Politics

How Likely is Trump to Lose the Popular Vote but Win the Electoral College?

Unlikely unless the race tightens over the last few months

Jonathan Cervas
Aug 24, 2020 · 6 min read

Jonathan Cervas, Carnegie Mellon University

Bernard Grofman, Distinguished Professor Political Science, University of California, Irvine

here is a great deal being written about the likelihood that Donald Trump will be re-elected President in November. Much of that discussion focuses on the idea of fundamentals (e.g., economic conditions) and on the predictive power of the ever-changing polls, but there is also work that focuses the peculiarities of the Electoral College that allow an Electoral College (EC) inversion, where the winner of the popular vote loses the election. That has happened four times in our nation’s history, with the most recent occurrence being President Trump’s election in 2016. Some make the point that it is at least theoretically possible for Joe Biden to win the popular vote by 5 million votes and still lose the Electoral College.

Here we will not try to forecast the 2020 election outcome. Instead, we will try to clarify how to understand the likely effect of the Electoral College in 2020. There are two different questions to answer. ‘What is the likelihood of an inversion in 2020?’ and ‘If there is an inversion, what is the likelihood that it will benefit the Republican candidate?’.

The first point we would emphasize is that we cannot assess the probability of an EC inversion in 2020 without taking into account the closeness of that election. To see the relevance of closeness for the probability of inversion we have created a simulation of hypothetical election outcomes over the past 38 elections by taking the actual election results at the state level in each year and introducing a small random element to simulate what might have happened had things been just slightly different. Figure 1 below shows our results in terms of the two-party vote share. The simulation techniques we use are adapted from seminal work done more than three decades ago by the statistician Andrew Gelman and the political scientist Gary King.

When one candidate wins with just barely more than 50% of the vote, the probability of inversion is over 40%. However, when one candidate wins more than 52% of the two-party vote, the probability of inversion is effectively zero. This data is averaged over our nation’s entire history. The plot shows a slight pro-Democratic advantage historically — narrow popular-vote victories tend to favor Democrats, slightly.

Figure 1. The probability of Inversion

Note: Data is combined for all 38 elections between 1868 and 2016 to find these probabilities.

Inversion Probability Specific to an Election

In any given election, because the distribution of vote shares across the states is unique to that election, the probability of an inversion needs to be calculated for that specific election using simulation techniques.

In 2016, Clinton lost the Electoral College despite winning nearly 3 million more than her opponent; 51.1% of the two-party vote. However, our simulations tell us that the inversion was not inevitable. In 44.3% of our simulations, Clinton won the Electoral College at her actual vote-share. In an election as close as 2016, we would normally expect about 21.8% to result in an inversion. Clinton’s inversion probability was twice the historic average.

The simulations for the year 2000 with Gore winning the popular vote by 547,398 resulted in an Electoral College win for Gore half of the time, with another 2.6% ending with an exact tie. Unlike in 2016 when the expected probability of inversion was one in twenty, we estimated that Gore would have been expected to lose in the EC about 45% of the time based on historical simulations. Electoral ties are also very likely when the margin of victory is that narrow, around 22% of the time at Gore’s popular vote. That the 2000 election resulted in an inversion should not have been surprising. Had Bush won the election by the same 547,398 vote difference, our simulations indicate that Gore would have been expected to win the Electoral College 35% of the time.

Are Inversions more likely for Democrats?

The second point we would emphasize is that regardless of how low (or high) the probability of inversion, there can be great differences in which party we expect would benefit from any inversion that does occur. This is closely linked to partisan bias.

In 2016, for example, had Trump instead won the popular vote by the same margin as Clinton did, our simulation tells us that the probability that he would have lost the Electoral College was essentially zero (1.4%).

We see this asymmetry even more clearly at the point where each candidate would have received the same number of votes. In 2016, with 50% of the vote we might expect each candidate to have an equal likelihood of winning the Electoral College vote, but at 50–50 Trump would have been expected to win 86% of the time.

In 2000, had the popular vote split 50–50 we estimate that George W. Bush would have won 55% of the time, Gore 42.2% of the time and there was about a 3% chance that the election would have gone to the House of Representatives because of an EC tie.

Of course, in both the 2000 and 2016 elections there was an Electoral College inversion favoring the Republican candidate and, in our simulations, it was the Republican candidate who could be expected to do better in EC seat share than in popular vote share. In contrast, although no inversion happened in 2004, Electoral College bias favored the Democrat candidate. Had Kerry won more votes, so that the popular vote been tied or nearly tied, Kerry would have been victorious 63% of the time. The election of 2004 is an example of what we call a “dog that do not bite” (inspired by Sherlock Holmes). Other examples of these near inversions include 1916, 1948, and especially 1960, where some experts dispute that Kennedy won the popular vote.

We show figures with our calculations for 2000, 2004, and 2016 in Figure 2. The red and blue areas represent simulated elections where the popular vote winner failed to win the Electoral College.

Figure 2 Seats and Votes for Simulated elections (2000, 2004, and 2016)

Note: Each election is simulated 1,000 times over every two-party vote share between 35 and 65% at one-tenth of one percent intervals. Each election contains over 10 million simulated elections.

That brings us to 2020. Polls show that President Trump is very likely to lose the popular vote. The claim that Joe Biden could lose if he won 5 million more votes than Donald Trump is technically true but, for all practical purposes, it is false. If Joe Biden does win by 5 million votes, which would be an estimated two-party vote share of around 53.8%, and if the states kept the same relative ranking in Republican support levels in 2020 as they had in 2016, then our estimated probability of inversion is close to zero — 0.6%. The latest RealClearPolitics polling average (accessed August 22, 2020) has Biden winning by 7.6 points. If that number holds, it is virtually impossible for him to lose in the Electoral College. The geographic distribution of voters in 2020 is more likely to look like 2016 than 2000 or 2004. Based on the figure for 2016 we can see that if Biden wins a majority but his victory margin is not that big, Donald Trump is very likely to win the Electoral College. But, if Biden wins by more votes than did Hillary Clinton, then it is Joe Biden who is likely to be our next president.

Author Biographies

Jonathan Cervas is a Post-doctoral Fellow at Carnegie Mellon University in the Institute for Politics and Strategy. His research is focused on American political institutions. He has published on both elections and gerrymandering and has worked on three federal redistricting court cases involving minority rights.

Bernard Grofman is the Jack W. Peltason Chair of Democracy Studies and professor of political science at the University of California at Irvine. He received his B.S. in Mathematics at the University of Chicago in 1966 and his Ph.D. in Political Science at the University of Chicago in 1972. He has been teaching at the University of California, Irvine since 1976 and a Full Professor since 1980, and the Jack W. Peltason Endowed Chair since 2008.

3Streams

A blog about politics, policy, and ideas

Jonathan Cervas

Written by

Carnegie Mellon University | Institute for Politics and Strategy | Postdoctoral Fellow

3Streams

3Streams

3Streams is a blog for anyone interested in the convergence of politics, policy & ideas. It elevates the work of scholars interested in reaching a wider audience on timely topics with novel perspectives. To write for the blog, just leave a message or email 3Streamsblog@gmail.com.

Jonathan Cervas

Written by

Carnegie Mellon University | Institute for Politics and Strategy | Postdoctoral Fellow

3Streams

3Streams

3Streams is a blog for anyone interested in the convergence of politics, policy & ideas. It elevates the work of scholars interested in reaching a wider audience on timely topics with novel perspectives. To write for the blog, just leave a message or email 3Streamsblog@gmail.com.

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