  This work examines the accuracy of different many-body methods for the
calculations of parity violating electric dipole ($E1_{\text{PV}}$) amplitudes
in atomic systems. In the last decade many different groups claim to achieve
its accuracy below 0.5\%, for the $6s ~ ^2S_{1/2} \rightarrow 7s ~ ^2S_{1/2} $
transition in $^{133}$Cs atom. One of the major issues in these calculations is
the opposite signs among the core correlation contribution from different
works. To estimate $E1_{\text{PV}}$ of the above transition, various groups
have used different many-body methods both in the linear response and
sum-over-states approaches. By examining how these methods capture various
electron correlation effects, we identify the underlying cause of sign
discrepancies in the previously reported results. We also demonstrate how the
double-core polarisation effects and scaled wave functions influence estimation
of the $E1_{\text{PV}}$ amplitudes. The comprehensive discussions provided in
this work will not only aid in our understanding on the potentials of the
employed many-body methods but it will also serves as a road map for improving
the $E1_{\text{PV}}$ calculation in the atomic systems further.
