A self-funded independent campaign by a well-known billionaire focused on attacking the two-party duopoly that has long defined presidential politics has the potential to reshape the dynamics of the race.

“We’re living at a most fragile time,” Schultz said. “Not only the fact that this president is not qualified to be the president, but the fact that both parties are consistently not doing what’s necessary on behalf of the American people and are engaged, every single day, in revenge politics.”

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Democrats fear a credible third-party candidacy could allow Trump to win states he otherwise would have lost or push a decision on the election to the U.S. House, where Republicans currently have an advantage in the number of state delegations they control. The majority view of the 50 delegations, not actual control of the House, would determine the outcome of any such vote.

“If this is about principles and not ego, Schultz would help Democrats defeat Trump or run as a Democrat and broaden the debate within the party,” said Center for American Progress President Neera Tanden, a former adviser to both Hillary Clinton and Barack Obama in their 2008 campaigns. “Every value he claims to hold dear is undermined by a Trump reelection.”

Former housing and urban development secretary Julián Castro, who is running for president in 2020 as a Democrat, said Sunday that he was also concerned, even as he praised Schultz for his business accomplishments. As Castro and others suggested, their worry is that a three-way race would split Trump’s opposition, while the president’s support would remain intact.

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“I have a concern that, if he did run, that, essentially, it would provide Donald Trump with his best hope of getting reelected,” Castro said on CNN’s “State of the Union.” “I would suggest to Mr. Schultz to truly think about the negative impact that might make.”

A Seattle-area chapter of Indivisible, the liberal grass-roots group, announced plans for a “Pick a Party” protest at Schultz’s Thursday appearance for his book tour in his hometown. Washington State Democratic Party Chair Tina Podlodowski, who is expected to speak at the protest, has requested a meeting with Schultz before his book event.

The potential run also runs a risk of ensnaring Schultz’s company, where he remains chairman emeritus. The Washington State Democratic Party tweeted a photo Saturday of a Starbucks coffee cup with the words “Don’t do it Howard!” written on the side.

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The last time a third-party presidential candidate won individual states was in 1968, when former Alabama governor George Wallace picked up 46 electoral college votes in the South on the American Independent Party ticket. Republican Richard Nixon nonetheless won that election, and third-party bids have been blamed by partisans since then for impacting election results indirectly.

Ralph Nader’s Green Party candidacy in 2000 attracted far more votes in Florida than the margin by which Republican George W. Bush won the decisive state over Democrat Al Gore. Some Republicans have blamed business executive H. Ross Perot’s 1992 Reform Party bid for drawing votes away from President George H.W. Bush. Democrat Bill Clinton won that election with just 43 percent of the popular vote.

Under the Constitution, if no single candidate receives a majority of the electoral college votes, which are awarded on a state-by-state basis, the election is decided by the House, with each state delegation receiving a single vote. In the current Congress, Republicans have more representatives in 26 of the 50 state delegations.

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Former New York mayor Michael Bloomberg, a former Republican who is now considering running for president as a Democrat, decided against an independent candidacy in 2016 after concluding that he could not win a majority of electoral votes in a three-way contest and might inadvertently help Trump’s election. A person close to Schultz, speaking on the condition of anonymity to discuss internal deliberations, said Schultz would run only if he sees a path to victory in a three-way battle.

Schultz, 65, who Forbes has said is worth about $3.4 billion, appeared on “60 Minutes” at the start of a national book tour to share his vision for reimagining “the promise of America.”

His interest in an independent campaign is premised on the recent ideological drift of both political parties, which have embraced more ideologically ambitious proposals in recent years, even as the number of Americans registering as independents has risen. Yet he also has said the country needs to “go after entitlements,” programs such as Social Security and Medicare, which most voters have long supported.

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In the interview broadcast Sunday, he said he favored a path to citizenship for undocumented immigrants and rejoining the Paris climate accords, and he criticized the Democratic promise of “free health care” for all as unrealistic.

The success of the effort would probably depend on expanding the electoral college fight beyond the traditional Midwestern and southern swing states. It would also hinge on the Democratic Party nominating a candidate who struggles to gain traction in the general election among moderate voters.

A independent Schultz bid would also require him to qualify for the televised general election debates, a major platform for candidates in the final months of a campaign. In 2016, the commission that oversees those debates required candidates to meet a two-part test to participate: They must appear on enough state ballots to have a mathematical chance of winning the electoral college and they must receive at least 15 percent support in five national public polls that meet certain criteria.

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Schultz has been advised by Steve Schmidt, a former campaign manager for Sen. John McCain’s 2008 presidential campaign, who recently renounced his membership in the Republican Party. Schmidt was supportive during that campaign of picking then-Sen. Joe Lieberman (I-Conn.) as McCain’s running mate as part of an effort to cast the ticket as transcending traditional partisan politics. Lieberman was a longtime Democrat and Gore’s running mate in 2000. The plan was abandoned over concerns about a Republican rebellion at the party’s convention.

Democratic politicians and strategists are not the only ones who have said an independent Schultz bid could help Trump.

“I think it would be terrible for the Democratic candidate to have a left-of-center, self-funding candidate running to siphon off voters,” said David Kochel, a Republican consultant who worked on the presidential campaigns of Sen. Mitt Romney (R-Utah) and former Florida governor Jeb Bush in Iowa. “I just think it would be a disaster for Democrats.”

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William Kristol, who has been encouraging a Republican primary challenge for Trump, said he made a strategic decision to avoid pushing a third-party bid.

“One reason we are focused on the Republican primary fight is that it runs no risk of inadvertently reelecting Trump,” Kristol said.