## The Relationship Between The Electoral College and Popular Vote

An interesting machine learning problem: Can one figure out the relationship between the popular vote margin, voter turnout, and the percentage of electoral college votes a candidate wins? Going back to the election of John Quincy Adams, the raw data looks like this:

 Electoral College Party Popular vote  Margin (%) Turnout Percentage of EC John Quincy Adams D.-R. -0.1044 0.27 0.3218 Andrew Jackson Dem. 0.1225 0.58 0.68 Andrew Jackson Dem. 0.1781 0.55 0.7657 Martin Van Buren Dem. 0.14 0.58 0.5782 William Henry Harrison Whig 0.0605 0.80 0.7959 James Polk Dem. 0.0145 0.79 0.6182 Zachary Taylor Whig 0.0479 0.73 0.5621 Franklin Pierce Dem. 0.0695 0.70 0.8581 James Buchanan Dem. 0.12 0.79 0.5878 Abraham Lincoln Rep. 0.1013 0.81 0.5941 Abraham Lincoln Rep. 0.1008 0.74 0.9099 Ulysses Grant Rep. 0.0532 0.78 0.7279 Ulysses Grant Rep. 0.12 0.71 0.8195 Rutherford Hayes Rep. -0.03 0.82 0.5014 James Garfield Rep. 0.0009 0.79 0.5799 Grover Cleveland Dem. 0.0057 0.78 0.5461 Benjamin Harrison Rep. -0.0083 0.79 0.58 Grover Cleveland Dem. 0.0301 0.75 0.6239 William McKinley Rep. 0.0431 0.79 0.6063 William McKinley Rep. 0.0612 0.73 0.6532 Theodore Roosevelt Rep. 0.1883 0.65 0.7059 William Taft Rep. 0.0853 0.65 0.6646 Woodrow Wilson Dem. 0.1444 0.59 0.8192 Woodrow Wilson Dem. 0.0312 0.62 0.5217 Warren Harding Rep. 0.2617 0.49 0.7608 Calvin Coolidge Rep. 0.2522 0.49 0.7194 Herbert Hoover Rep. 0.1741 0.57 0.8362 Franklin Roosevelt Dem. 0.1776 0.57 0.8889 Franklin Roosevelt Dem. 0.2426 0.61 0.9849 Franklin Roosevelt Dem. 0.0996 0.63 0.8456 Franklin Roosevelt Dem. 0.08 0.56 0.8136 Harry Truman Dem. 0.0448 0.53 0.5706 Dwight Eisenhower Rep. 0.1085 0.63 0.8324 Dwight Eisenhower Rep. 0.15 0.61 0.8606 John Kennedy Dem. 0.0017 0.6277 0.5642 Lyndon Johnson Dem. 0.2258 0.6192 0.9033 Richard Nixon Rep. 0.01 0.6084 0.5595 Richard Nixon Rep. 0.2315 0.5521 0.9665 Jimmy Carter Dem. 0.0206 0.5355 0.55 Ronald Reagan Rep. 0.0974 0.5256 0.9089 Ronald Reagan Rep. 0.1821 0.5311 0.9758 George H. W. Bush Rep. 0.0772 0.5015 0.7918 Bill Clinton Dem. 0.0556 0.5523 0.6877 Bill Clinton Dem. 0.0851 0.4908 0.7045 George W. Bush Rep. -0.0051 0.51 0.5037 George W. Bush Rep. 0.0246 0.5527 0.5316 Barack Obama Dem. 0.0727 0.5823 0.6784 Barack Obama Dem. 0.0386 0.5487 0.6171

Clearly, the percentage of electoral college votes a candidate depends nonlinearly on the voter turnout percentage and popular vote margin (%) as this non-parametric regression shows:

We therefore chose to perform a nonlinear regression using neural networks, for which our structure was:

As is turns out, this simple neural network structure with one hidden layer gave the lowest test error, which was 0.002496419 in this case.

Now, looking at the most recent national polls for the upcoming election, we see that Hillary Clinton has a 6.1% lead in the popular vote. Our neural network model then predicts the following:

 Simulation Popular Vote Margin Percentage of Voter Turnout Predicted Percentage of Electoral College Votes (+/- 0.04996417) 1 0.061 0.30 0.6607371 2 0.061 0.35 0.6647464 3 0.061 0.40 0.6687115 4 0.061 0.45 0.6726314 5 0.061 0.50 0.6765048 6 0.061 0.55 0.6803307 7 0.061 0.60 0.6841083 8 0.061 0.65 0.6878366 9 0.061 0.70 0.6915149 10 0.061 0.75 0.6951424

One sees that even for an extremely low voter turnout (30%), at this point Hillary Clinton can expect to win the Electoral College by a margin of 61.078% to 71.07013%, or 328 to 382 electoral college votes. Therefore, what seems like a relatively small lead in the popular vote (6.1%) translates according to this neural network model into a large margin of victory in the electoral college.

