Berlin 2018 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 12: Focus Session: Opinion Formation and Voter Models
SOE 12.3: Talk
Tuesday, March 13, 2018, 14:30–14:45, MA 001
The biased-voter model — •Raul Toral1, Maxi San Miguel1, and Agnieszka Czaplicka2 — 1IFISC (CSIC-UIB), Palma de Mallorca, Spain — 2BIFI, U. de Zaragoza, Spain
Most of the voter-model literature assumes that each one of the possible options are equivalent. In this work we focus in the situation where there is a bias. This situation has been considered previously as, for example, indicating the lack of asymmetry in the social preference for one or another language in a bilingual community. We introduce bias by letting a fraction of the agents to copy with a higher probability one of the two options. We address the question of how the ratio of the density of connections between biased nodes and unbiased nodes influences the behavior. It seems that a crucial role for reaching consensus are the degrees of biased and unbiased nodes, rather than the number of links between pairs of biased or unbiased nodes. Even if the majority of the nodes is biased but weakly connected, the probability to reach consensus cannot be larger than in a random network. On the other extreme case, when biased nodes form a well-organized minority, one obtains in some cases a higher probability to order for the preferred state. In the thermodynamic limit any non-zero value of the bias leads to preferred consensus, but when the network is finite, there is always a chance to order in the not preferred state. For a random network case we find that behavior of the system depends of the effective bias, which is the value of bias parameter multiplied by the number of biased nodes. When the topology is not random that scaling disappears. Our analytical results are supported by numerical simulations.