Declining response rates and increasing costs have led to greater use of non-probability samples in election polling. But non-probability samples may suffer from selection bias due to differential access, degrees of interest and other factors. Here we estimate voting preference for 19 elections in the US 2014 midterm elections by using large non-probability surveys obtained from SurveyMonkey users, calibrated to estimated control totals using model-assisted calibration combined with adaptive LASSO regression, or the estimated controlled LASSO, ECLASSO. Comparing the bias and root-mean-square error of ECLASSO with traditional calibration methods shows that ECLASSO can be a powerful method for adjusting non-probability surveys even when only a small sample is available from a probability survey. The methodology proposed has potentially broad application across social science and health research, as response rates for probability samples decline and access to non-probability samples increases.