Independent candidates are the scourge of major party candidates, who complain that they serve no other purpose than to spoil the race for one of the major party candidates.

But in the case of two high-profile Democrats-turned-independents, it may be the Republican Party that suffers from the spoiler effect.

In Arizona, Republican Kari Lake, who narrowly lost a bid for governor last year (but still refuses to concede the loss) announced Tuesday night that she will run for the U.S. Senate seat now held by Sen. Kyrsten Sinema, who last year flipped her party affiliation from Democrat to independent. Rep. Ruben Gallego is running for the Democratic nomination, setting up a potential three-way race if Sinema runs as an independent.

On paper, that sounds like a nightmare for Democrats, who lag behind both Republicans and independents in voter registrations in Arizona, but won the state in the 2020 presidential election and also won the open governor’s race and the U.S. Senate race in 2022.

But polling shows that Sinema and Gallego would not simply divide the Democratic vote, handing the race to GOP firebrand Lake. And it’s not because Arizonans are moving away from Republicans, analysts and pollsters say, but because Lake – and the former president who endorsed her in a video Tuesday night, Donald Trump – are turning off a critical mass of voters.

A Public Policy Polling survey released Tuesday found that Gallego would best Lake, 48% to 43%, in a hypothetical head-to-head race. But if former Democrat Sinema runs as an independent, Gallego still prevails in the poll, getting 41% of the vote. Lake gets 36% support in the survey, and Sinema has 15% support, the poll found.

“It really matters what kind of Republican comes out of the primary” in Arizona, says Mike Noble, CEO of the polling firm Noble Predictive Insights. For example, the group’s July polling found that Gallego has the backing of 45% of Arizona voters, compared to 35% for Lake – and that’s despite the fact that when offered a generic ballot, Grand Canyon Staters prefer Republicans (44%) over Democrats (38%) to run the state.

In a three-way race, Gallego is ahead in Noble’s polling, with 34% support, compared to 26% for Sinema and 25% for Lake.

“There’s a different current in the state; we did see it at the presidential level, with [President Joe] Biden winning the state by a very narrow margin. In some ways, that’s a product of who the candidates are, as opposed to the politics of the state,” says Fred Solop, a former Northern Arizona University political science professor who specializes in polling and state politics.

While Lake may alienate some independent and moderate voters she would need to win a general election, Sinema has turned off a lot of Democrats. She became nationally known for holding up legislation her party pushed and opposed getting rid of the Senate filibuster, angering progressives.

“Sinema is the reason why things you want, if you’re a Democrat, aren’t happening,” Solop explains.

Arizona’s electorate is 35%”other”, 34% Republican and 30% Democratic, according to the secretary of state’s office. In both 2020 and 2022, independents had an outsized impact – representing 39% of the voting electorate in the 2020 presidential race and 40% in the 2022 gubernatorial race, according to exit polls. In both races, independents favored the Democratic candidate, with 53% casting ballots for Biden and 44% for Trump, in 2020, and 52% of independents voting for Democratic Gov. Katie Hobbs in 2022, with 45% casting ballots for Lake.

Solop cautions that a lot can change in the coming year: Sinema (who hasn’t announced a run) has yet to spend any money on the race, and Trump, furious at his 2020 loss in Arizona, is likely to make a big strategic and financial effort there in 2024, should he win the nomination. That would motivate Trump’s base for Lake as well, and perhaps boost her numbers, Solop says.

A similar situation is unfolding with Robert F. Kennedy, Jr., who announced this week he is abandoning his uphill fight for the Democratic nomination for president and will run as an independent instead.

The candidate with the storied political surname initially attracted the backing of as much as a fifth of Democratic voters in early polling. But since Kennedy’s anti-vaccine comments – and his remarks that the COVID-19 virus was “ethnically targeted” to hurt white and Black people more than Ashkenazi Jews and Chinese people – he has lost favor among Democratic voters.

A poll by Quinnipiac University last month, for example, found that nearly half of Republicans – 48% – had a favorable view of Kennedy, with 18% of GOPers having a negative view. Meanwhile, just 14% of Democrats had a favorable view of the son of the slain 1968 presidential candidate, with 57% of Democrats disapproving of him.

No primary challenge is welcomed by a candidate, and Republicans initially gave Kennedy a platform, inviting him to testify before a House hearing. But once Kennedy said he was running as an independent, Republicans rushed to separate themselves from him.

“Make no mistake – a Democrat in independent’s clothing is still a Democrat. RFK Jr. cannot hide from his record of endorsing Hillary, supporting the Green New Deal, fighting against the Keystone Pipeline, and praising AOC’s tax hikes – he is your typical elitist liberal and voters won’t be fooled,” Republican National Committee chair Ronna McDaniel said in a statement.

In a three-way race with Biden, “probably he would draw slightly more from Republicans, once Democrats find out who he is – he’s not his father, he’s not the Kennedy [voters] have associated with in their minds,” says Hans Noel, a Georgetown University professor who is an expert in third-party candidacies and independent voters.

Kennedy is not expected to win a single state where he makes the ballot, experts agree. but he could have an impact in one of the handful of battleground states that will determine next year’s election.

“A lot of things can matter, on the margins,” Noel says.