The nonmesonic weak decay of polarized Λ hypernuclei is studied with a microscopic diagrammatic formalism in which one- and two-nucleon-induced decay mechanisms, → Λ N → N N and → Λ N N → N N N , are considered together with (and on the same ground of) nucleon final state interactions. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation. Our approach adopts different one-meson-exchange weak transition potentials, while the strong interaction effects are accounted for by a Bonn nucleon-nucleon interaction. We also consider the two-pion-exchange effect in the weak transition potential. Both the two-nucleon-induced decay mechanism and the final state interactions reduce the magnitude of the asymmetry. The quantum interference terms considered in the present microscopic approach give rise to an opposite behavior of the asymmetry with increasing energy cuts to that observed in models describing the nucleon final state interactions semiclassically via the intranuclear cascade code. Our results for the asymmetry parameter in 12 Λ C obtained with different potential models are consistent with the asymmetry measured at KEK.