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Strong gravitational lensing offers constraints on the Hubble constant thatare independent of other methods. However, those constraints are subject touncertainties in lens models. Previous studies suggest that using an ellipticalpower law + external shear (EPL+XS) for the lensing galaxy can yield resultsthat are precise but inaccurate. We examine such models by generating andfitting mock lenses which produces multiple images of a background quasar-likepoint source. Despite using the same model for input and output, we findstatistical bias in the Hubble constant on the order of 3% to 5%, depending onwhether the elliptical lenses have noise or not. The phase space distributionhas a `flared' shape that causes the mass power law slope to be underestimatedand the Hubble constant to be overestimated. The bias varies with imageconfiguration, which we quantify through annulus length between images with thefirst and second time delays ($\Delta r_{1,2}$). The statistical bias is worsefor configurations that have narrow annuli (e.g., symmetric crossconfigurations). Assuming a source at redshift 2.0 and an EPL+XS lens atredshift 0.3, we find that the bias can be reduced, but not eliminated, if welimit the sample to systems with annulus lengths $\Delta r_{1,2} \gtrsim 0.3$arcsec. As lens samples grow, it may be helpful to prioritize this range ofimage configurations for follow-up observation and analysis.

Statistical Bias in the Hubble Constant and Mass Power Law Slope for Mock Strong Lenses