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We present simulations of multi-year RV follow up campaigns of the {\it TESS}small exoplanet yield on the Automated Planet Finder telescope, using fourdifferent schemes to sample the transiting planets' RV phase curves. Forplanets below roughly 10 M$_\oplus$ we see a systematic bias of measured massesthat are higher than the true planet mass, regardless of the observing schemeused. This produces a statistically significant difference in the mass-radiusrelation we recover, where planet masses are predicted to be too high and toosimilar across the entire super-Earth to Neptune radius range. This bias is duein part to only reporting masses that are measured with high statisticalsignificance. Incorporating all mass measurements, even those that areessentially only upper limits, significantly mitigates this bias. We also findstatistically significant differences between the mean number of planetsmeasured at the 1-, 3-, and 5$\sigma_{\rm K}$ level by the differentprioritization schemes. Our results show that prioritization schemes that moreevenly sample the RV phase curves produce a larger number of significant massdetections. The scheme that aims to most uniformly sample the phase curveperforms best, followed closely by the scheme which randomly samples, and thenan in quadrature sampling approach. The fourth scheme, out of quadrature,performs noticeably worse. These results have important implications fordetermining accurate planet compositions and for designing effective RV followup campaigns in the era of large planet detection surveys such as $K2$, $TESS$,and $PLATO$.

Simulating the M-R Relation from APF follow up of TESS targets: Survey design and strategies for overcoming mass biases