increases with p. Also, τ increases respect to the standard voter model, although it still scales linearly with N. The p = 1 case is special, with a relaxation to coexistence that scales as t−2.73 and a consensus time that scales as τ ∼ N β , with β ' 1.45.

Item Type:	Journal Article
Subjects:	J Political Science > JF Political institutions (General) Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Physics
Library of Congress Subject Headings (LCSH):	Voting -- Mathematical models, Statistical physics, Quantitative research
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
ISSN:	1539-3755
Official Date:	25 September 2017
Dates:	Date Event 25 September 2017 Available 11 September 2017 Accepted
Volume:	96
Number:	3
Article Number:	032313
DOI:	10.1103/PhysRevE.96.032313
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	3 October 2017
Date of first compliant Open Access:	2 May 2018
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID NSF PHY11-25915 National Science Foundation http://dx.doi.org/10.13039/100000001 EP/M003620/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/E501311/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 PIP0443/2014 Consejo Nacional de Investigaciones Científicas y Técnicas http://dx.doi.org/10.13039/501100002923
Related URLs:	Other Repository
Open Access Version:	ArXiv Other

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