  An analysis of the decay $\Lambda_b \to J/\psi(\to\mu^+\mu^-)\Lambda(\to p
\pi^-)$ decay is performed to measure the $\Lambda_b$ polarization and three
angular parameters in data from pp collisions at $\sqrt{s} =$ 7 and 8 TeV,
collected by the CMS experiment at the LHC. The $\Lambda_b$ polarization is
measured to be 0.00 $\pm$ 0.06 (stat) $\pm$ 0.06 (syst) and the
parity-violating asymmetry parameter is determined to be 0.14 $\pm$ 0.14 (stat)
$\pm$ 0.10 (syst). The measurements are compared to various theoretical
predictions, including those from perturbative quantum chromodynamics.
