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EPL Association, European Physical Society Letters, 1(82), p. 18007, 2008

DOI: 10.1209/0295-5075/82/18007

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Dynamics of non-conservative voters

Journal article published in 2008 by R. Lambiotte ORCID, S. Redner
This paper is available in a repository.
This paper is available in a repository.

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Abstract

We study a family of opinion formation models in one dimension where the propensity for a voter to align with its local environment depends non-linearly on the fraction of disagreeing neighbors. Depending on this non-linearity in the voting rule, the population may exhibit a bias toward zero magnetization or toward consensus, and the average magnetization is generally not conserved. We use a decoupling approximation to truncate the equation hierarchy for multi-point spin correlations and thereby derive the probability to reach a final state of a given consensus as a function of the initial magnetization. The case when voters are influenced by more distant voters is also considered by investigating the Sznajd model.