What if France Had an Electoral College?
Emmanuel Macron won the French presidential election held on April 24, 2022 by 17 percentage points. Macron won with 58.5 percent of the popular vote; the other 41.5 percent went to Marine Le Pen.
Presidential elections in France are held in two rounds. If no candidate wins an absolute majority in the first round, a run-off election is held two weeks later between the two candidates with the highest vote totals from Round 1. The winner in Round 2 is decided by the popular vote — the candidate who receives the most votes in the country is declared the winner.
But what if the French election had been held under the procedures used in the United States? In the US, the presidential election is decided by the Electoral College. Would the result of the election in France have been the same under this system?
How the Electoral College Works
For US presidential elections, each state plus the District of Columbia is assigned a number of electors equal to the size of its Congressional delegation. For the 2020 US election, California, with 53 members in the House of Representatives and 2 senators, had 55 electoral votes; Wyoming, with 1 member in the House of Representatives and 2 senators, had 3 electoral votes.
States with smaller populations have disproportional influence for determining the election result. According to the 2020 census, Wyoming had population 576,581 and California had population 39,538,223. Thus, Wyoming had one Electoral College vote in 2020 for every 192,000 residents; California had one Electoral College vote for every 720,000 residents. A Wyoming vote counted 3.75 times as much in the presidential election as a California vote.
The US Constitution does not prescribe how each state should allocate its electoral votes. But over time most states have passed laws saying that all electoral votes for the state are allocated to the winner of the state’s popular vote.* This feature means that the Electoral College percentages can differ substantially from the nationwide popular vote percentages. Candidate A receives all 55 electoral votes from California as long as Candidate A receives the most votes — the result is the same whether Candidate A wins with 100 percent of the vote or if Candidate A’s margin of victory is one vote. In five US presidential elections (1824, 1876, 1888, 2000, and 2016), the loser of the popular vote has won the Electoral College.
Figure 1 shows the disparity between the percentage of Electoral Votes and the percentage of the popular vote for winners of US presidential elections since 1860. The Electoral Vote percentage is higher than the popular vote percentage for every election and shows much more year-to-year variation.** There are wide disparities between the popular vote and the Electoral College vote.
Figure 1. Percentage of Electoral College (top line) and popular (bottom line) vote received by the winner of the US presidential election, 1860-2020. The black circles indicate years in which the winner in the Electoral College lost the popular vote.
What if France Used an Electoral College System?
What if the same system had been used for the recent election in France, treating the 18 regions (13 regions in Europe and 5 overseas regions) as if they were states? The US House of Representatives has 436 members (if you include the nonvoting member from the District of Columbia) and the US population is about 332 million, so on average there is one Representative for about every 760,000 persons. Using the same ratio in France, where the 18 regions have total population of about 67 million, a French “House of Representatives” would contain 88 Representatives. The “equal proportions” method used for apportioning the US House of Representatives*** would allocate one Representative to each region with population less than 760,000 (such as Corsica and Guadeloupe), and allocate 15 Representatives to the most populous region, Île-de-France (home to Paris). This gives Corsica 3 Electoral Votes and Île-de-France 17 Electoral Votes (see spreadsheet, tab “Election Results”).
With the results that occurred in the recent French election, Macron would have won under an Electoral College system too. After all, his popular vote percentage exceeded that of all but 5 of the 41 US presidential election winners in FIgure 1. With the allocation of Electoral Votes to regions shown in the attached spreadsheet, Macron would have received 88 of the 124 Electoral Votes (71 percent).****
How to Win in the Electoral College with 22 Percent of the Popular Vote
But Macron could have lost under an Electoral College system, even with the same percentage of the popular vote. Under small reallocations of voters to regions, Le Pen would have won the Electoral College vote even though she lost the popular vote by 17 percentage points.
For simplicity, let’s again exclude the 532,704 expatriate voters, whose region is unknown. If 289,551 Le Pen voters in Île-de-France swapped with Macron voters in other regions — for example, 54,499 Le Pen supporters in Île-de-France moved to Grand Est and 54,499 Macron supporters in Grand Est moved to Île-de-France — then Le Pen would have 66 Electoral Votes to Macron’s 58 Electoral Votes, and would be declared the winner of the election under Electoral College rules (see spreadsheet, tab “Swap Voters”). The national popular vote for each candidate under this scenario is exactly the same as in the real election, but Le Pen would be declared the winner with the majority of the Electoral Votes.†
How can this work? In an Electoral College system, a candidate only needs a majority of the vote in each state or region to be declared the winner. In the election, Macron won 3,496,439 votes in Île-de-France, compared with Le Pen’s 1,292,212. In a popular vote system, as is used by France, each one of those votes counts toward the total. But in an Electoral College system, Macron would need only a bare majority of the votes (2,394,326) to win — the extra 1,102,113 votes he received in Île-de-France would be “wasted.”
