Dynamics of Non-Conservative Voters
arXiv:0712.0364 · doi:10.1209/0295-5075/82/18007
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.
4 pages, 4 figures, 2-column revtex4 format; a minor typo in Eq. (16) fixed; current version is the final published manuscript that contains minor changes in response to referee comments
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