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How these Republican impeachment supporters survived their primaries

(CNN) Following Rep. Liz Cheney's primary loss in Wyoming Tuesday, just two of the 10 House Republicans who backed Donald Trump's 2021 impeachment will be on the ballot in November: Reps. David Valadao of California and Dan Newhouse of Washington state.

They are joined by the only Republican who voted to convict Trump in his Senate impeachment trial and is up for reelection in 2022, as Sen. Lisa Murkowski advanced to the general election in Alaska Tuesday.

How were these three Republican impeachment supporters able to beat the odds and overcome the wrath of the Trump base? The answer may lie in the unique primary systems all three ran in.

Murkowski, Newhouse and Valadao did not face a traditional Republican primary. Instead, they participated in contests where all candidates, regardless of party, appeared on the same ballot. In California and Washington, the top two finishers move on to the general election, while the top four advance in Alaska.

With all voters in the mix, these Republicans didn't just have to appeal to the party faithful, which diluted the impact of Trump's most ardent followers. And in some cases, it meant they only needed a fraction of the total vote to clear their primaries.

Newhouse and Valadao each only captured roughly a quarter of the primary vote on their way to securing a spot in the general election. By comparison, Cheney actually took a slightly larger share (29%) of the vote in her primary, which was open only to registered Republican voters, even as she lost to the Trump-backed Harriet Hageman by 37 points.

Murkowski was posting a stronger performance, with the latest results Wednesday showing her as the top finisher with roughly 44% of the primary vote. Unlike Newhouse and Valadao, though, she's not done with her Trump-backed challenger. Republican Kelly Tshibaka was among the four candidates who advanced to the general election, where ranked choice voting will be utilized.

There were, of course, other factors at play in these races that helped them avoid the same fate as their fellow GOP impeachment backers, the rest of whom either lost their primaries or declined to run for reelection.

Valadao and Newhouse kept relatively quiet about their feelings regarding Trump following their impeachment vote. The former President didn't even end up endorsing a primary challenger to Valadao, who was supported by House Minority Leader Kevin McCarthy, a district neighbor. As for Newhouse, his Trump-backed opponent, Loren Culp, struggled to raise money.

Murkowski was the greatest focus of the three for Trump, who traveled to Alaska for a rally last month. But she benefited in the primary from her deep ties to the state: she has served two decades in the Senate (and even won her 2010 campaign as a write-in candidate), and her father was a senator and a governor.

Still, the all-party primaries undoubtedly played a significant role -- one that may serve to bolster the argument put forth by the system's proponents. The case is that these sorts of primaries create incentives for candidates to play to the middle, rather than the most partisan elements that usually dominate primaries, resulting in a less polarized political environment overall.

That goal is still a very long way off from being realized. But for now, the all-party primary system seemed to have provided the dwindling number of impeachment-supporting Republicans their best chance for political survival.

The Point: The 2022 primary season has shown that it takes a unique set of circumstances for Republicans who have antagonized Trump to thread the needle and maintain their place in the party.

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