The Sznajd model, which describes opinion formation and social influence, is treated analytically on a complete graph. We prove the existence of the phase transition in the original formulation of the model, while for the Ochrombel modification we find smooth behaviour without transition. We calculate the average time to reach the stationary state as well as the exponential tail of its probability distribution. An analytical argument for the observed 1/n dependence in the distribution of votes in Brazilian elections is provided.PACS. 89.65.-s Social and economic systems -05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion -02.50.-r Probability theory, stochastic processes, and statistics 1 −1 φ c (x)ψ c ′ (x)dx = 0 for c = c ′ . This is due to the fact that the operator L is not self-adjoint.