  We formulate and investigate the nonlinear $q$-voter model (which as special
cases includes the linear voter and the Sznajd model) on a one dimensional
lattice. We derive analytical formula for the exit probability and show that it
agrees perfectly with Monte Carlo simulations. The puzzle, that we deal with
here, may be contained in a simple question: "Why the mean field approach gives
the exact formula for the exit probability in the one-dimensional nonlinear
$q$-voter model?". To answer this question we test several hypothesis proposed
recently for the Sznajd model, including the finite size effects, the influence
of the range of interactions and the importance of the initial step of the
evolution. On the one hand, our work is part of a trend of the current debate
on the form of the exit probability in the one-dimensional Sznajd model but on
the other hand, it concerns the much broader problem of nonlinear $q$-voter
model.
