  A new approach to the old problem of the predominance of prolate deformations
among well deformed nuclei is proposed within the shell model framework. The
parameter space is explored using the ensemble of random rotationally-invariant
interactions. Subsets with rotational energy ratio $E(4^{+})/E(2^{+})$ and the
rigid-rotor relation between the quadrupole moment $Q(2^{+})$ and the
transition probability $B(E2;2^{+}\to 0^{+}))$ are found exhibiting prolate
predominance. We identify matrix elements of the effective forces responsible
for the predominance of prolate deformation.
