In the 48 hours after former vice president Joe Biden won a dominant victory in the South Carolina Democratic presidential primary, two of his competitors for the party’s nomination suspended their campaigns. Both Sen. Amy Klobuchar (D-Minn.) and former South Bend, Ind. Mayor Pete Buttigieg joined Biden in Texas on Monday evening to offer him their endorsements prior to the state’s primary on Tuesday.

Those endorsements were important, though the effects are hard to evaluate at the moment. What may be more important are the 33 delegates that Buttigieg and Klobuchar have already won. Buttigieg finished in the top tier in both Iowa and New Hampshire, holding the lead in delegates briefly. Klobuchar parlayed a strong debate performance (largely targeting Buttigieg, incidentally) into a smaller pile in New Hampshire.

So what happens to those delegates now? What happens to delegates moving forward as candidates withdraw? The best way to answer that question is to look at the rest of the campaign in two parts: before and during the Democratic convention.

It’s worth quickly reviewing how delegates are allocated.

Most states hold primaries in which several different pools of delegates are awarded as follows. (The process for caucuses ends up in the same place but with more cumbersome math.)

The upshot for our discussion is those candidates pledged to Buttigieg and Klobuchar. Are they still pledged?

Josh Putnam is a political scientist who focuses on delegate rules. He both considered the question on his website, Frontloading HQ, and spoke with The Post about what happens.

One distinction Putnam draws is that while we generally talk about who won how many delegates in the contests so far, for the most part no one actually has any delegates at this point. Those delegates will be assigned at party conventions later in the year. Instead, candidates have mostly won “delegate slots” — placeholders for delegates to be assigned later. (The “mostly” qualifiers there are a carve-out for some district delegates in New Hampshire who’ve already been selected.)

This is important because, in some cases, those slots will be filled with delegates for only those candidates who are still in the race. In New Hampshire, for example, if Buttigieg is no longer a candidate by the time of the state convention, the three delegates he won by virtue of his statewide vote total would be redistributed among the other candidates still in the race who’d crossed the 15 percent statewide threshold. Since the other two candidates earning statewide delegates in New Hampshire were Klobuchar and Sen. Bernie Sanders (I-Vt.), the effect would be that Sanders gets all of those delegates.

Except that Buttigieg and Klobuchar haven’t dropped out. They’ve just suspended their campaigns. If you’re curious why candidates suspend instead of dropping out, well, this is one reason.

“As long as they are still in campaign mode — and they technically and barely still are,” Putnam said, “they protect those delegates from being reallocated.”

So Buttigieg’s zombie campaign is still allocated his three delegates in New Hampshire and Klobuchar gets her two.

When we get to the convention, though, those delegates get to play by different rules.

Once the convention rolls around, the party will hold a vote among the delegates in attendance to determine the party’s nominee. On the first ballot, pledged delegates are expected to vote for the delegates they are there to represent. If there’s no majority on the first ballot, another round of voting is held in which unpledged superdelegates (mostly party leaders and elected officials) have a vote and in which delegate pledges are set aside.

That “expected to vote for” is important, of course. Pledged delegates are pledged in the same way that teenagers pledge not to smoke: the success of the pledge largely comes down to their willingness to abide by it — and their relationship with the candidates they’re meant to represent.

Campaigns do their best to make sure that their pledged delegates uphold those pledges.

“During the selection process, once delegates at any level, of any type, are selected, the campaigns have the ability to review those candidates that are selected to represent them at the convention,” Putnam said. “So, typically, these are pretty loyal people — if you’re talking about a well-organized campaign, anyway — that’s been involved in this process from the start. And if they’re involved at the presidential level, they usually are.”

In other words, Biden’s campaign will work to ensure that its pledged delegates are fervent Biden supporters and not people who might get to the convention and suddenly decide that maybe Sanders is worth a vote. That’s useful, too, for any second (or third) round of voting: a die-hard Biden loyalist will probably keep voting for Biden as long as the Biden campaign wants him to.

You’ll notice that we haven’t yet talked about the congressional district delegates representing candidates who’ve suspended their campaigns. Those delegates and the statewide delegates the candidates protected by suspending their campaigns would go to the convention unpledged — meaning that they can vote for anyone they want on the first ballot.

“While both candidates may retain some control over who gets selected,” Putnam wrote Monday, “they do not have full control over any delegates selected to represent them.” The delegates who are going to the convention on Buttigieg’s behalf probably aren’t going to be the sorts of loyalists that Biden or Sanders would send, making it somewhat less likely that Buttigieg can effectively wield those delegates in negotiations over the nominee. One of the biggest effects Buttigieg and Klobuchar have over delegates, Putnam argues, is that, by technically staying in the race, they deny the reallocation of their delegates to Sanders.

Assuming the convention moves through multiple rounds of voting without a candidate earning a majority of delegates, Buttigieg, Klobuchar and other suspended candidates can encourage their delegates to vote for a particular candidate (Biden, for the first two), but that request is less like a parent insisting a kid stop smoking than it is like a random adult passing by and yelling at teenagers smoking cigarettes in a park. (Just to extend that particular analogy.) The weight is limited.

Putnam notes that we’re not talking about many delegates here anyway. If the Democratic nomination comes down to a 20-delegate margin between Sanders and Biden, these calculations and the decisions of the delegates themselves become fraught. It’s more likely that it will be the unpledged superdelegates who are the determining factor.

The party decides, as it were.

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