When Howard Schultz dipped his toe into presidential political waters on Sunday, the former Starbucks chief executive likely did not get the response he was aiming for.

In a sit-down with CBS’s “60 Minutes,” Schultz announced he was giving serious thought to a 2020 White House run as an independent candidate.

“I will run as a centrist independent outside the two-party system,” said Schultz, who is set to begin a national book tour. “Both parties are consistently not doing what’s necessary on behalf of the American people and are engaged, every single day, in revenge politics.”

Almost immediately, reactions began pouring in at a furious clip. Some responses found the humor in the coffee titan’s idea. Others on the left, replaying past memories of third-party and independent candidates like Ross Perot and Ralph Nader, fumed that a Schultz run would split the anti-President Trump vote, essentially handing the incumbent the election.

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“I’m an American political historian and I can assure you that the only thing you’ll accomplish by running for president as a centrist independent is helping reelect Donald Trump,” author Kevin M. Kruse wrote on Twitter.

But if anything, Schultz’s announcement reignited a perennial debate among political talking heads: Are third-party and independent candidates essentially quixotic historical footnotes? Or real specters of significance that can upend a general election?

“It’s not at all clear IMO whether an Old Rich Business Guy running a 3rd party bid would be more likely to hurt Trump or to help him. People are assuming the latter but not really presenting much in the way of proof,” Nate Silver, founder of FiveThirtyEight, tweeted out amid the uproar over Schultz’s plans. “If you think Ross Perot and Ralph Nader belong in the same category you probably ought to be doubting yourself a lot more.”

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“This is a good example of where @NateSilver538 and his often-useful models fall short. For those of us who covered John Anderson, Ross Perot and Ralph Nader, there is zero doubt — zero — that a ‘goo-goo’ indy candidate like Schultz hurts Democrats,” veteran journalist Jonathan Alter responded. “Promise.”

For much of the 20th century, the American political scene was locked into the two-party system, and third-party and serious independent contenders have been infrequent.

According to French sociologist Maurice Duverger, the winner-take-all structure of American elections leaves little room for coalition building between political parties, and therefore the system itself favors a two-party setup, as political scientist Amanda C. Skuldt explained in The Washington Post in 2016.

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But third-party contenders have memorably popped up over the years. The question still being fiercely debated is what impact, if any, they had on the general election.

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In 1912, already with two terms in office under his belt, Theodore Roosevelt took on his handpicked successor, William Howard Taft, for the GOP nomination. According History.com, when Roosevelt failed to win, he broke with the party and ran under the Progressive Party banner.

Roosevelt and Taft each took away swaths of the Republican vote, leading to Democrat Woodrow Wilson’s election. Roosevelt, however, finished second behind Wilson, winning six states and 88 votes in the electoral college — the best third-party showing in American political history.

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But as History.com pointed out, since 1920, only three third-party candidates have notched significant electoral college votes: Robert La Follette in 1924 (13 electoral votes); Strom Thurmond in 1948 (39 electoral votes); and George Wallace in 1968 (46 electoral votes).

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Since 1980, the impact of third-party candidates has become a much-argued debate in political circles.

Rep. John B. Anderson (R-Ill.), a moderate Republican, ran against Ronald Reagan for the 1980 GOP nomination, then ran as an independent in the general election. Some have postulated that Anderson’s candidacy spelled the end for Democrat Jimmy Carter by siphoning away moderate Republicans.

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But writing in Salon in 2011, Steve Kornacki punctured that formulation, arguing that although Anderson polled as high as 24 percent of the electorate, his problems with funding essentially doomed his campaign. Also, his appeal was the same as Reagan — he was the anti-Carter.

“But at a practical level, [Anderson] was simply another option for frustrated voters who had already decided not to back Carter for another term,” Kornacki wrote. “Polls found Anderson voters nearly as likely to list Reagan as their second choice as Carter.”

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Texas billionaire Perot’s impact on the 1992 presidential election has been similarly debated. Perot jumped into the race, dropped out in July, then reentered in October. Eventually he tallied nearly 19 percent of the popular vote, but no electoral college votes. In some political circles, Perot was blamed for George H.W. Bush’s loss by cannibalizing the conservative vote.

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But exit polls showed that Perot voters were equally split on their second choice. As Kornacki also argued in 2011, economic anxiety had turned the electorate away from the Republican incumbent.

Ralph Nader’s run in the 2000 election could arguably be the most consequential third-party performance in recent election history.

Nationally, the Green Party presidential candidate received 2.74 percent of the popular vote. The real impact, however, was on the tallies in Florida, the state that ultimately decided the contest for George W. Bush.

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After the U.S. Supreme Court stopped the recount and called the election for Bush, the GOP candidate won by 537 votes. Nader, however, earned almost 100,000 votes in Florida — votes that would have handed Vice President Al Gore the election if more than 537 of those voters would have turned to the Democratic ticket than the GOP nominees.

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But following Schultz’s announcement, FiveThirtyEight’s Silver pointed out the essential difference between a candidate like Nader and third-party centrists, the same mold the Starbucks executive appears to be considering.

“Nader hurt Gore because he was a leftist 3rd party candidate,” Silver wrote. “The centrists didn’t affect things much. Johnson (2016), Perot (1996, 1992), Anderson (1980) all drew about equally from both major-party candidates.”

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