Ms. Murkowski and Ms. Tshibaka won enough votes to advance to the general election in the fall as part of Alaska’s new open primary system. Ms. Murkowski is hoping to fend off a conservative backlash over her Senate vote to convict former President Donald J. Trump of inciting the Jan. 6, 2021, attack on Capitol Hill. With an estimated 50 percent of the vote counted, Ms. Murkowski and Ms. Tshibaka were neck and neck on just over 40 percent each. The closest rival after them was single digits. Ballots are still being counted and two other candidates will also qualify as part of the state’s top four system, but it was unclear which two. Ms. Murkowski, 65, is the only Senate Republican on the ballot this year who voted to convict Mr. Trump in his impeachment trial. She has been outspoken about her frustration with Mr. Trump’s dominance of the Republican Party, though she has maintained support for the Senate Republican campaign. He has also repeatedly crossed the aisle to support bipartisan compromises and Democratic nominees, including the nomination of Justice Ketanji Brown Jackson to the Supreme Court and the confirmation of Deb Haaland, the secretary of the interior. And she is one of two Senate Republicans who support abortion rights and have expressed dismay at the Supreme Court’s decision to overturn Roe v. Wade, a move that eliminated the constitutional right to abortion after nearly 50 years. Those positions have rallied both national and local Republicans against her, and her vote to impeach her led to censure from the Alaska Republican Party. Mr. Trump, furious at her vote to impeach him, called on his supporters to rally behind Ms. Tshibaka, a former commissioner at the Alaska Department of Management, who has positioned herself as an “America First” candidate who could represent more adequately the conservatives in the state. “It is clear that we are at a point where the next senator can either stand with Alaska or continue to allow the disastrous Biden administration that is hurting us more every day,” Ms Tshibaka wrote in an opinion piece published a few days ago from the primaries. “When I am the next senator from Alaska, I will never forget the Alaskans who elected me and I will always stand up for the values of the people of this great state.” But the new open primary system, combined with the use of ranked-choice voting in the general election, was designed in part with centrist candidates like Ms. Murkowski and supported by her allies in the famously independent state. Voters in November can rank their top four candidates. If no candidate receives a majority, officials will eliminate the last-place finisher and redistribute the votes of his supporters to voters’ second choices until a candidate receives more than 50 percent of the vote. Although she has never crossed that threshold in a previous election, Ms. Murkowski has overcome difficult odds in the past: In 2010, she memorably triumphed with a write-in campaign after a stunning primary loss to a Tea Party opponent. This victory came largely because of a coalition of Alaska Natives and centrists. Ms. Murkowski has used her seniority and bipartisan credentials to galvanize voters in Alaska, highlighting the billions of dollars she has pumped into the state through her role on the Senate Appropriations Committee and her role in passing the bipartisan Affordable Care Act. $1 trillion in infrastructure. She cites her friendships with Democrats like Sen. Joe Manchin III of West Virginia and the legacies of Alaskan lawmakers like former Sen. Ted Stevens and Rep. Don Young, who died in March, to show there’s still room in Congress for the style of its legislation. . “You have to show that there are other possibilities, that there is a different reality — and maybe it won’t work,” Ms. Murkowski said in an interview this year. “Maybe I’m completely politically naive and that ship has sailed. But I won’t know unless we—unless I—stay out there and give the Alaskans a chance to weigh in.” Her challengers, however, are seeking to exploit frustrations about Ms. Murkowski in both parties. As well as branding her too liberal for the state, Ms Tshibaka has seized on resentment over how Ms Murkowski’s father, Frank, chose her to finish his term as a senator when he became governor in 2002. Alyce McFadden contributed reporting.
