Consensus Building on a Scale-Free Network

In the 2008 V.Sood, T.Andal and S.Redner studied the Voter Model and the Invasion Process starting from a single actor with opinion 1 (see [1]). They give the analytical form of the consensus 1 probability, using the Annealed Approximation, in the unbiased case (when opinions have the same strength) and in the case of low bias value s (opinion 1 slightly stronger than opinion 0). In this talk these results will be confirmed through numerical simulations on an uncorrelated and static Scale-Free Network and we will discuss the behaviour of the models outside of the range of Sood et al’s theory. The emergence of correlations between the consensus 1 probability and other quantities will be showed and a new theoretical approach that gives a good estimate for the consensus 1 probability for large enough s values will be proposed.

[1] V.Sood, T.Andal, S.Redner, Voter model on heterogeneous networks. Phys.Rev. E 77 041121, 2008J. A. .