See Original Article for more details
A Postmortem of the Final Results
In 2016, we analyzed the state of the Presidential election using a Gaussian Process (GP) methodology. GPs are an extremely flexible statistical analysis tool that can provide strong insight into ones data. Our analysis focused on the popular two person votes: namely the percentage of votes going to Clinton Vs. Trump ignoring other candidates and ignoring the electoral college. In the end, we estimated that Clinton had an 87% chance of having a greater vote count than Trump with an expected 2 person spread of 4.1%. The final votes indeed had Clinton beating Trump with the popular vote by a 2.3% spread. Of course the electoral college produced a different result with Trump soundly defeating Clinton.
This led to much being made in the press that the polls were materially flawed. But is this in fact the case? In retrospect the national polls which focus on the popular vote essentially ignore the possibility of an electoral college / popular vote difference. In the history of US, there have been five presidential elections where, in fact, the electoral college led to a different result to the popular vote. The Trump / Clinton election was not even the largest reversal between the two methods. We have to go back to the election of 1824 where Adams beat Jackson in the electoral college but lost by more than 10% on the popular vote. In total there have been 5 of the 45 presidential elections which had differing electoral college / popular vote results. This historic event frequency is surprisingly high with differing popular vote / electoral college results occurring 1 in 9 times.
Going back to our final GP analysis conducted on Nov 7, 2016, the model suggested that the chance that Clinton vote would be less than the Trump popular vote by 2.3% (namely the final result) was 30%. This suggests that the end popular vote count was not in fact much of a surprise, and the polls, while having a bias towards Clinton were not statistically out-of-line with the final outcome. Trump overperformed the polls on a national basis, but not to a great extent.
Nevertheless, it is clear that focusing on the national polls obscured the probability electoral college win by Trump and this perhaps is the most important lesson to learn.
Technical Analysis
We use a Gaussian Process model to analyze the state of the race. This model produces a smooth set of estimated spreads and probabilities of winning over the analysis time period. In time series analysis, there is the concept of “smoothing” and the concept of “filtering”. With smoothing, the estimated spread at any particular point in time represents the best estimate given all past and future data. If you had a noisy set of points on a page, and you are trying to draw a single line that represents the average position of the dots, then you would naturally choose to draw a smooth line that is consistent with the statistical definition of smoothing. Thus a colloquial understanding of smoothing and the statistical process of smoothing are consistent. Filtering is subtly different. With filtering the best estimate at a particular point in time of the state of the race is represent by the best estimate given all historic data, but ignoring data after that point in time, if any. Thus the filtered line and the smoothed line would match up only at the very right hand side of the graph (when there is no future data), but earlier points could differ.
A key question is how much smoothing should be applied. In turns out that the degree of smoothing is a key output that is automatically determined by the Gaussian Process model. The model uses a Bayesian process to solve for the degree of smoothing parameter.
Date: Nov 7, 2016, 9.37 am EST
- Probability of Clinton Win: 87%
- Probability of Trump Win: 13%
- Clinton – Trump Spread: 4.1%
See how Gaussian Processes can be applied in Actuarial Science. For more details on our implementation in polling, see here.