Do Quasars Lens Quasars?

If the unexpectedly high frequency of quasar pairs with very different component redshifts is due to the lensing of a population of background quasars by the foreground quasar, typical lens masses must be $\sim {10}^{12}{M}_{\text{sun}}$ and the sum of all such quasar lenses would have to contain $\sim 0.005$ times the closure density of the Universe. It then seems plausible that a very high fraction of all $\sim {10}^{12}{M}_{\text{sun}}$ gravitational lenses with redshifts $z\sim 1$ contain quasars. Here I propose that these systems have evolved to form the present population of massive galaxies with M${}_{\mathrm{B}}\le -22$ and $M

5\times10^{11} M_{\sun}$.