  In this paper we introduce modified version of one-dimensional outflow
dynamics (known as a Sznajd model) which simplifies the analytical treatment.
We show that simulations results of the original and modified rules are exactly
the same for various initial conditions. We obtain the analytical formula for
exit probability using Kirkwood approximation and we show that it agrees
perfectly with computer simulations in case of random initial conditions.
Moreover, we compare our results with earlier analytical calculations obtained
from renormalization group and from general sequential probabilistic frame
introduced by Galam. Using computer simulations we investigate the time
evolution of several correlation functions to show if Kirkwood approximation
can be justified. Surprisingly, it occurs that Kirkwood approximation gives
correct results even for these initial conditions for which it cannot be easily
justified.
