There has been much controversy incited by the role the Electoral College plays in our presidential elections, especially in recent years as results have diverged from national popular vote totals. In this essay we will try to dispel some of that controversy with a more dispassionate statistical analysis of the 2016 results supported by a normative argument about how we might wish our democracy to choose its national leaders.
There are a lot of assumptions that underlie the issues — about democratic voting, the common will, and national objectives — that infuse the debate over the EC. What does democracy mean in the context of the USA? What is the objective in choosing a national leader? How is political and social justice best served? We won’t necessarily answer these questions to everyone’s satisfaction, but hopefully our analysis can inform the debate.
To briefly set the stage, in 2016 the two major party candidates, Hillary Clinton and Donald Trump split roughly 94% of the votes cast, with Clinton receiving 48% and Trump 46%. In the Electoral College, Trump won 30 of the 50 states, roughly translating into a 304 to 227 EC vote win, granting him the presidency. Even as Clinton won 2.9 million more votes, Trump won 77 more EC votes. Does that seem fair? How can that be? Before we answer that, let us pose the questions empirically rather than emotionally: Who really was the preferred choice of the nation? (We should keep in mind a voting system is an attempt to infer that preference and all voting systems are imperfect in that respect. See Arrow’s Impossibility Theorem.)
The EC and popular vote have diverged only 5 times in our history of 58 presidential elections. In normal times, the EC and the popular vote often converge and confirm the result (suggesting there is probably something abnormal about our current national politics). Basically, they diverge when the population is closely split between two candidates or parties and/or when the geographical distribution of support is highly skewed. Under these circumstances, the final result is less accurate as an inference of the popular will — in other words, we don’t really know except what the vote tallies and their distribution tell us. (We would be even less confident of the result if we thought about the 103 million eligible voters who Did Not Vote at all.) So, answering the question of which candidate American citizens preferred is a bit more complicated than stating the obvious.
Let’s start with the popular vote. Comparing the voting results to a coin flip where each vote is a random toss that turns up either Clinton or Trump would yield a mean probability of 68 million votes for each. Clinton’s total was 2.5 million votes short of that, while Trump’s was 5.3 million less than the mean. In simple statistical terms, given a normal binomial statistical distribution, we could say that Clinton’s total was twice as significant as Trump’s in terms of distance from the random mean. This would lead us to conclude that Clinton was the clear winner.
But that simple conclusion ignores a significant difference between a national vote and a coin toss that relates to the underlying distribution of the results. This map of the dispersion of Trump and Clinton votes may give us an indication of why this is no normal distribution like a coin toss. Instead, the results are highly skewed geographically. For instance, if we take away the votes of LA County, Cook County (Chicago), Manhattan, and Brooklyn, Clinton loses the popular vote by almost half a million. Does this matter?
The best way to answer this is to use a more granular level of analysis. There are several ways we can observe the vote according to different categorizations. For instance, there were 50 state populations, where Trump won a majority of votes in 30 while Clinton won 20. Votes tabulated by 435 congressional districts show Trump winning 230 to Clinton’s 205. In the Electoral College Trump collected 304 votes to Clinton’s 227. These results illustrate the issue of breadth of support versus the depth of support exemplified by the popular vote. Trump shows significant winning margins in each of these categories of the vote.
But we can go further into the weeds by referring to the 3,141 county vote tallies represented in the graphic map above. This gives us a much larger statistical dataset, albeit severely skewed: Trump won 2,654 counties to Clinton’s 487. This is where partisans and ideologues began to assert that, by virtue of one person-one vote, high density populations should have greater sway than low density populations in a democracy. (The frequent comment I’ve heard is that acreage doesn’t vote, to which I must agree. I’ve never seen a plot of dirt mosey into a voting booth.) The counter-argument is that we have a federal republic, not a democracy. Both sides have a point, though not as strong as each assume.
