Charles Petzold

Two candidates face off in a Presidential election: One candidate gets 22% of the popular vote and the other gets the remaining 78%, but the one who gets 22% is declared the winner. How is this possible?

Rest assured that such a scenario is extremely unlikely. In a practical sense, it’s never going to happen. But strictly speaking, given the mechanics of the Electoral College, it’s not impossible. A candidate who wins with 22% of the popular vote might provoke disbelief and outrage, but judges and Constitutional scholars would have nothing to say but “So it goes.”

Let’s review the rules:

To win a Presidential election, a candidate must get a majority of the 538 electoral votes that are distributed among the individual states. In all states except two, a candidate is awarded all the state’s electors by getting a plurality of the popular vote in that state — that is, more than any other candidate. (In Maine and Nebraska, the electors are divided into Congressional districts.)

It sounds straightforward but it’s actually quite dangerous. This two-stage process makes possible wacky scenarios that in an engineering context might be categorized as edge conditions, worse case scenarios, or (the scariest term) pathologies. These are combinations of conditions that result in a disastrous outcome.

Here’s a table to help analyze this phenomenon:

This table is similar to one in my previous blog entry with some unique features. It’s sorted by state population in the second column, but the third column is a running total of the state populations starting with the least populated state. The fourth column shows that running total as a percent of the total population.

The fifth column lists the number of electors in each state. This is followed by another running total and then expressed as a percentage of the total electors.

Look at those last two columns as you vertically scroll the table. When we get to the state of Virginia — the 40th state on the list, including the District of Columbia — the Accumulated Electors equals 570, and the Percent of Total Electors is 50.19%. This means that this collection of 40 low-population states from Wyoming through Virginia is sufficient to achieve an Electoral College majority.

Now look at the fourth column for the Virginia row. Those 40 states contain only 43.11% of the country’s population.

The worst case scenario — or let’s call it the most bizarre case scenario — is a race between (let’s say) Ann and Bill. Ann gets 50.001% of the vote in each of those 40 low-population states but nothing in the 11 high-population states. Bill gets everything else: 49.999% in the 40 low-population states and 100% of the votes in the 11 high-population states. Ann wins the election, but her share of the popular vote is only 50.001% of states that account for 43.11% of the U.S. population, or (rounding up) 22% of the popular vote.

It gets crazier if more than two candidates are involved. If three candidates Ann, Bill, and Cal split a state 34%, 33%, and 33%, respectively, Ann gets all that state’s electors. In the most extreme case, a three-candidate contest could result in a winner who gets only 15% of the popular vote. If there are four candidates, it drops down to 11%. (These exercises are left to the reader.)

In the history of the United States, it’s not very often that the Electoral College selects a President who does not receive the most popular votes. It happened in 1876 (Hayes over Tilden) and 1888 (Harrison over Cleveland) but after than, not until 2000 and 2016, and now we’ve all become increasingly nervous that it could happen again.

Statistics on the 2000 election are available from the Federal Election Commission website, from which I’ve adapted the following table. The Total row at the bottom shows that George W. Bush received 47.9% of the popular vote while Al Gore got 48.4%.

Notice the slider under the table. I was curious what variation there could be in those popular votes in each state and still maintain the same electoral votes. The slider lets you shift Bush votes to Gore and vice versa. Turns out that in the pathological scenarios — one candidate getting all the votes in the states he won and just under a half in the states he lost — Al Gore could have received 72.7% of the popular vote and still lose.

The 2000 race was notorious not only for the difference between the popular and the Electoral College votes, as well as the role played by the Supreme Court in halting recounts of votes in Florida, but also for the influence of third parties. When third parties are involved in a Presidential race, everything gets worse and the nightmare scenarios become more horrifying.

This is unfortunate, because third parties sometimes offer new ideas and perspectives. They can bend major parties towards less moderate positions, and they can occasionally even become major parties. But third-party candidacies are often referred to as “spoilers,” and for good reason. They tend to draw votes away from the candidate with whom they are most ideologically aligned, thereby splitting the vote. Third parties only work well in elections that require a majority win rather than just a plurality. The problem with a plurality is that we don’t know people’s second preferences, and getting that alternative vote necessitates either runoff elections or (preferably) a ranked-voting system.

Although the Electoral College was not specifically designed for a two-party system, it works best when there are only two candidates. The big problem is the winner-take-all plurality elections in the states. Third parties muck it all up in subtle and insidious ways. The Electoral College is not (to use another engineering term) a robust system. It can be very sensitive to small changes that introduce elements of chaos.

