  Pauli blocking is carefully investigated for the processes of $NN \rightarrow
N \Delta$ and $\Delta \rightarrow N \pi$ in heavy-ion collisions, aiming at a
more precise prediction of the $\pi^-/ \pi^+$ ratio which is an important
observable to constrain the high-density symmetry energy. We use the AMD+JAM
approach, which combines the antisymmetrized molecular dynamics for the time
evolution of nucleons and the JAM model to treat processes for $\Delta$
resonances and pions. As is known in general transport-code simulations, it is
difficult to treat Pauli blocking very precisely due to unphysical fluctuations
and additional smearing of the phase-space distribution function, when Pauli
blocking is treated in the standard method of JAM. We propose an improved
method in AMD+JAM to use the Wigner function precisely calculated in AMD as the
blocking probability. Different Pauli blocking methods are compared in
heavy-ion collisions of neutron-rich nuclei,
${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$, at 270 MeV/nucleon. With the more
accurate method, we find that Pauli blocking is stronger, in particular for the
neutron in the final state in $NN \rightarrow N \Delta$ and $ \Delta \to N\pi$,
compared to the case with a proton in the final state. Consequently, the
$\pi^-/\pi^+$ ratio becomes higher when the Pauli blocking is improved, the
effect of which is found to be comparable to the sensitivity to the
high-density symmetry energy.
