  We revisit the deduction of the exit probability of the one dimensional
Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys.
Lett. 82, 18006 (2008)]. This approximation is peculiar in that in spite of the
agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006
(2008), R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008), A. M.
Timpanaro and C. P. C. Prado, 89, 052808 (2014)] the hypothesis about the
correlation lenghts behind it are inconsistent and fixing these inconsistencies
leads to the same results as a simple mean field. We use an extended version of
the Sznajd model to test the Kirkwood approximation in a wider context. This
model includes the voter, Sznajd and "United we Stand, Divided we Fall" (USDF)
models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975), K.
Sznajd-Weron and J. Sznajd, Int. Journ. Mod. Phys. C 11, 1157 (2000)] as
different parameter combinations, meaning that some analytical results from
these models can be used to evaluate the performance of the Kirkwood
approximation. We also compare the predicted exit probability with simulation
results for networks with $10^3$ sites. The results show clearly the regions in
parameter space where the approximation gives accurate predictions, as well as
where it starts failing, leading to a better understanding of its reliability.
