CNN, which released its debate criteria in May, is planning to use an average of public polls dating to mid-July to determine which 10 candidates will appear in the main debate Sept. 16.

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WASHINGTON — When Carly Fiorina was relegated to the so-called undercard stage for the first Republican primary debate this month, she seized the opportunity to stand out. Clad in a bright pink suit — the only woman in a sea of men — she delivered a forceful performance that catapulted her into the national spotlight and generated a bounce in public polls.

But Fiorina, a former Hewlett-Packard chief executive, wants to be on the main stage at the second Republican debate next month. And she is waging a public war with CNN, which is hosting the debate, and the Republican National Committee (RNC), which her campaign accused Wednesday of “rigging the game” to keep her out of the event.

CNN, which released its debate criteria in May, is planning to use an average of public polls dating to mid-July to determine which 10 candidates will appear in the main debate Sept. 16.

Because that calculation would include many surveys done before the first debate, in which Fiorina delivered a strong performance, it would not fully capture her gains in recent polls, some of which show her near the top of the main 17-member Republican field.

Recognizing that Fiorina may be excluded from the debate, costing her crucial exposure and dampening fundraising efforts, her campaign has sought to turn the likely snub into a public-relations victory, in an effort to attract support from anti-establishment Republicans.

The dispute with CNN and the RNC, which awarded the debate to the network, allows Fiorina to emphasize her outsider status, in a category with Donald Trump and retired surgeon Ben Carson, both of whom are winning over voters, in part because they are not career politicians.

Debate criteria

Quiz: How many of the 2016 presidential candidates can you name?

Are you good with names at parties? Because we've got a lot of names and two parties here.

Asked about her battle over the debate criteria at a packed event in Cushing, Iowa, on Wednesday night, Fiorina criticized the network and the party.

“Let’s forget that I’m a woman,” Fiorina, who is the only female Republican candidate, said when asked about the debate. “I’m in the top five in every state poll and the top 10 in national polls. So what does that say about CNN and the RNC?”

She continued: “I’m going to keep doing what I’ve been doing, coming out here and talking to voters. As people get to know me, they support me. And you see that in the polls, and you’re going to continue to see that in the polls. I’ll let CNN and the RNC decide how they look if I’m not on that stage.”

CNN and the RNC have said that since the rules for the debate were released months ago, all the candidates knew the ground rules, and it would be improper — and illegal — to change them now.

Fiorina’s campaign nevertheless called on the RNC to push CNN to change its criteria.

“All candidates are aware of the law that the media organizations set the debate criteria, as the candidates asked,” said Sean Spicer, a spokesman for the committee. “CNN released its criteria over four months ago. All candidates were well aware of what it would take to get into the two segments that CNN is hosting.”

Some Republican strategists said Fiorina could emerge a winner even by losing a shot at the top-tier debate.

“Social media will light up in anger if she is consistently polling at 5 percent — consistently in the top 10 — and ends up being denied because of a technicality,” said Frank Luntz, a Republican political consultant and pollster. “Social media is running this election cycle, and it’s a voice that’s outside and powerful.”

On the other hand, Fiorina might not have stood out so much in the first debate Aug. 6 in Cleveland if she were on the stage with the top-polling candidates at an event that was dominated by Trump. So there may be an advantage to her to continue to face the candidates trailing the field.

The networks themselves are struggling with how to deal with the large Republican field. Their criteria need to be fair, but can inadvertently end up excluding certain candidates, such as Fiorina, who could be good for ratings.

“I am sure Priebus would gladly trade Fiorina for Trump,” said John Feehery, a Republican strategist, referring to Reince Priebus, the RNC chairman. “CNN, of course, wants both because it maximizes the ratings.”

CNN’s strategy

In retrospect, CNN’s criteria for inclusion in its debate seems intended to make it hard for a second-tier candidate to move up to the first tier — or for a top-tier individual to be excluded.

Unlike Fox News, which hosted the first debate and used the five most recent national polls to determine who made the cut, CNN is using an average of national polls released from July 16 to Sept. 10, conducted by 14 pollsters it identified as meeting its standards. The top 10 will participate in the main debate. The rest will be invited to participate in their own event before the main one.

Of the polls that qualify, nine were conducted before the first debate and only two since then, according to the Fiorina campaign. In both postdebate polls, Fiorina was at 5 percent, up from 1 or 2 percent in polls conducted before the first debate.

A New York Times analysis of polls that fit CNN’s criteria found that if the debate were held today, Fiorina would not qualify for the main stage.

Not only that, but if she were to maintain the same level of support she received in the two surveys conducted after the first debate, she would need 10 additional qualifying polls to be conducted before the next debate to eclipse Gov. Chris Christie of New Jersey, who is the last candidate to be included based on his support in an average of qualifying polls.

The Fiorina campaign is arguing that CNN should give more weight to the polls conducted after the first debate, and it has called on the party to pressure the network to make the change.

Some polling experts say CNN’s formula is misguided.

“I think they did not have a pollster at the table when they decided this,” said J. Ann Selzer, who conducts one Iowa poll. “I think it’s hard to defend, purely from a math perspective.”

Many Republican strategists lamented that Fiorina might not make the main debate, even as they said it would be wrong for CNN to change its selection criteria.

Using “more recent polls makes sense,” said Newt Gingrich, a former House speaker and a 2012 Republican presidential candidate. But, he added: “Rigging it to help or hurt one candidate does not.”

Katie Packer Gage, a partner at Burning Glass, a firm that advises Republicans on tailoring their messages to women, said that while Fiorina had gained a lot of attention and had “made a real impact” on the debate in the Republican Party, she should not receive special treatment.

“It is unfortunate, but I don’t think the party or the network can change the rules for any one candidate,” Packer Gage said. “What about the Hispanic candidates? The African-American candidate? The Indian-American candidate? Should they all have different rules? The rules were made ahead of time, and everyone knows them.”