  We discuss the exit probability of the one dimensional $q$-voter model and
present tools to obtain estimates about this probability both through
simulations in large networks (around $10^7$ sites) and analyticaly in the
limit where the network is infinetely large. We argue that the result $E(\rho)
= \frac{\rho^q}{\rho^q + (1-\rho)^q}$, that was found in 3 previous works (2008
EPL 82 18006 and 2008 EPL 82 18007, for the case $q=2$ and 2011 PRE 84 031117,
for $q>2$) using small networks (around $10^3$ sites), is a good approximation,
but there are noticeable deviations for larger system sizes. We also show that,
under some simple and intuitive hypothesis, the exit probability must obey the
inequality, $\frac{\rho^q}{\rho^q + (1-\rho)} \leq E(\rho) \leq
\frac{\rho}{\rho + (1-\rho)^q}$, in the infinite size limit. We believe this
settles in the negative the suggestion made (2011 EPL 95 48005) that this
result would be a finite size effect, with the exit probability actualy being a
step function. We also show how the result, that the exit probability cannot be
a step function, can be reconciled with the Galam unified frame, which was also
a source of controversy.

Physics and Society