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.

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

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

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. |

*less*than 25% is due to the disproportionate representation of small states.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.