Dynamics of non-conservative votersR. Lambiotte1 and S. Redner2
1 INMA, Université catholique de Louvain - 4 avenue Georges Lemaitre, B-1348 Louvain-la-Neuve, Belgium, EU
2 Center for Polymer Studies and Physics Department, Boston University - Boston, MA 02215, USA
received 4 December 2007; accepted in final form 17 March 2008; published April 2008
published online 26 March 2008
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 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.
89.75.-k - Complex systems.
02.50.Le - Decision theory and game theory.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
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