Written by We have reached the end. Early voters are already voting and by late Tuesday a new president will have been elected.
So who will that new president be?
The polls show a handful of close races, but overall the states that have supported Donald Trump six months ago are still supporting him. And the states that have supported Hillary Clinton are still supporting her.
So what do these polls say about Tuesday’s outcome?
The model used to predict the election uses a Monte Carlo method with the most current polls to simulate the vote result in each state and the district. The electoral vote of each trial is tabulated and a winner determined. This is repeated a million times to enable each combination of state wins to occur.
From the model, Secretary Clinton wins the election 94% of the time with Mr. Trump taking the electoral college majority just over 5% of the time. Not a certainty but it does give Clinton 16:1 odds for winning.
The expected number of electoral votes for Clinton is 308 to 230 for Trump. Of course this results is actually quite infrequent – happening less than 2% of the time. A more reasonable predictive value is that the interval from 261 to 355 will include the actual electoral result 95% of the time.
The median result – the value at which each candidate would expect to be above 50% of the time is also 308 for Clinton and a vote less at 229 for Trump. The middle 50% interval is 294 to 324 for Clinton – all above the critical value of 270, and 219 to 245 – all below 270 – for Trump.
Much has been said and written about the polls this election season. They are fixed. They are biased. They are just plain wrong. Could errors in the polls be forcing erroneous predictions?
To check if polling bias might change the outcome, a sensitivity analysis was run on the data with two additional simulations being run.
The first adjusted the polling data so that all of Donald Trump’s results are increased by one percentage point and Hillary Clinton’s reduced by one point. This was to test the sensitivity on the much touted shadow Trump supporter – the voter who does not want to tell a pollster that they will actually vote for Trump – or just to counter the claim that the polls are biased to the Democratic candidate.
When this reduction is made on all fifty states and the District of Columbia, the percentage of times that Trump wins does indeed increase, but not significantly. Instead of winning 5% of the time, Trump’s win percentage increases to just over 31%. This is a far better result – 1:2 odds – but still a long term losing position.
If the Trump polls are increased by 1% what about the same for Clinton? In a third run each of the fifty-one percentages were changed by 1% but this time increasing Clinton’s polls by 1% and decreasing Trump’s by 1%. This idea was to take into account the possibility of voters who while publicly supporting Trump, when they go in to vote they simply change their mind. Or – the counter to the previous bias issue – the polls are all biased but now in favor of the Republican candidate.
With the increase in the percentage for Clinton, her probability climbs to a certainty – winning 100% of the time.
The sensitivity issue appears to be moot. The probabilities change but Hillary Clinton still becomes the President-elect almost every time. To change this outcome would require a large scale drop in the results of almost all of the polls.
The model results are, of course, based on polls. And while the often repeated mantra that “the only polls that count are those on election day” is often considered the last breath of a losing campaign, election day will determine how close these predictions will be.
But at this point – forty eight hours from the final tally – the question for November 8th is still not who should win, but by how much will Clinton win?
J. Brian Adams
J. Brian Adams, Ph.D. is a Lecturer in the Department of Mathematics and Computer Science at Penn State Harrisburg.