One can see that the predicted percentage of electoral college votes really depends on popular vote margin and voter turnout. For example, if we reduce the popular vote margin to 1%, the results are less promising for the leading candidate:

 Pop.Vote Margin Voter Turnout % E.C. % Win E.C% Win Best Case E.C.% Win Worst Case 0.01 0.30 0.5182854 0.4675000 0.5690708 0.01 0.35 0.5244157 0.4736303 0.5752011 0.01 0.40 0.5305820 0.4797967 0.5813674 0.01 0.45 0.5367790 0.4859937 0.5875644 0.01 0.50 0.5430013 0.4922160 0.5937867 0.01 0.55 0.5492434 0.4984580 0.6000287 0.01 0.60 0.5554995 0.5047141 0.6062849 0.01 0.65 0.5617642 0.5109788 0.6125496 0.01 0.70 0.5680317 0.5172463 0.6188171 0.01 0.75 0.5742963 0.5235109 0.6250817

One sees that if the popular vote margin is just 1% for the leading candidate, that candidate is not in the clear unless the popular vote exceeds 60%.

## 2016 Real-Time Election Predictions

Further to my original post on using physics to predict the outcome of the 2016 US Presidential elections, I have now written a cloud-based app using the powerful Wolfram Cloud to pull the most recent polling data on the web from The HuffPost Pollster, which “tracks thousands of public polls to give you the latest data on elections, political opinions and more”.  This app works in real-time and applies my PDE-solver / machine learning based algorithm to predict the probability of a candidate winning a state assuming the election is held tomorrow.

The app can be accessed by clicking the image below: (Note: If you obtain some type of server error, it means Wolfram’s server is busy, a refresh usually works. Also, results are only computed for states for which there exists reliable polling data. )

## 2016 Michigan Primary Predictions

Using the Monte Carlo techniques I have described in earlier posts, I ran several simulations today to try to predict who will win the 2016 Michigan primaries. Here is what I found:

For the Republican primaries, I predict:

Trump: 89.64% chance of winning

Cruz: 5.01% chance of winning

Kasich: 3.29% chance of winning

Rubio: 2.06% chance of winning

The following plot is a histogram of the simulations:

## The Effect of Individual State Election Results on The National Election

A short post by me today. I wanted to look at the which states are important in winning the national election. Looking at the last 14 presidential elections, I generated the following correlation plot:

For those not familiar with how correlation plots work, the number bar on the right-hand-side of the graph indicates the correlation between a state on the left side with a state at the top, with the last row and column respectively indicating the national presidential election winner. Dark blue circles representing a correlation close to 1, indicate a strong relationship between the two variables, while orange-to-red circles representing a correlation close to -1 indicate a strong anti-correlation between the two variables, while almost white circles indicate no correlation between the two variables.

For example, one can see there is a very strong correlation between who wins Nevada and the winner of the national election. Indeed, Nevada has picked the last 13 of 14 U.S. Presidents. Darker blue circles indicate a strong correlation, while lighter orange-red circles indicate a weak correlation. This also shows the correlation between winning states. For example, from the plot above, candidates who win Alabama have a good chance of winning Mississippi or Wyoming, but virtually no chance of winning California.

This could serve as a potential guide in determining which states are extremely important to win during the election season!

## Hillary Clinton Still Has the Best Chance of Being The Democratic Party Nominee in 2016

A great deal of noise has been made in the previous weeks about the surge in the polls of Donald Trump and Bernie Sanders. This has led some people to question whether Hillary Clinton will actually end up being the Democratic party nominee in 2016. This was further evidenced by the fact that Sanders is now leading Clinton in the latest New Hampshire polls.

However, running an analysis on current polling data, I still believe that even though it is very early, Hillary Clinton still has the best chance of being the Democratic party nominee. In fact, running some algorithms against the current data, I found that:

Hillary Clinton: $\boxed{99.9 \%}$ chance of winning Democratic nomination.

Bernie Sanders: $\boxed{0.01\%}$ chance of winning Democratic nomination.

These numbers were deduced from an algorithm that used non-parametric methods to obtain the following probability density functions.

Thanks to Hargun Singh Kohli for data compilation and research.