In this extraordinary presidential election, when the presumptive nominees of both major parties have historically low approval ratings, many Americans are looking for other options.

But the structural obstacles facing third-party and independent candidates — ranging from campaign-finance regulations to ballot-access rules — prevent viable alternatives. Add in the common sentiment that a vote for someone other than a Republican or Democrat is “wasted,” and it’s clear that, assuming they do get their respective parties’ nomination, nobody other than Donald Trump or Hillary Clinton has a chance to win, right?

Actually, it’s not so simple. While it’s inconceivable that anyone other than the major-party candidates could win the popular vote, it’s possible that nobody wins a majority in the electoral college.

If there’s no electoral majority, the 12th Amendment specifies that the House of Representatives, voting by state, will choose the president among the top three. It’s only happened once — in 1824, when John Quincy Adams won despite Andrew Jackson’s having gained popular and electoral pluralities — but it’s not too much to expect in this bizarre political year.

One could imagine a scenario where former New Mexico governor Gary Johnson, the Libertarian Party nominee, wins his home state and possibly others. He’s apparently drawing slightly more support from Clinton than from Trump — which would prevent Hillary from simply sweeping pluralities in all the swing states — and has been polling in double-digits in a three-way race.

Or maybe Mitt Romney gets into the mix, or outspoken Sen. Ben Sasse, R-Neb., or someone else conjured by Weekly Standard editor Bill Kristol (a leader of the #NeverTrump movement). If such candidates campaign strategically, they could win electoral votes. In 1968, the segregationist George Wallace won five states and 46 electors.

Moreover, faithless electors, who don’t vote for the candidate to whom they’re pledged, have appeared in seven of the 14 elections since Alaska and Hawaii began voting in 1960. (John Edwards got one in 2004) Given the major candidates’ (un)favorability ratings, the “faithlessness” probability is high — and it won’t take many votes in a close race to deny either Trump or Clinton a majority.

So what happens if the election goes to the House? There are currently 33 states with Republican-majority delegations, 14 with Democratic majorities, and three that are tied. Let’s say that, come January — it’s the “new” House that matters — the Republican-Democratic ratio is 30-20. If even five of those red states refuse to vote for Trump, there’s no majority and no president.

But simultaneously, the Senate picks the vice president from the top two finishers. If the Democrats take the upper chamber, House Republicans will have to reach a presidential agreement to prevent Hillary’s vice presidential nominee from becoming acting president. And if the Republicans keep the Senate, it could be that they prefer Trump’s vice president to The Donald himself.

Oh, and there’s one more possibility: If the Senate is tied — or enough senators abstain to again prevent a majority of the whole body — then we’ll have four years of President Paul Ryan, who as House speaker is next in line. Wouldn’t that be huge?

Ilya Shapiro is a senior fellow in constitutional studies at the Cato Institute.