Three candidate chaos and the Electoral College

The American presidential system is particularly bad at handling three-candidate races

One of the striking mathematical features of voting systems in general is that once you have three or more major candidates, elections tend to become chaotic, that is to say that a smaller shift in public opinion and voters’ behavior produces a more dramatic shift in results.

At this point in time, we have a high likelihood of having three major candidates, both based on current indicators and based on historical precedent. The Electoral College is chaotic to start with, as I discuss in my book; three candidate elections are chaotic; and it is therefore no surprise that when there are three major candidates in a US presidential race, the results are especially chaotic.

Why worry? Aren’t three candidate races rare?

Normally, yes. But Donald Trump is currently running for office as a former president, which is not normal. Former presidents have run for office four times, losing three times. All four of these elections featured three major candidates.1

Left to right: Martin Van Buren, Millard Fillmore, Grover Cleveland, and Teddy Roosevelt.

In 1848, Martin Van Buren broke with his former party and took third place in the contest. Millard Fillmore similarly placed third in 1856 after the disintegration of his former party (the Whigs). In 1912, Theodore Roosevelt placed second, ahead of incumbent president William Taft.

Only one former president was renominated by his old political party: Grover Cleveland.2 However, the election of 1892 still featured a significant third party candidate: Populist James Weaver won five western states.

Plurality chaos

When there are three or more candidates in a plurality vote, odd things can happen. This includes center squeezes, spoiler effects, and strategic collapse.

Because a plurality vote does not account for secondary preferences, moderate candidates are subject to a “center squeeze” effect — they must compete against candidates on the right and on the left.

Illustration of the “center squeeze.”

If every voter votes for the candidate closest to their own position, a moderate candidate who would win in a 60% to 40% landslide in a two-candidate race might earn only 20% of the vote in a three-way contest.

However, voters don’t always vote for their first choice preference, and moderate voters concerned about polls showing the moderate candidate at 20% may choose to vote for the “lesser of two evils” instead, bringing the moderate candidate’s support down to 10%, 5%, or even nearly nothing. In a three-candidate plurality race, one candidate can very suddenly have a strategic collapse based on a bad news cycle and a momentary dip in the polls that accelerates into total collapse.

Illustration of a major spoiler effect.

Another major problem is that if two of the candidates have similar positions, they are competing for the same voters. This is the spoiler effect, and it means that a divided majority of voters can lose to a united minority of voters. Thus, two right-wing candidates who individually would win in a 60% to 40% majority against a single left-wing opponent can lose 40% to 30% to 30%.

Electoral College chaos

Functionally, because the Electoral College system takes fifty-one separate plurality elections and combines them into a fifty-second plurality election, it has roughly fifty-two times as many opportunities for chaotic behavior as an ordinary plurality election. The Electoral College has often been decided by popular vote margins in key states adding up to less than a hundred thousand votes — in the case of the 2000 election, less than a thousand votes in Florida.

The Mexican-American War can be traced to a spoiler effect in the election of 1844. The timing and nature of US intervention in World War I was probably also affected by the spoiler effect in the presidential election of 1912, though this is a slightly more complicated case.

Spoiler effects, therefore, can be radically amplified. In 1844, James G. Birney was not a serious presidential candidate. Anti-slavery Liberty Party ballots were only distributed and cast in eight states. However, one of those states was the key battleground state of New York, where pro-slavery candidate James Polk won by a margin of five thousand votes … leading to the Mexican-American War. To be a spoiler in the Electoral College, a candidate has to only tip one key state into the wrong column.

The elections of 1856 and 1860 were both multi-candidate elections impacted by a regionally-amplified “center squeeze” effect that elected first James Buchanan and then Abraham Lincoln. The result: Civil war.

The center squeeze becomes much worse in the Electoral College, as it is applied in each state separately. Candidates who are more regionally polarizing win more states. In 1860, for example, this meant that Stephen Douglas, who won nearly twice as many votes as John Breckinridge, earned a small fraction of the electoral vote, placing fourth.

Left: Popular vote shares. Right: Electoral vote shares. Note the dramatic underperformance of Douglas and fusion tickets.

More complicated is strategic collapse in the Electoral College. In a simple plurality election, strategic collapse can sometimes be a good thing, preventing the election of the worst candidate through a spoiler effect. However, each state’s contest is independent in the Electoral College.

In 1860, a voter who preferred Abraham Lincoln in Virginia would be better off voting for John Bell, who had a better chance to carry the state. However, in California, a voter who preferred Bell would be better off voting for Lincoln. In a regionally-divided election, a strategic collapse is likely to lead to contingent elections for president and vice president. This nearly happened in 1860; Lincoln won the critical state of New York by a narrow margin.

The contingent election process

Very few Americans would like to see the president and vice president elected by Congress in a contingent election. This is particularly true of experts aware of how the contingent election process works.

First, the House selects from the top three presidential candidates; the Senate selects from the top two vice presidential candidates, meaning that the resulting president and vice president may be from different parties. This is particularly likely if the natural compromise candidate is center squeezed into third place.3

At some points, polling suggested a contingent election was likely for the 1992 election, which could have led to the House appointing Bill Clinton (Democrat) and the Senate appointing James Stockdale (Reform).

Senators vote normally in the Senate’s contingent election process, but the House’s contingent election process is uniquely dysfunctional. It requires a majority of state delegations (26 out of 50), and state delegations can tie (especially but not only delegations with even numbers of representatives). If the process in the House deadlocks for long enough, the presidency passes to the current vice president.

One consequence of the House contingent election of 1800 was a duel in which Vice President Aaron Burr shot Alexander Hamilton.

It’s very easy for the House contingent election process to deadlock, and this happened for thirty-six ballots in a contingent election between two candidates.4 The second time the House contingent election was used, it was resolved on the first ballot, but only by a margin of a single vote by a single member of Congress.

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1 Definitions of “major” third party candidates vary, but these races all qualify.

2 He’s also the only one of those four former presidents who won office. It’s worth noting that Grover Cleveland won the popular vote in 1884 and 1888 before winning it a third time in 1892 as a former president — his 1888 loss was as much an unusual fluke of the Electoral College as Donald Trump’s 2016 win.

3 With four major candidates, the most natural compromise candidate may be center-squeezed all the way down to fourth place.

4 This was due to an exact tie in the Electoral College between Thomas Jefferson and his running mate Aaron Burr.