  We study a model of opinion formation where the collective decision of group
is said to happen if the fraction of agents having the most common opinion
exceeds a threshold value, a \textit{critical mass}. We find that there exists
a unique, non-trivial critical mass giving the most efficient convergence to
consensus. In addition, we observe that for small critical masses, the
characteristic time scale for the relaxation to consensus splits into two. The
shorter time scale corresponds to a direct relaxation and the longer can be
explained by the existence of intermediate, metastable states similar to those
found in [P.\ Chen and S.\ Redner, Phys.\ Rev.\ E \textbf{71}, 036101 (2005)].
This longer time-scale is dependent on the precise condition for
consensus---with a modification of the condition it can go away.
