Former Starbucks CEO Howard Schultz at a news conference after speaking at Purdue University Feb. 7. (Joshua Lott/Getty Images)

Sen. Kamala D. Harris and Howard Schultz have already gotten their golden tickets. Sen. Amy Klobuchar gets hers Monday night.

But a number of Democratic presidential candidates are still wondering: Where’s my TV town hall, CNN?

The network launched a series of live, one-hour programs spotlighting a single candidate last month, starting with Harris. Such televised Q&As are a political prize at any time, but they’re especially valuable now, as the Democratic field begins to stack up with contenders like the starting line at the Boston Marathon. A turn in CNN’s spotlight could help a candidate catch on — with voters, with donors, with the news media — and bust out of the pack.

CNN has kept most of the details of its potentially kingmaking productions quiet, particularly how it selects those it favors with their own forum. The most likely criteria — who can draw an audience — has proved to be a bit of a moving target: Harris’s town hall was a hit with viewers; Schultz’s was a dud.

CNN managers declined to respond to questions about their selection criteria.

All of which leaves a good dozen or more Democrats guessing about when, or whether, they’ll get the same shot as Harris, Schultz and Klobuchar.

During the 2016 cycle, CNN hosted town halls starring major and minor candidates from both parties, including President Trump, Hillary Clinton, Bernie Sanders, Martin O’Malley, Marco Rubio, Ted Cruz, Jeb Bush and John Kasich, as well as third-party candidates Jill Stein and Gary Johnson.

But not everyone was invited to CNN’s party back then. The list of Democratic and Republican candidates who were deemed not ready for prime time by CNN was longer than those who were: Rick Perry, Scott Walker, Jim Webb, Lincoln Chafee, Bobby Jindal, Lindsay Graham, George E. Pataki, Mike Huckabee, Rick Santorum, Rand Paul, Chris Christie, Carly Fiorina, Jim Gilmore, Ben Carson and Evan McMullin.

The puzzlement, as well as the grumbling, about this cycle intensified last week when Schultz, the billionaire former chief executive of Starbucks, got CNN’s call. Democrats noted that Schultz isn’t a Democrat (he’s a self-declared independent), and he hasn’t even formally declared his candidacy. What’s more, his public support is virtually nonexistent; he polled just 4 percent in CNN’s own pre-town hall poll.

It’s not likely that Schultz gained many converts during his televised performance, highlighting both the high reward and high risk of being the sole figure onstage. A number of critics savaged Schultz’s vague responses to questions, including a commentary on CNN.com titled “13 strange and awkward lines from Howard Schultz’s CNN town hall.”

The program was seen by just over 1 million viewers, or about a third fewer than CNN’s regular 10 p.m. program, hosted by Don Lemon, attracts on an average night. Given the cost of staging a live forum from a remote location, CNN could have saved money and had higher ratings by airing a routine program.

The underwhelming response to Schultz raised the concerns of those working for other candidates, especially those with little name recognition and thin bankrolls. They fretted that the poor result could make CNN even more reluctant to offer their bosses airtime.

“Do we want a full hour? Absolutely,” said one campaign operative, who like others spoke on background so as not to jeopardize ongoing discussions with CNN. “But at the same time, we know this is all about ratings,” and such expectations may be unrealistic.

The unusually crowded field of Democrats so far includes such relatively well-known names as Klobuchar (Minn.), Harris (Calif.), Sen. Cory Booker (N.J.), Sen. Elizabeth Warren (Mass.), Sen. Kirsten Gillibrand (N.Y.) and former HUD secretary Julián Castro. Five others — Rep. Tulsi Gabbard (Hawaii), former congressman John Delaney (Md.), author Marianne Williamson, South Bend, Ind., Mayor Pete Buttigieg and entrepreneur Andrew Yang — have also declared.

Squeezing all of them in now will be hard enough, but the line will probably grow longer in coming weeks. The list of undeclared but likely candidates includes former vice president Joe Biden, Sen. Bernie Sanders (Vermont), Sen. Sherrod Brown (Ohio), former congressman Beto O’Rourke (Tex.), former New York mayor Michael Bloomberg and former Colorado governor John Hickenlooper.

One campaign aide said CNN has discussed hosting a town hall with three or four candidates at once, giving each about 20 minutes or so to field questions from a moderator and audience members.

That’s less than ideal, the aide said, but he acknowledged that CNN has all the leverage: In the absence of any regulation guaranteeing candidates equal time, the network can choose to ignore any candidate it wants. And so far, it’s the only game in town. CNN’s cable-news competitors, MSNBC and Fox News, both say they will air their own candidate town halls, but neither has announced plans.

At the same time, this aide said, “We don’t want to see CNN make the same mistake it made in 2016 by giving away insane amounts of free airtime to one candidate.” He was referring to President Trump, whose candidacy benefited from constant TV exposure in 2015 and 2016 (CNN president Jeff Zucker said in late 2016 that CNN made a “mistake” by airing so many of Trump’s campaign rallies live).

An aide to another campaign said CNN’s town halls come at a critical moment for the burgeoning field of candidates, when national TV exposure can help establish fundraising momentum to tide a candidate over until the first televised debates in June.

“The opportunities are very important, especially if you’re a candidate who is looking to get his name out to as many people as possible,” she said. “Free media is hard to quantify, but it’s very valuable. . . . Obviously, our hope is to get a one-on-one town hall.”