With Alaska’s special House election coming up on August 16, the race is looking closer than expected — and is shaping up as a likely defeat for Governor Palin.

Key to this story is the mechanics of Alaska’s new ranked choice voting system, which the Last Frontier is using this year after voters approved the change in the 2020 election. According to the Alaska elections division, the system “allows voters to rank candidates in order of preference.”

This creates a system with “rounds” of voting — though voters only cast one ballot. If any candidate wins a simple majority in the first round, he or she is declared the winner.

If no candidate wins a majority, then the candidate with the fewest votes is eliminated and their votes are redistributed to the voters’ second choices. This process repeats itself until only two candidates remain and the candidate with the most votes wins.

The current race is to fill the seat of Congressman Don Young, who died in March after serving as Alaska’s representative for 50 years. Three candidates remain in the race: Mrs. Palin, Nicholas Begich III, and an Alaska state representative, Mary Peltola.

The independent candidate Al Gross placed third in the primary but dropped out on June 20, saying that “it is just too hard to run as a nonpartisan candidate in this race.”

Mr. Begich is the grandson of Representative Nicholas Begich Sr. Young took his House seat after Begich Sr. disappeared during a flight to Juneau from Anchorage in 1972. Mr. Begich’s family is a political dynasty in Alaska. Two of his children — Senator Begich and an Alaska state senator, Tom Begich, are both Democrats.

Mr. Begich, the son of Nicholas Begich Jr., is himself a lifelong Republican, arguing that “Don Young and I share many of the same views on a number of policies.”

As it stands now, Mr. Begich appears to be the favorite to win in the August 16 special election. However, due to Alaska’s voting system, that is far from certain.

Polling conducted by Alaska Survey Research between July 20 and July 25 shows a tight race for second place in the first round between Ms. Palin and Mr. Begich.

The poll of 1,219 likely Alaskan voters found that Ms. Peltola is carrying the largest plurality of the vote, at 41.1 percent, with Mrs. Palin and Mr. Begich at 29.4 percent and 29.6 percent, respectively, well within the poll’s margin of error.

The poll suggests dramatically different results in the second round of voting depending on whether Mrs. Palin or Mr. Begich takes second place.

If Mr. Begich takes second, he would likely win, with the poll finding that he would defeat Ms. Peltola 54.7 percent to 45.3 percent.

This would be roughly in line with Alaska’s 2020 presidential results, where President Trump defeated President Biden in the state with 52.8 percent of the vote compared to Mr. Biden’s 42.7 percent of the vote.

The election would, however, likely have a different outcome if Mrs. Palin comes in second place. If Mr. Begich is eliminated and his votes are redistributed, Ms. Peltola is predicted to defeat Mrs. Palin with 50.8 percent of the vote to 49.2 percent, again within the poll’s margin of error.

“Holy smokes, it’s on a knife edge,” pollster Ivan Moore tweeted. “So again, just like in our last survey, Begich is the presumptive winner and will go to DC to finish out Don Young’s term.”

Yet if Mrs. Palin comes in second place in the first round, the chance of a Democratic victory increases significantly, meaning that a win for the GOP probably means a defeat for Mrs. Palin.