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We discuss the exit probability of the one dimensional $q$-voter model andpresent tools to obtain estimates about this probability both throughsimulations in large networks (around $10^7$ sites) and analyticaly in thelimit 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 (2008EPL 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 theinequality, $\frac{\rho^q}{\rho^q + (1-\rho)} \leq E(\rho) \leq\frac{\rho}{\rho + (1-\rho)^q}$, in the infinite size limit. We believe thissettles in the negative the suggestion made (2011 EPL 95 48005) that thisresult would be a finite size effect, with the exit probability actualy being astep function. We also show how the result, that the exit probability cannot bea step function, can be reconciled with the Galam unified frame, which was alsoa source of controversy.

On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks