Social media is increasingly used for large-scale population predictions, such as estimating community health statistics. However, social media users are not typically a representative sample of the intended population -- a "selection bias". Within the social sciences, such a bias is typically addressed with restratification techniques, where observations are reweighted according to how under- or over-sampled their socio-demographic groups are. Yet, restratifaction is rarely evaluated for improving prediction. In this two-part study, we first evaluate standard, "out-of-the-box" restratification techniques, finding they provide no improvement and often even degraded prediction accuracies across four tasks of esimating U.S. county population health statistics from Twitter. The core reasons for degraded performance seem to be tied to their reliance on either sparse or shrunken estimates of each population's socio-demographics. In the second part of our study, we develop and evaluate Robust Poststratification, which consists of three methods to address these problems: (1) estimator redistribution to account for shrinking, as well as (2) adaptive binning and (3) informed smoothing to handle sparse socio-demographic estimates. We show that each of these methods leads to significant improvement in prediction accuracies over the standard restratification approaches. Taken together, Robust Poststratification enables state-of-the-art prediction accuracies, yielding a 53.0% increase in variance explained (R^2) in the case of surveyed life satisfaction, and a 17.8% average increase across all tasks.