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:

electoralmap.png

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

nnetplot

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%.

 

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ikjyotsinghkohli24

Sikh, Theoretical and Mathematical Physicist, main research in the structure and dynamics of Einstein's field equations.

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