Fitness voter model: damped oscillations and anomalous consensus
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, s...
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| Autores principales: | , , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
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2017
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/87729 |
| Aporte de: |
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I19-R120-10915-87729 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Ciencias Exactas Damped oscillations Consensus time Linear behavior Opinion dynamics Opinion formation |
| spellingShingle |
Matemática Ciencias Exactas Damped oscillations Consensus time Linear behavior Opinion dynamics Opinion formation Woolcock, A. Connaughton, C. Merali, Y. Vazquez, Federico Fitness voter model: damped oscillations and anomalous consensus |
| topic_facet |
Matemática Ciencias Exactas Damped oscillations Consensus time Linear behavior Opinion dynamics Opinion formation |
| description |
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 agent that keeps its opinion (winning agent) 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∼Nβ, with β≃1.45. |
| format |
Articulo Articulo |
| author |
Woolcock, A. Connaughton, C. Merali, Y. Vazquez, Federico |
| author_facet |
Woolcock, A. Connaughton, C. Merali, Y. Vazquez, Federico |
| author_sort |
Woolcock, A. |
| title |
Fitness voter model: damped oscillations and anomalous consensus |
| title_short |
Fitness voter model: damped oscillations and anomalous consensus |
| title_full |
Fitness voter model: damped oscillations and anomalous consensus |
| title_fullStr |
Fitness voter model: damped oscillations and anomalous consensus |
| title_full_unstemmed |
Fitness voter model: damped oscillations and anomalous consensus |
| title_sort |
fitness voter model: damped oscillations and anomalous consensus |
| publishDate |
2017 |
| url |
http://sedici.unlp.edu.ar/handle/10915/87729 |
| work_keys_str_mv |
AT woolcocka fitnessvotermodeldampedoscillationsandanomalousconsensus AT connaughtonc fitnessvotermodeldampedoscillationsandanomalousconsensus AT meraliy fitnessvotermodeldampedoscillationsandanomalousconsensus AT vazquezfederico fitnessvotermodeldampedoscillationsandanomalousconsensus |
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Repositorios |
| _version_ |
1764820489343074304 |