The top four candidates in the race will advance to the special elections in August. Ms Palin has almost 30% of the vote so far. Nick Begich, the offspring of an Alaskan political dynasty, has 19.3 percent. Al Gross, a surgeon and commercial fisherman who ran for the Senate two years ago, has nearly 12.5 percent. and Mary S. Peltola, a former state legislator, has about 7.5 percent. Ms Palin and Mr Begic are Republicans, Mr Gross is not affiliated with any party and Ms Peltola is a Democrat. The special election was triggered in March by the death of Representative Don Yang, a Republican who was first elected to Parliament in 1973. The election will cover the rest of Mr. Yang’s current term. Extraordinary elections will be held on August 16, which is also the day of the Alaska qualifying round for the 2023-2025 term of Parliament. Thus, voters will see the names of certain candidates twice on a ballot paper: once to decide the outcome of the special election and once to select candidates for the autumn general election for the entire two-year term. For Ms. Palin, the struggle is a political comeback. As a running mate for Sen. John McCain in the 2008 presidential race, Ms. Palin lost a Democrat ticket to Joseph R. Biden Jr., and resigned as governor, seeking to transform her work into a new profile. well-paid political expert. Ms. Palin had taken advantage of a similar anti-establishment, anti-journalistic vein of the Republican Party that later pushed Donald Jay Trump’s unexpected rise to the White House in 2016. The results announced on Sunday are preliminary and may change in the coming weeks as more ballots are processed and counted. Alaska is a sparsely populated state, with two U.S. senators but only one member of Parliament. This small population is spread over an area larger than Texas, California and Montana combined, with about 82 percent of the state’s communities being inaccessible to the streets. Counting ballots there can be a challenge. Every voter in the state was mailed a ballot, starting April 27, and polls were due to return on Saturday. At least three more rounds of preliminary results will be announced by government officials before the results are certified in about two weeks. Alyce McFadden contributed to the petition.