A nugget of political arithmetic is suddenly everywhere: “Two-thirds majority.” This is the share of votes required to convict President Trump in an impeachment trial in the United States Senate. That’s 67 senators, if you’re counting—or, in the glass-half-empty variation, the number of Republican senators required to jump ship is 20.

Mostly, these numbers are used to cast doubtful sentiments on the prospect of impeachment. As CNN correspondent Manu Raju reports, convicting Trump “would require support from a two-thirds majority of the Senate—a highly unlikely proposition.” The same numbers, and the same conclusion, have been popularized by Chris Matthews, Rachel Maddow, and Chris Hayes; presidential candidates and members of Congress; USA Today and Reuters, CNBC and Vox’s Matthew Yglesias.

This is especially true among the President’s champions, who cheerfully assure the GOP faithful that Trump’s fortunes are sealed by math. Hans von Spakovsky did that on Fox News this week, when he argued that “67 votes are needed in the 100-member Senate to remove the president…a very high hurdle that’s probably impossible to leap over in the case of President Trump.”

If Fox News is to believed, the 67 figure is ironclad. Airtight. Right?

Not so fast.

The Constitution doesn’t indicate that removal from office requires two-thirds of the Senate. It requires two-thirds of senators present for the proceedings.

The inclusion of this single word in the Constitution’s impeachment clauses shifts the mathematical ledger of how impeachment, however unlikely, could go down. It allows for the all-important two-thirds threshold to exist along a sliding scale—far from the full attendance of the 100-member Senate. In theory, a vote to convict the President (or anyone else) would count as legal with as few as 34 members, not 67, assuming the absolute minimum (51) participated.

“The Constitution contains quorum requirements [elsewhere] and clearly distinguishes between percentages of a particular chamber and percentages of ‘members present,'” said Laurence Tribe, a professor of constitutional law at Harvard Law School and the co-author of the book To End a Presidency: The Power of Impeachment. “That language in the provision for Senate conviction on impeachment charges is quite deliberate, creating precisely the possibility” described above.

The Senate’s formal rules on impeachment, last updated in 1986, repeat the Constitution’s “present” provision numerous times.

“It’s a sliding scale,” says Alan Frumin, the former Parliamentarian of the Senate who now holds emeritus status. “In other words, it’s not an absolute two-thirds, it’s two-thirds of some number. And there you get to the question of the denominator.”

This rule could become relevant in a variety of ways. The most significant is the number of Republicans actually required to “jump the fence,” as Democrats hope. Twenty Republicans is a tall order: Even for Republicans who are shielded from reelection in 2020, a vote to convict Trump is obviously hazardous. If a few Republicans didn’t appear, that would reduce the number of Republicans required to vote with Democrats.

There’s also a more stark scenario. Recently, former Senator Jeff Flake speculated that at least 30 Republican senators would cast their vote for impeachment against Trump—but only if it were held on a secret ballot. (Flake went further, suggesting the number might be as high as 35.)

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But suppose those 30 senators were seeking a way, as Flake suggested, to remove Trump while avoiding the rage of his base. They might boycott the proceedings—or, when the big day of the vote arrived, mysteriously not show up. With 70 members now present, the number of senators required to convict Trump is no longer 67. It’s 47: exactly the number of seats Democrats and independents currently hold in the Senate.

“You’re talking about Republicans who want to remove him but don’t want to say something. How does their absence make that more likely? They might otherwise be a vote for conviction. But they’re not going to show up,” says Frumin. “Conceptually, that’s sound.”

The above scenario isn’t entirely foolproof, though. The rule isn’t operative in the case of abstentions—or, as Frumin puts it, “They could ‘show up’ and ‘shut up.'” Senators in the chamber who abstain, or even refuse to vote, are still in essence voting “no,” because their very presence inflates the denominator required to reach two-thirds, explained Frumin. This became clear during the impeachment trial of Bill Clinton, when Arlen Specter refused to vote “guilty” or “not guilty,” instead registering a vote of “not proven.” Chief Justice William Rehnquist ordered the vote to be tallied as “not guilty.”

And the Senate could, in theory, exercise its power for compulsory attendance, directing the sergeant-at-arms to arrest fugitive senators and haul them back to the chamber for the vote. But such power is only used in cases where a quorum is missing—to go from, say, 49 to 51—but never from 70 to 100, making its use in such a scenario unprecedented, and likely an abuse of power. (Frumin thinks it would violate the rules.) Of course, that hasn’t stopped Mitch McConnell before. But any measure to enlist the sergeant-at-arms would require a majority of the senators who were—well, present. (See how useful this word is?) If 30 members were absent, Democrats would presumably defeat the motion to compel the missing senators’ attendance, 47-23.

How likely is the above scenario? Not very. But as long as the country is preparing itself for any outcome, we might as well start using the correct numbers. “The rule,” says Frumin, “is pretty clear.”

Note: This piece has been updated to reflect late comment from Alan Frumin, Parliamentarian Emeritus of the Senate.

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