It’s been 40 years since a major political party opened its national convention without knowing who its presidential candidate would be. But Republicans are looking at that possibility in 2016.

Donald Trump has a substantial lead over Sen. Ted Cruz (R-Texas) and Ohio Gov. John Kasich. But unless they quit the race or Trump starts winning primaries by heftier margins than he’s done so far, Trump will arrive at the GOP convention in Cleveland this July with a plurality of delegates, not a majority.

That could result in delegates themselves deciding at the convention who the party’s nominee should be — a throwback to decades ago, when primaries played almost no role. Here’s a look at contested or brokered national conventions and the possibilities for 2016.

Q: What is meant by a “brokered” or “contested” convention?

A: It connotes that no candidate has secured a majority of a party’s delegates before the convention, meaning that the selection will be made at the convention itself. “Brokered” applies to scenarios in which more than one ballot is necessary for a candidate to emerge with a majority. “Contested” is used to describe times when a winner is established on the first ballot — as in 1976, when President Gerald Ford edged insurgent Ronald Reagan for the Republican nomination. That was the last contested convention. The last brokered convention occurred in 1952, when Democrats selected Adlai Stevenson on the third ballot. (Dwight Eisenhower didn’t receive a majority on the first vote at the 1952 GOP convention, but through some maneuverings that vote wasn’t counted as official; he secured the win on the first official ballot.)

Q: Weren’t these common in history?

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A: Yes, for the bulk of the 19th century and most of the 20th century.

The poster child for brokered conventions came in 1924, when Democrats selected John W. Davis — on the 103rd ballot! Davis, a former ambassador and West Virginia congressman, was a compromise candidate after neither New York Gov. Alfred Smith nor Sen. William G. McAdoo of California could wrangle a majority.

But the days of men in a “smoke-filled room” deciding the nominee faded long ago.

Q: Why?

A: Because of the rise of the primary system. State primaries weren’t so common decades ago and often statewide delegations arrived at conventions without being bound to a particular candidate. If the party wasn’t squarely behind someone, leaders and delegates bickered, negotiated and cast ballots until someone emerged with a majority.

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But the primary system gained momentum, especially in the 1970s, as a way to give rank-and-file party members a voice rather than leaving it to leaders. Quickly, more states began holding primaries or caucuses and binding delegates to the results.

The practical result has been that, even in years with crowded fields, the nominee is settled before the conventions start — reducing conventions to ceremonial, four-day advertisements for either party.

Party leaders also sought to avoid a brokered scenario, figuring division wouldn’t be good for their side. So, typically, once a front-runner emerges, the party tries to encourage challengers to leave the field. There was talk of a brokered Republican convention in 2012, until the party unified behind Mitt Romney. Same goes for the Democrats in 2008, before they rallied behind Barack Obama.

Most times, talk of a brokered convention fizzles.

Q: Why not this time?

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A: Because a significant portion of the Republican Party establishment wants to stop the front-runner rather than support him.

Q: What does Trump need to lock up the GOP nomination?

A: He needs 1,237 delegates to achieve a majority. And despite his front-runner status, he has a way to go.

Q: How so?

A: Trump has 845, Cruz 559 and Kasich 148. (Other candidates who garnered delegates have since dropped out.) Though well ahead, Trump may not be on a pace to reach 1,237. He could get there if he wins the remaining big state (California, June 7) and does well enough in the others.

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Q: Do the others have a chance?

A: Of obtaining a majority? Kasich doesn’t. Cruz has a long shot — but says he can get there if Kasich quits. Failing that, each wants to campaign hard enough to block Trump, then take their chances at an open convention.

Q: What happens if no one gets a majority on the first ballot?

A: Delegates would become free agents, no longer bound to the state’s primary results and able to vote for whomever they wished on the next go-round. Anti-Trump forces already are talking about a delegate-by-delegate fight to persuade party loyalists to back someone other than the brash developer. Trump has suggested there would be “riots” if the party tries to deny him the nod.

Q: Could another candidate altogether emerge in a brokered convention?

A: Don’t rule it out. Wisconsin Gov. Scott Walker, who ran but dropped out early, predicts that if no one has a majority of delegates when the convention starts, the nominee likely will be someone not currently in the race. Former House Speaker John Boehner said that in such a scenario he would support current Speaker Paul Ryan (R-Wis.). Ryan has said he will not accept the nomination.