The voter swapping technique works because it reallocates Le Pen supporters from Île-de-France, which she will lose anyway, to other regions in just enough numbers to give her the vote total needed to win those regions. The Macron supporters from those regions are swapped to Île-de-France, where they become “wasted” votes, increasing his margin of victory in Île-de-France but not increasing the number of Electoral Votes he receives from that region. And this is achieved by moving fewer than two percent of the persons casting votes.
Think you can’t swap voters? That’s exactly what gerrymandering does. One version of gerrymandering draws districts so that supporters of Candidate A are highly concentrated in a few districts, whereas supporters of Candidate B have a narrow majority in multiple districts. This type of packing ensures that a high percentage of the votes for Candidate A are wasted and thus gives Candidate B an unfair advantage.
How big can that unfair advantage be? Let’s look at the regions in France. Suppose that the least populous regions contain a bare majority of supporters of Candidate B (half of the district’s voters plus one), and the most populous regions contain no supporters of Candidate B. This scheme takes advantage of the “winner-takes-all” property and the disproportional influence that the Electoral College system gives to small regions. Then (see spreadsheet, tab “Minimum EV to win”) Candidate B could win the “Electoral College” in France with less than 22 percent of the popular vote!
Elections systems present many interesting mathematical problems for students, and of course numerous researchers have studied the mathematical properties of elections. Here are some questions students might look at:
Are the results presented above the optimal values? Could Candidate B win in an Electoral College system with fewer votes swapped, or with an even smaller percentage of the popular vote?
The results in France depend on the population and voter turnout in each region. What is the minimum popular vote percentage that would have been required to win the 2020 US presidential election? You can download the state-by-state popular and electoral vote totals from here. (Answer: as in France, it’s less than 22 percent.)
The number of electors per state is established in the US Constitution and can be changed only by a constitutional amendment. But laws enacted by the states determine how each state’s electors are appointed.
Suppose that, instead of using the current winner-take-all system, each state specified that electors would be apportioned proportionately to the popular vote in the state. That is, if Candidate A received 4 million votes and Candidate B received 1 million votes, then Candidate A would receive 80 percent of the state’s electors and Candidate B would receive 20 percent. Under this setup, using the total number of votes cast in each state in 2020, what would be the minimum percentage of the popular vote needed to win in the Electoral College? Assume for purposes of this exercise that fractional electors are allowed.
For a variation of this problem, assume that the number of electors assigned to each candidate must be an integer. Set up a rule for allocating an integer number of electors that is approximately proportional to the popular vote in the state. What is the minimum percentage of the popular vote required to win the Electoral College?
Copyright (c) 2022 Sharon L. Lohr
Footnotes
*Maine and Nebraska allow their electoral votes to be split. Two electoral votes go to the winner of the state’s popular vote, and one electoral vote goes to the winner of the popular vote in each Congressional district.
**Although the two percentages are positively correlated (r = 0.69), the Electoral Vote percentage has mean 70.8 and standard deviation 14.7, while the popular vote percentage has mean 51.8 and standard deviation 5.2. Several of the popular vote percentages for election winners are less than 50 percent because of third-party candidates.
***Wright (2012) discussed how the equal proportions method relates to allocation in stratified sampling. Also see Exercise 47 of Chapter 4 in Lohr (2022).
****For these analyses I excluded the 532,704 expatriate voters in the election, whose region is unknown. These account for less than 2 percent of the electorate. The results will be approximately the same if these voters are allocated proportionally to regions.
† Note that Le Pen could be declared the winner even if fewer votes were swapped. Swapping 271,911 votes results in each candidate having 62 Electoral Votes. Under American rules, the election would then be decided by the House of Representatives with each region casting one vote. If Le Pen’s party had the majority of seats in the House of Representatives in 10 or more regions, she would be declared the winner of the election.
References and Data Sources
270 To Win (2022). Historical presidential elections. Provides interactive maps of US presidential election results from 1788/89 to present.
Institut national de la statistique et des études économiques (2022). Populations légales 2019. Population counts for regions of France.
Lohr, S. (2022). Sampling: Design and Analysis, 3rd ed. Boca Raton, FL: CRC Press.
Ministère de l'Intérieur (2022). Election présidentielle 2022, 10 et 24 avril 2022. https://www.resultats-elections.interieur.gouv.fr/presidentielle-2022/index.html. Official results from the 2022 French presidential election.
Wikipedia (2022). List of United States presidential elections by popular vote margin.
Wolf, Z. B. (2020). The electoral college, explained. Short article on CNN.com giving the history of the Electoral College and explaining how it works.
Wright, T. (2012). The equivalence of Neyman optimum allocation for sampling and equal proportions for apportioning the U.S. House of Representatives. The American Statistician 66(4) 217-224.