  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.
