fact that most prolate doubles are seen along the long axis of the halo implies that $\Delta q_{0.75}$ between doubles and random halos must be significant, and thus doubles tend to be more circular than the typical halo.

In short, then, the quantity $\Delta q_{0.75}$ between doubles and quads and between doubles and random halos can, at least in principle, help determine whether most halos are oblate or prolate. If halos are prolate, the difference $\Delta q_{0.75}$ between doubles and random halos is large. If this difference is small, we can then look at the difference $\Delta q_{0.75}$ between doubles and quads. If this last difference is large, then halos are typically oblate, whereas if the difference is small, then halos are neither strongly oblate nor strongly prolate and $q_2\approx q_1^2$.

In practice, however, the above test is difficult to execute. In particular, while lens modeling can provide some measure of the axis ratio $q$ in quad systems, there remains a fair amount of uncertainty due to the approximate degeneracy between galaxy ellipticity and external shear [see e.g. @keetonetal97]. This degeneracy is even stronger for doubly-imaged systems, and worse, there is no way of determining the axis ratio of the 