$\Delta q_{0.75}$ between doubles and quads (i.e. $q_{0.75}^{doubles}-
q_{0.75}^{quads}$, solid line) and between doubles and the overall halo populations (i.e. $q_{0.75}^{doubles}-q_{0.75}^{halos}$, dotted line) as a function of the axis ratios $q_1$ and $q_2$. However, rather than using $q_1$ as an axis, we follow standard practice and parameterize the shape of the halo in terms of the shape parameter $T$ defined in Eq. \[eq:shape\_parameter\]. There are several interesting things to be gathered from Figure \[fig:axis\_ratio\]. First, when comparing doubles to quads, note that while $\Delta q_{0.75}$ is indeed large ($q_{0.75}\gtrsim 0.1$) for both prolate and oblate halos, the difference can be larger for oblate halos than for prolate halos. Moreover, note that in going from oblate to prolate halos, the difference $\Delta q_{0.75}$ goes through a minimum when $q_2 \approx q_1^2$ (solid line), in which case values as low as $\Delta q_{0.75} \approx 0.05$ for $q_2\approx 0.5$ are possible. Turning now to the comparison between doubles and random halos, we see that the difference in $q_{0.75}$ for these two halo populations becomes negligible in the case of oblate halos, reflecting the near uniform distribution of lines of sights for doubles for oblate halos (see Figure \[fig:losdist\]). On the other hand, the 