Consider a population of N agents on a network. Let nb(i) denote the set of neighbours of agent i, i.e. if j ∈ nb(i) then j is a neighbour of i. The opinion x_i of an agent can assume one of the three values {−1,0,1}. Think of x_i = −1 as against, x_i = 0 as undecided and x_i = 1 as for. The sum of the opinions of the neighbours of i is given by

We introduce the following function F : R → (0,1/2):

We assume that the exchange of ideas and arguments between the members of the population is such that the probability P(xi) that a randomly chosen agent has opinion xi is given by the following table:

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3 = * Xi jenb(i)