Collective decision making in self-organized systems is challenging because it relies on local perception and local communication. Globally defined qualities such as consensus time and decision accuracy are both difficult to predict and difficult to guarantee. We present the weighted voter model which implements a self-organized collective decision making process. We provide an ODE model, a master equation model (numerically solved by the Gillespie algorithm), and agent-based simulations of the proposed decision-making strategy. This set of models enables us to investigate the system behavior in the thermodynamic limit and to investigate finite-size effects due to random fluctuations. Based on our results, we give minimum requirements to guarantee consensus on the optimal decision, a minimum swarm size to guarantee a certain accuracy, and we show that the proposed approach scales with system size and is robust to noise.
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