Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2011-12-20
Nonlinear Sciences
Adaptation and Self-Organizing Systems
23 pages, 5 figures
Scientific paper
A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ more than a tolerance parameter. In pairwise interactions, one of the pair, randomly selected, converts to the opinion of the other. The model can be used to simulate cases where no compromise is possible, such as exclusive choices or competing brands. The fully-mixed case with maximum tolerance is equivalent to the Gambler's Ruin problem. A fully-mixed system always ends up in an absorbing state, which can have one or more surviving opinions. An upper bound for the final number of opinions is given. The distribution of absorption times fits the generalized extreme value distribution. The diffusion coefficient of an opinion increases linearly with the number of opinions within the tolerance parameter. A general master equation and specific Markov matrices are given. The software code developed for this study is provided as a supplement.
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