  The inferential model (IM) framework offers alternatives to the familiar
probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in
statistical inference. Allowing this uncertainty quantification to be imprecise
makes it possible to achieve exact validity and reliability. But is imprecision
and exact validity compatible with attainment of the classical notions of
statistical efficiency? The present paper offers an affirmative answer to this
question via a new possibilistic Bernstein--von Mises theorem that parallels a
fundamental result in Bayesian inference. Among other things, our result
demonstrates that the IM solution is asymptotically efficient in the sense that
its asymptotic credal set is the smallest that contains the Gaussian
distribution whose variance agrees with the Cramer--Rao lower bound.
