In order to understand why the median estimator achieves a 50% breakdown level, we consider a fictional analysis using 10 genetic variants, six of which are valid IVs and four of which are invalid. Figure 2 (left) shows a scatter plot of 10 gene‐exposure (γ^j) and gene‐outcome (Γ^j) association estimates for an Mendelian randomization study with a finite sample size (Kang et al., 2015). The ratio estimate for each genetic variant is the gradient of the line connecting the relevant datapoint for that variant to the origin. The true causal effect is shown by the dotted black line, the median estimate by the dashed line, and the IVW estimate by the solid line. Estimates from valid IVs are shown by hollow circles, estimates from invalid IVs are shown by solid circles. Although the valid IVs follow the true slope, the IVW estimate is pulled away from the true value by the invalid instruments, which yield biased estimates of the causal effect. Figure 2 (right) shows the same scatter plot for an infinite sample size. Now the six valid instruments lie