In the 2000 election, the final tally in Florida put George W. Bush ahead of Al Gore by just 537 votes. That difference is less than the third-party votes in Florida for Green Party candidate Ralph Nader (97,488 votes), Reform Party candidate Pat Buchanan (17,484), Libertarian Party candidate Harry Browne (16,415), Natural Law Party candidate John Hagelin (2,291), Workers World candidate Monica Moorehead (1,804), Constitution Party candidate Howard Phillips (1,371), Socialist Party candidate David McReynolds (622), and Socialist Workers candidate James Harris (562).

You would have thought that the 2000 experience would have cured everyone of ever wanting to run as a third-party Presidential candidate or vote for a third-party candidate, but that has not been the case. Candidates still offer themselves as Presidential material — most often to get attention or money for national parties, but perhaps also from messiah complexes — and voters still buy into the concept, perhaps to register a “protest” vote that neither of the two major candidates aligns exactly with their interests, or out of spite or nihilism. I think we would all be better off to conceive of the vote not as a form of personal expression, but as a tiny part of a process to move the country in a direction that’s best for the country and the world. Voting for a third party Presidential candidate does not achieve that goal.

How can you tell when a third-party candidate is having an adverse effect on a Presidential election? Look at the vote tallies in each state. If a candidate wins all a state’s electoral votes with a plurality rather than a majority, then one or more third parties are at fault. Look back at that table of the 2000 results: Not only in Florida did neither of the candidates get a majority of the votes, but also in Iowa, Maine, Minnesota, Nevada, New Hampshire, New Mexico, Ohio, Oregon, Vermont, Washington, and Wisconsin.

The problem is this: We don’t know who these voters would have chosen in the absence of the third party. We can certainly speculate whether the Ralph Nader voters would have preffered Bush or Gore, but we don’t know for sure.

The 2016 Presidential election had 14 states in which neither Trump or Clinton got a majority of the popular vote: Colorado, Maine, Minnesota, Nevada, New Hampshire, New Mexico, and Virginia, all of which went for Clinton; and Arizona, Florida, Michigan, North Carolina, Pennsylvania, Utah, and Wisconsin which went for Trump. (All the information about the 2016 race that I’ll be citing comes from the “Federal Elections 2016” pamphlet published by the Federal Election Commission.)

In 2016, people who voted for third parties could have shifted the election. For example, here are three states that Trump won in 2016 without achieving a majority of the popular vote. This table shows the votes for Trump and Clinton as will as for Jill Stein, who ran as the Green Party candidate:

It’s plausible that people who voted for Jill Stein would consider Hillary Clinton a second-best choice. If they had instead actually voted for Hillary Clinton, then Trump’s electors would have decreased from 304 to 258, and Clinton’s electors would have increased from 227 to 273, making her the winner.

Of course, this goes both ways. In 2016, the major third-party alterntive was Libertarian candidate Gary Johnson. If the people who voted for Johnson had instead voted for Trump — under the assumption that these voters were plutocratic libertarians rather than legal-heroin libertarians — then those votes would have offset any Jill Stein votes shifted to Clinton. But we don’t know, and that’s the problem.

In the 2020 Presidential Election, the “Federal Elections 2020” pamphlet reveals that no candidate got a majority of the popular vote in Arizona, Georgia, North Carolina, Pennsylvania, and Wisconsin. Here’s a table showing the votes for Trump, Joe Biden, and Libertarian candidate Jo Jorgensen in three of those states:

The Jo Jorgensen votes are the primary reason why neither Biden nor Trump got a majority of votes in these states. If just 21% of the Jorgensen voters in Arizona, and 19% of the Jorgensen voters in Georgia, and 54% of the Jorgensen voters in Wisconsin, had voted instead for Trump — we’re talking 43,000 votes here or less than three-hundredths of 1% of the total votes cast in the country — then Biden’s win of 306 electoral votes would have been reduced to 269, and Trump’s 232 electoral votes would have been increased to 269, resulting in...

Yikes! Resulting in a tie.

An Electoral College tie? Now what the hell happens?

By the Twelfth Amendment to the Constitution, an Electoral College tie requires that the House of Representatives select a winner from the three candidates with the highest number of Electoral College votes. Each state gets one vote, and they keep voting until one candidate gets a majority.

How is each state’s vote computed? Do the House members huddle and take a vote among themselves? Or does it go back to the state legislature? That’s not spelled out. Each state would be making its own decision.

Would you like one more pathological scenario? Go back to the first table in this blog entry and count down a 26-state majority from the top, excluding the District of Columbia, which has no further role in the process. The 26th state will be Louisiana, which means that the President could be selected by 26 states representing less than 18% of the country’s population.

It is highly unlikely that the Electoral College will soon be replaced by a nationwide popular vote, but if it is, then let’s also hope that it incorporates some kind of ranked-voting mechanism. I don’t want to eliminate third parties, but it’s essential that those voters also express a preferance for someone else — just in case their special first-choice candidate prevents anyone else from getting a majority.