Postelection analysis of presidential election/poll data

This paper concerns analyses of the 2016 and 2020 U. S. presidential election data, including the data of pre-election polls and the actual elections. Our analyses unveil statistical evidence of discrepancy between the polls and real elections that is consistent across these two elections. Specifi-cally, the polls had consistently over-estimated advantages of the Democratic candidates, or, equivalently, under-estimated the true population support of the Republican candidate, Donald Trump, in both elections. The analyses are stratified by state, reflecting the U. S. electoral college system, by the means of small area estimation. We have found recurrent patterns suggesting that the polls have been underestimating the Republican candidate, especially in swing states of critical importance. Our findings also suggest an improvement of the 2020 polling methods to mitigate the size of underestimation. We show that a small-area model built upon the actual election data from one election can provide a better prediction than the poll-based projection to another election involving the same Republican candidate. Ranking of pollsters based on prediction bias using mixed model prediction is also considered.