Why Trump won the electoral vote while losing the popular vote. An analysis.

In the final tally of the 2016 election, Donald Trump won 306 electoral votes compared to Hillary Clinton’s 232, despite losing the popular vote 46% to 48%. How was it possible to lose the popular vote and win the electoral college? Some have suggested that the electoral college inherently favors low population states, and since those states tend to vote Republican, the electoral college inherently favors Republicans. In this piece I will investigate this claim and attempt to determine if the data supports it.

How electoral votes are allocated

It’s helpful to review how the electoral college works. We all know that the number of electors is 538. The legal underpinning of this seemingly arbitrary number is actually are laid out in laid out in Article 2, Section 1 of the constitution, the Apportionment Act of 1911, 23rd amendment, which was ratified in 1961.

In short, every state gets a number of electors equal to it’s number of representatives plus it’s number of senators, except for special case Washington D.C., which gets to pretend like it’s a state during the presidential election. The constitution fixes the number of representatives at 435. Representatives are allocated in proportion to state population as determined by the census, although the minimum number of representatives per state is one. The constitution also says that each state gets 2 senators no matter what. (50 states * 2 senators) + 435 representatives + 3 special Washington D.C. electors = 538 electors.

The mathematical formula for determining the number of electors for a state is:

Where E is the number of electors for the given state, Ps is the population of that state, and Pn is the population of the United States.

Very low-population states are highly over-represented

This system gives very low population states an advantage thanks to the fact that no state can have fewer than three electors. In fact, if we plot the number of electoral votes per person (EVPP) in each state versus state population, a very clean inverse relationship is seen:

High population states like California, Texas, Florida, and New York rank low on the EVPP scale, and low population states like Wyoming, Alaska, Montana, the Dakotas, Vermont, New Hampshire, and Maine rank high. Wyoming, the least populous and most over-represented state, has nearly 3.6 times the per capita representation as California, the most populous and most under-represented state.

There is no doubt that the electoral college favors low population states. But does it provide an advantage to Republicans? And did it thereby cause Trump to win?

Some people have suggested that the electoral college over-represents swing states in the upper midwest, or swing states in general for that matter. Here is a map of per capita representation by state (Hawaii and Alaska excluded):

Here we can see that few swing states are among the over-represented states. The over-represented states consist of very low-population states in the north-east and upper inter-mountain west, not in the population dense and electorally decisive upper midwest. Nor is Florida, North Carolina, or Colorado particularly over represented. New Hampshire and Nevada (both of which Clinton won) are the only truly over-represented swing states.

This is not surprising given the earlier observed inverse relationship between electoral votes and population. Such a relationship implies that the electoral college distortion will be very significant for the lowest population states, but much less so between states with larger populations, which includes most swing states.

In fact, most of the swing states of this cycle are underrepresented in the electoral college. Supposing perfect electoral representation, each state would theoretically have an EVPP of 538/Pn, which assuming a national population of 308 million people, comes out to 1.74*10^-6 electoral votes/person. The figures for swing states, along with some populous states for comparison are as follows (in units of 10^-6 EV’s/person):

California (the least represented state): 1.48

New York: 1.49

Florida: 1.54

Ohio: 1.56

North Carolina: 1.57

Pennsylvania: 1.57

Michigan: 1.61

Wisconsin: 1.75

Ideal national mean: 1.74

It therefore seems unlikely that electoral college over-representation can explain the Trump victory.

But before we make any declarations, let’s entertain a counterfactual.

Suppose we were to retain the electoral college, but we allocated electoral votes solely by population fraction. That is,

We retain the cap of 538 electors, but we allow electoral votes to be divided into fractions. We assume that each state uses a winner take all system, conveniently ignoring the silly states of Maine and Nebraska. In this scenario, Wyoming is allocated 0.98 electoral votes rather than their actual 3. North Dakota gets 1.9 electoral votes instead of 3. California gets 65 votes instead of 55, Texas gets 44 instead of 38, and so on.

Here is a chart of the actual electoral votes by state, compared to expected electoral voted based on population percentage for every state:

Our system corrects the electoral college’s bias towards low population. But will it change the outcome of the 2016 election? If we take the difference between the “expected” electoral vote based on our population model, and the actual electoral vote under the current system, we can define that state’s overall electoral handicap. Here’s a plot of each state’s electoral handicap, labeled red of blue depending on whether the state went to Trump or Clinton:

The sum of these handicaps tells us the difference between the outcome in the electoral college as it exists, and the outcome in our pure population allocated model. It turns out that in our scenario the electoral vote shifts by a mere 2.1 votes towards Clinton. In other words, the outcome of the election would be exactly the same.

This election was not decided because the electoral college is biased towards underpopulated states. Democratic leaning low-population states, particularly those in New England, mostly balance out the advantage of Republican leaning low-population states in the inter-mountain west. What then explains the discrepancy between the electoral vote and the popular vote?

The answer lies in the winner take all system that most states use to award electoral votes. In the vast majority of states, the winner of the state’s popular vote takes all of the electoral votes. This has a geographical boxing effect. It does not matter by what margin a candidate wins a state, all that matters is that they win it. In a winner take all system, each surplus vote is useless to goal of gaining electoral votes. Clinton overwhelmingly ran up the popular vote margin in two states in particular: California and New York. But mostly California. Clinton’s margin in California was the largest in any state by either candidate, by an order of magnitude. It was larger than Trump’s top seven state margins combined:

In case you wanted to see it in map form:

Ok, so it’s clear now. Clinton won the popular vote because she ran up huge margins in California, and to a lesser extent in New York. Trump won the electoral college because he won a larger number of electorally valuable states by relatively narrow margins. I’ve demonstrated that the electoral college’s low-population bias didn’t significantly favor Trump.

The actual bias is anti-partisan. The more heavily your state leans one way or the other, the less your vote counts. Every vote over the winning threshold is a vote that contributes nothing to the candidate. In this cycle, California, our most populous state, leaned far more heavily in terms of absolute numbers than any other state in the nation.

One last thing

Democrats are going to be thinking about where to allocate resources going forward. One way to look at this problem is to think about where the smallest number of votes can deliver the largest number of electoral votes. If we divide electoral votes of each state by the 2016 vote margins, the resulting map is totally surprising…

…Just kidding, it’s exactly what you expected. The highest bang for the buck states are Michigan, Wisconsin, Pennsylvania, New Hampshire, Florida, Minnesota, Nevada. They don’t call them swing states for nothing:

Thanks for reading!