  The next generation of solar observatories aim to understand the magnetism of
the solar chromosphere. Therefore, it is crucial to understand the polarimetric
signatures of chromospheric spectral lines. For this purpose, we here examine
the suitability of the three Fraunhofer Mg I b1, b2, and b4 lines at 5183.6,
5172.7, and 5167.3 A, respectively. We start by describing a simplified atomic
model of only 6 levels and 3 line transitions for computing the atomic
populations of the 3p-4s (multiplet number 2) levels involved in the Mg I b
line transitions assuming non-local thermodynamic conditions and considering
only the Zeeman effect using the field-free approximation. We test this
simplified atom against more complex ones finding that, although there are
differences in the computed profiles, they are small compared with the
advantages provided by the simple atom in terms of speed and robustness. After
comparing the three Mg I lines, we conclude that the most capable one is the b2
line as b1 forms at similar heights and always show weaker polarization signals
while b4 is severely blended with photospheric lines. We also compare Mg I b2
with the K I D1 and Ca II 8542 A lines finding that the former is sensitive to
the atmospheric parameters at heights that are in between those covered by the
latter two lines. This makes Mg I b2 an excellent candidate for future
multi-line observations that aim to seamlessly infer the thermal and magnetic
properties of different features in the lower solar atmosphere.
