## How Unpopular Can the President Be?

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On today, Election Day in the United States of America, it seems fitting to post about the Presidential Election. Because of how our Electoral System works, it is possible for the president to be elected with less than half the popular vote; indeed, it is possible for a president to be elected even if another candidate received more of the popular vote. This has happened several times:

• In 1876 Republican Rutherford B. Hayes won the presidency (in a complicated procedure) although his Democratic opponent, Samuel J. Tilden, received more than half of the popular vote. (51.0% to 47.9%)
• In 1888 Republican Benjamin Harrison won 20 states, but only barely, while the Democrat Grover Cleveland won the remaining 18 states, several by a landslide; Harrison won the presidency even though Cleveland had more popular votes (48.6% to 47.8%)
• As recently as 2000, Democrat Al Gore received more of the popular vote but Republican George W. Bush received most of the electoral vote (50,996,582 people voted for Gore and 50,456,062 people for Bush, making it 48.4% to 47.9%; however Bush received 271 electoral votes while Gore only received 266).

So that leads to the question: if there were only two candidates running, and every eligible voter voted for one of them, what is the smallest percentage of a popular vote that a candidate could receive and yet still be elected to the Presidency?

The answer is just under 25%. Isn’t that amazing? The reasoning is that to win, a candidate has to win more than half the electoral votes for the states. But to win the electoral votes in a state, the candidate only needs to get a majority of the popular voe. So if a candidate were to barely win in the states they won, and to lose by a landslide in the states they lost, they’d only need just over half the votes in just over half the states (roughly speaking) to win the election. This would be just over 25% of the popular votes.

But in fact it’s less than that because electoral votes aren’t distributed evenly. The electoral votes for each state are the number of representatives that state has (which is distributed by population) and the number of senators (2). This means that the 2 senators carry more weight (proportionally) in states with a small population, so if the just-over-half states that the candidate wins are the ones with the smallest populations, it turns out that the candidate can get less than 25% of the popular vote (compared to the opponent’s just over 75%) and yet still win the presidency.

The thought makes presidential elections THAT much more exciting to watch!

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### 4 Responses to “How Unpopular Can the President Be?”

1. David Petersen Says:

Well, to take it to the full extremes, in the “key states” there could just be 1 person in the whole state who votes for the one candidate and everyone else in all the other states vote for the other. Highly unrealistic, but “possible” (at least in the sense that most mathematicians count).

2. Barry Leiba Says:

Indeed; the top 11 electoral states confer enough electors to win. So in the absolute extreme, as David points out, it’s theoretically possible for someone to take the presidency with only eleven votes against many tens of millions (I don’t know how many voters there are in the other 39 states (plus DC and the territories), but I believe the technical term is “a lot”).

Even if we don’t take it to those extremes, this sort of thing is clear evidence that our electoral college system is badly broken (the technical term for this involves “up” used with a word that the Supreme Court is today considering). As I said in 2000: No matter who will or won’t win, you have to accept that there’s something seriously wrong with a system where a change in 500 votes in Florida would change the result for the country, while a change in 5,000,000 votes in New York would have no effect.

3. jd2718 Says:

And by taking half + 1 in 270 worth of small states, the percentage could be driven down further. Why? Well, the small states carry more than their share of electoral votes! Each state has, roughly proportional representation in the house. But then, add two each for the electoral votes, no matter how big, no matter how small. Pennsylvania has 19 reps, Montana has 1, but in electoral votes, it’s 21 to 3.

So, take Montana, North Dakota, South Dakota, Alaska, Wyoming, DC, Deleware, Vermont. That’s 24 electoral votes, but less than 2.4 million votes.
Next: Hawaii, Idaho, New Hampshire, Rhode Island, Maine. That’s 44 EV, and under 5.4 million votes.
Next: Nevada, New Mexico, Utah, Nebraska, West Virgina, then Kansas, Arkansas, Mississippi, then Oregon, Oklahoma, Iowa, Connecticut. That’s 115 EV and under 18.8M votes.
Next: South Carolina, Kentucky. Then Arizona, Colorado, Louisiana, Alabama. Then Minnesota, Wisconsin, Maryland. That’s 198 EVs and under 40M.
Finally: Washington, Missouri, Indiana, Tennessee and then Virginia and North Carolina (skipping Massachusetts so we can reach 270 exactly), and under 58M votes.

The winner would need half plus one in each state (which I’ve safely overtallied, so no more than 29M votes. Out of about 124M cast. No more than 23%, and probably with careful counting could bring it closer to 20.

4. Just under 25 percent of the vote? Says:

[…] I guess you just have to visit 360 and read this post – a candidate in the U.S. could technically with the election with just under 25% of the […]