Field of Science

You can win the Electoral College with 22% of the vote

Donald Trump is poised to become the next US president, despite the fact that Hillary Clinton received over a million more votes than him (and counting). This would mark the second time in sixteen years, and either the fourth or fifth time in history (depending on how you count) that the Electoral College winner has lost the popular vote.

How is it possible to win the Electoral College but lose the popular vote?  The answer lies in a combination of two factors.  The first is the winner-take-all nature of the state contests. All states except for Maine and Nebraska deliver all their electors to the candidate with the plurality of votes.  This means that if you win by slim margins in a sufficient set of states, you can lose badly in all other states and still secure an Electoral College victory.

The second factor is the disproportionate representation of small states.  Each state has a number of electors equal to its total number of congresspeople (senators plus representatives).  The number of representatives is roughly proportional to population size, but adding in the two senators per state gives the smaller states more per-capita representation.  For example, Wyoming has approximately 7 electors per million elligible voters, while California has 2 per million.  So a Wyomingite has more over three times the Electoral College representation of a Californian (calculations here).

So if you want to become president without winning the most votes, your strategy is to aim for narrow victories in a set of smaller states that add up to 270, while ceding the other states to your opponent.  This begs the question: what is the smallest popular vote percentage one could receive while still winning the presidency?

The answer—according to my best calculations—is 22%.  You could capture the Electoral College, and become President of the United States, with only 22% of the vote.

I got this number by starting with the states with the most electors per elligible voter (Wyoming, Vermont, Delaware, Alaska, ...).  For each of these, I gave 50.1% of the vote to "Team Red", and the remaining 49.9% to "Team Blue".  I continued down the list of states with the most electors per capita, giving 50.1% to Team Red, until the total electoral votes exceeded the 270 needed to win.  I then gave Team Blue 100% of the vote for all other states.  It turns out Team Red didn't need New Jersey, so I threw that over to Team Blue as well.  The result: Team Blue captures 77.7% of the popular vote, but Team Red wins the Electoral College vote 270 to 268.  You can check my math in this spreadsheet.  My answer agrees with a similar calculation done in 2011.

Figure 1: One can capture the Electoral College with only 22.3% of the vote, by receiving 50.1% of the vote in the red states above and 0% in the blue states.

It makes sense that the 22.3% figure is close to one quarter.  If all states were equal in both population and electoral votes, one could tie the electoral college with slightly more than one quarter of the vote, by winning slightly more than half the vote in half the states, while losing the others completely (see below).  The fact that one can win the US electoral map with less than 25% is due to the disproportionate representation of small states.

Figure 2: A hypothetical electoral map of four states with equal populations and electoral votes.  Pie charts show the popular votes in each state.  One can tie the electoral college with slightly more than 25% of the vote, by winning narrow majorities in two states and receiving no votes in the other two. 
The above calculations assume that there are no third party candidates, and that voter turnout is the same in each state.  Dropping these assumptions can lead to even more lopsided possibilities.  For instance, with one third-party candidate, we only need to give Team Red 33.4% in the red states of Figure 1, while Team Blue and the third party each get 33.3%.  This leads to an Electoral College win for Team Red with 14.9% of the vote.  Alternatively, suppose that the turnout in the red states of Figure 1 is half that of the blue states.  Then Team Red wins with 14.3% of the vote.

Of course, possible is not the same as likely.  It would be very unlikely, for instance, for a candidate to receive 50.1% of the vote in Oklahoma but 0% in Texas.  What does not seem unlikely, on the other hand, is that the Electoral College winner loses the popular vote.  This has happened in at least 4 out of 58 elections, or 6.8%, which is not that rare of an occurrence.  What we need to decide, as a country, is whether we support an electoral system that does not always align with the majority of votes.


  1. The winner take all (in contrast to proportional representation) elections of the overwhelming majority of the States, and the disproportional representation of voters from lightly populated States (in contrast to proportional representation) are both essential and valuable in dodging the tyranny of the majority that Article II, Section 1 of the U.S. Constitution was intended to prevent.

    For those interested in democracy, The Economist magazine invited the philosopher Karl Popper to write an article on democracy. Reading it may shed some light on otherwise occult democratic practices.

    1. I don't think the Electoral College system does anything to prevent the tyranny of the majority. It sometimes gives power to the minority instead, but not in any systematic way that would prevent a tyrant--either majority or minority--from coming to power. Nor does it provide a check on the party that is in power.

      I don't even understand the logic of this argument. Could you explain exactly how the Electoral College system prevents tyranny of the majority, or point to a single instance in which it has done so?

      The Karl Popper piece is about winner-take-all versus proportional representation at the national level. It doesn't say anything about the Electoral College or its potential to give power to candidates without majority support.

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    3. Not understanding the reasoning for the Electoral College is an inadequate basis for criticizing it. The men who designed it had seen in Europe what absolute majorities had done to minorities, and wished to avoid those failures. The Electoral College has not yet failed in that capacity.

      As for your assertion that the Electoral College gives power to the minority, I suggest that a more accurate characterization is that by over representing the smaller (by population) Sates, it diminishes without eliminating the significance of the popular vote – as was intended. I refer you to the recent Blue/Red delta and that it is less that the votes cast for the Libertarian candidate. This difference of 2,080,877 is swamped in comparison to the 5,805,666 of the Libertarian and Green candidates. Indeed, the Libertarian vote count was itself greater than the difference between the Democrat and the Republican. ( )

      As for being able to point to a single instance in which it has prevented a tyranny of the majority, I refer you to the Presidential Election held November 8, 2016. As you may be aware 60% of the States of the United States were carried by one candidate, while 40% were carried by the other. Without the protection provided by the Electoral College, the less than 2% popular vote difference between the top two candidates would be the only count that is meaningful. Are those 2,080,877 more than twice as important as the Libertarian 4,414,171? While considering that, keep in mind that the candidate with the larger vote count did not even get a majority of the votes cast.

      As the Electoral College includes the significance of the States in addition to the popular vote, it does lower the probability of an individual securing that office based on only the popular vote, as would have happened in this last election. It was not designed to, nor does it provide a check on the party that is in power. It’s purpose is to include the significance of all the States, and to not render the less populated ones irrelevant.

      You are correct that the Karl Popper piece is about winner-take-all versus proportional representation at the national level. Your closing sentence, "What we need to decide, as a country, is whether we support an electoral system that does not always align with the majority of votes." is a direct reference to proportional representation at the national level. You make it clear that you think it should be so. Popper shows why that is a mistake.

      In re your claim that the Electoral College’s potential to give power to candidates without majority support; as neither candidate received 50% of the votes cast, whatever the outcome may be by the vote in the Electoral College, the next president will not have received a majority of the votes cast. ( )

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