  We develop a theoretical framework to study the feed-down effect of
higher-lying strange baryons on the spin polarization of the $\Lambda$ hyperon.
In this framework, we consider two-body decays through strong, electromagnetic,
and weak processes and derive general formulas for the angular distribution and
spin polarization of the daughter particle by adopting the helicity formalism.
Using the realistic experimental data as input, we explore the feed-down
contribution to the global and the local $\Lambda$ polarizations and find that
such a contribution suppresses the primordial $\Lambda$ polarization, which is
not strong enough to resolve the discrepancy between the current theoretical
and the experimental results on the azimuthal-angle dependence of $\Lambda$
polarization. Our paper may also be useful for the measurement of spin
polarization of baryons heavier than $\Lambda$ (e.g., $\Xi^-$) in future
experiments.
