By Stephen L. Carter

Bloomberg Opinion

Advocates for reforming the Electoral College will doubtless get a boost by a new and important paper by University of Texas economists Michael Geruso, Dean Spears and Ishaana Talesara. They find that in close presidential elections, the probability of an “inversion” — the popular vote going one way and the electoral vote another — is far higher than most of us suppose.

By now, most people who follow debate on the issue know that in 54 of the nation’s 58 presidential elections — better than 9 times out of 10 — the popular vote and the electoral vote have gone to the same person. Thus we tend to think of an inversion as an anomaly.

Geruso, Spears and Talesara insist that we’re wrong. Once we subtract the landslides and focus only on the close elections, matters are different:

“In elections decided by a percentage point or less (equal to 1.3 million votes by 2016 turnout), the probability of inversion is about 40%,” the researchers write. “For races decided by two percentage points or less, the probability of inversion is about 30%. Significant likelihood of inversion persists at larger vote margins.”

This likelihood, the authors insist, isn’t simply a matter of today’s political conditions. Independent of era, independent of particular personalities, independent even of the number of states, the probability seems to be baked into the system. “Asymmetry,” the authors tell us, “is a general property of the Electoral College system.”

Their approach easily accommodates the 2016 result. Hillary Clinton won the popular vote by 2.1 percentage points but lost by 74 electoral votes. In the paper’s model, even a 3-percentage-point popular-vote win by a Democrat would lead to about a 1 in 6 chance of a Republican electoral victory.

To reach their results, Geruso, Spears and Talesara don’t simply count the electoral results over time. In fact, the actual results don’t matter to the model, which takes into account such factors as the distribution of electoral votes across states and the concentration of political affiliation in particular regions — not just now, but through history. The authors ran multiple Monte Carlo simulations to calculate the likelihood of an inversion in a particular election without regard to whether an inversion actually occurred. And the results seem accurate:

“Our models predict that the 1876, 1888, 2000, and 2016 inversions were likely events,” the authors write. “For example, our models — armed only with the information that the two-party popular vote outcome in the 2000 election was 49.7% R / 50.3% D, and estimated from a sample that excludes 2000 — predict that an inversion was more likely than not for a generic Republican and Democrat candidate pair.”

The authors concede that at our present political moment, matters are just as everyone thinks: The chance of an asymmetric electoral result favors Republicans. The authors calculate that this has been true for at least 30 years. For many younger left-leaning voters, this means their entire lives.

Still, according to the authors, there have been historical eras when the odds of an inversion favored the Democrats. This was particularly true during Reconstruction. And while it’s true that no Democratic candidate has ever won the presidency without winning the popular vote, the authors insist that this historical artifact doesn’t mean no Democrat could. In fact, their models estimate that under current conditions, a Democrat who loses the popular vote by less than a single percentage point would have a 35% chance of winning the Electoral College. Not shabby.

But here’s the statistic that is bound to make the heads of true-blue commentators spin: The authors estimate that under current conditions, a Republican who narrowly loses the popular vote has a 65% chance of winning the election. For those whose affection or disaffection for the Electoral College is essentially a matter of partisan outcome, this will surely be the single most important calculation in the paper.

As for myself, I don’t consider an electoral inversion to be a disaster that we must undo the constitutional system to remedy. One needn’t like the outcome of a particular election to see the virtue of a process that keeps the states with large populations from swamping their smaller cousins. My advice to those who wish that the candidate who wins the popular vote would always win the election is simple: Turn out enough of your side’s voters to earn a landslide victory. As Caruso, Spears and Talesara would be the first to note, in that case an inversion is all but impossible.

Stephen Carter is a Bloomberg Opinion columnist.