US politics is divided between urban interests and non-urban rural and suburban interests, where swing districts are usually found in the outer suburbs. There is nothing shocking or objectionable about this, it’s just the way interests and party politics have been carved up. (Geographical location has historically defined US voting patterns for more than 200 years.) Democracy is also defined as “rule by the people,” whereas one-person-one vote is merely one of many voting rules. So, we do have a democracy and it’s politically organized as a federal republic.
The more problematic issue is that the Republican Party candidate is highly favored across the exurban and rural landscape, while the Democratic Party candidate dominates the metros and inner suburbs. The challenge for a strong union is to keep these two diverging populations tethered together.
We can address the problem of skewedness in county vote tallies by taking more homogeneous subsets of the 3141 cases. One method would be to look at swing counties that were closely contested, say with a margin of 5% or less. We could expand those margins to 10%, 15%, and 20% to see how the sample distributions pan out. Another way to control for county size is to take a random subset of the range around the average size county and see how the results differ. The average size county is 43.6K voters, whereas the median is 11K voters. Thus, we used the 35–50K sample around the mean of 43K to capture generic counties by size across the nation. In this way we eliminate the small or large county bias.
All these possibilities can help reinforce our confidence in a more definitive result. Here is a Summary Table of those results:
We can see from the table that in those counties where the margins were close (<5%, <10%), Trump eked out a win. His winning margins increased as the voting diverged, but where the counties were normalized by size, his winning margin ballooned to almost 24% of the vote. We can see by comparing means and medians, that the county size sample was the most normalized.
It’s difficult to interpret these sample results as anything other than confirmation of Trump’s surprising win. It’s just as difficult to imagine that any kind of election interference from any source would have been able to engineer such an unpredictable result. There have been arguments made that if only 3 counties had been shifted by a mere few thousand votes, Clinton would have won the Electoral College. But that’s cherry picking; the significant fact is that none of those possible scenarios did happen, while Trump’s “perfect storm” did. It suggests that the Electoral College corrected for a highly skewed popular vote. Clinton voters and urban Democrats may not like that, but the numbers don’t lie.
But is the Electoral College method just?
That depends on what we believe is the objective of a national democratic vote. Is the objective to maximize voter participation by making everyone believe their vote can influence the outcome? Is the objective to establish the mandate of a simple majority? Or is it perhaps a strong and stable democracy that sustains the American ideals of liberty and justice for all as a beacon? These goals are not mutually exclusive, but we do need to set our priorities.
In our last, and hopefully only, civil war, President Lincoln explicitly acted on the goal of preserving the union above all else, including ending slavery. We can argue for our own particular objectives, but because there’s only one winning candidate, democratic voting can never make everyone happy or satisfied with the results. Therefore, those who lose the contest must accept that the process was fair and the results just according to an agreed upon set of established rules. Participating in elections on the premise that our vote determines outcomes is a bit irrational — we need a better principled reason to participate. And just imagine the problems inherent to a popular vote across 230 million eligible voters across fifty states? Look to the 2000 voting fiasco in Florida and imagine scaling the conflict to a 50-state recount that could never arrive at anything more than a random result. It would be unworkable and unthinkable and render presidential leadership impossible. On the other hand, the Electoral College seems to support a pragmatic method and just compromise for choosing a national leader by balancing our priorities and objectives as a nation.
Ironically, both sides of the debate have been making exactly the same argument: we cannot choose a national leader that appeals to a narrow base of support and leaves the wider population out of the process. This is why our system seeks to balance the depth of support with its breadth. When the depth and breadth of regional support coincide, the EC and popular vote are redundant; when they diverge, the breadth of support wins out. Critics of the Electoral College often disparage the outsized influence of swing states, but a swing state is one that is not beholden to partisan favoritism. This is exactly what we want when trying to discern the centrist national, rather than parochial, interest. Simply put: swing state good, partisan state bad; so we should continue to reward swing states as more representative of the national will and the necessary compromises for democracy.
Urban, suburban, and rural populations have almost complete control over their local and regional politics. That just doesn’t and shouldn’t extend to dictating the choices of the entire nation.