Unifying Local Dynamics in Two-State Spin Systems
Galam, Serge
Original · EN
We present a new two-state +- opinion dynamics model which defines a general frame to include all local dynamics in two-state spin systems. Agents evolve by probabilistic local rules. In each update, groups of various sizes k are formed according to some probability distribution aₖ. Given a specific group with an initial (j) agents sharing opinion + and (k-j) agents opinion -, all k members adopt opinion + with a probability mₖ,ⱼ and opinion - with (1-mₖ,ⱼ). A very rich and new spectrum of dynamics is obtained. The final opinion is a polarization along the initial majority, along the initial minority or a perfect consensus with an equality of opinions as function of the parameters aₖ, mₖ,ⱼ. In last case, two regimes exist, monotonic and dampened oscillatory. The transition from polarization to consensus dynamics occurs for values of the parameters which reproduce exactly the Voter model. A scheme is presented to express any local update in terms of a specific set aₖ, mₖ,ⱼ. Most existing opinion models are exhibited at particular limits.
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