Trump's name is not on the ballot Tuesday, but his thumb rests heavily on the scale

This Tuesday brings another round of important primaries for Congress and statewide office and the likelihood that big-name candidates will go down to defeat.

But the news next week will not focus on those household-familiar names or what their losses mean for their states. It will focus on what those outcomes may mean for Donald Trump.

That is all the more remarkable considering that these could be the last bids for seats in Congress for two of the best-known women in American politics — Republican icons Liz Cheney of Wyoming and Sarah Palin of Alaska.

Cheney is vice chair of the committee investigating the Jan. 6 attack on the U.S. Capitol and has often been the sharp point of the spear for that probe. Until she voted to impeach Trump in January 2021, she was on track to someday be the first Republican woman to be speaker of the House. She may also be a candidate for president in 2024.

Cheney is, of course, also the daughter of former Vice President Richard B. Cheney, who served two terms in the White House (2001-2009) and was often described as the most powerful No. 2 executive in U.S. history. The former vice president has released an ad and a video in which he appears in a cowboy hat and growls out his support for his daughter and dismisses Trump's claims about the 2020 election. The tag line is: "Only a coward would lie to his own supporters."

Sarah Palin is, of course, Sarah Palin

Palin was the first woman since Geraldine Ferraro in 1984 to be on the national ticket of either of the two major parties, chosen for the vice-presidential slot by GOP nominee John McCain in 2008. She delivered one of the most memorable speeches in recent history at the party's St. Paul convention that summer and headlined packed rallies that autumn that in many ways anticipated Trump's own.

Before that she was the governor of Alaska and since then she has been a TV reality star, though far less successful in that career than Trump. She has also been a Fox News contributor prior to her current campaign and a contestant on "The Masked Singer."

She is running now for the seat held for 49 years by the late Rep. Don Young, the longest serving Republican member of Congress in history. If she wins the special election Tuesday, she will complete his term, and a primary vote on the same ballot would nominate her for a full term starting in 2023.

Just over a year ago, the prospect of Cheney and Palin both serving in the same chamber of Congress at once would have been enough to draw media attention of all kinds at all levels of sophistication.

With first names that easily fit in headlines and last names sure to be click-bait, the two could have driven traffic for years. That would have been especially true had one or the other or both run for president in 2024 or thereafter. And even if neither did, either would be an automatic mention for vice president in 2024 or thereafter.

It is still possible, but developments in both their states and nationally have made it increasingly unlikely that either will be on the House floor next year.

A loss for Liz or a launch?

In another time — say one cycle ago — Cheney would be breezing to another GOP nod for the seat she first won in 2016 and has held since. In November she would expect to win with more than two-thirds of the vote, as she has three times.

But this time, she is expected to lose badly to state legislator Harriet Hageman, who has been leading in the polls – including a University of Wyoming poll published Aug. 12 showing Hageman ahead 30 points.

Trump endorsed Hageman the day she announced way back in September 2021, a swift move that helped to freeze out other Republican rivals who might have divided the anti-Cheney vote.

"We love President Trump here," Hageman says, thanking him for also coming to the state for her. Trump has made good on his vow to oppose the 10 House Republicans who voted to impeach him in January 2021 (two have survived their primaries, three have lost and four others did not seek re-election).

Hageman was a strong supporter of the presidential aspirations of Sen. Ted Cruz of Texas in 2016, at the time dismissing Trump as "racist and xenophobic." She now says she was the victim of lies about Trump told by Democrats and Liz Cheney at that time, but now regards him "as the greatest president of my lifetime."

In interviews, Cheney has strongly suggested she has already accepted the verdict of the Wyoming voters but is not ready to end her career. After completing her current term, observers have suggested, she could be the anti-Trump campaigner in a 2024 field of pro-Trump Republicans – quite possibly including Trump himself.

While no data exist to suggest Cheney could still win on Tuesday, her candidacy has prompted an unprecedented outpouring of support from outside the state and from longtime adversaries as well. Led by former Gov. Mike Sullivan, many Wyoming Democrats are expected to switch their party registration (as state law permits on primary day) so as to vote for Cheney. But it's highly unlikely there would be enough of these to make the difference.

There may have been some erosion of Trump support in Wyoming, where he got 70% of the vote twice. But that slippage probably ended when the FBI searched his home at Mar-a-Lago on Aug. 8. Republicans in Wyoming, as elsewhere, closed ranks behind the former president this past week and denounced the search as politically motivated.

After that FBI search, the blood is up in Trump states.

Stymied by a voting system

But even this latest rallying around Trump might not be enough to save Palin.

She has his endorsement, and he dialed in for one of her rallies as recently as the day his home was searched. What's stopping Palin is not her relationship with the former president, it's a voting system.

Alaska has an open primary that lists all candidates together regardless of party. In the first round of the vote there this spring, there were 48 candidates on the ballot. Palin, no surprise, came in first with 27% of the total. She has often complained that she "got the most votes" and should not be subjected to a second round of voter assessment.

But under Alaska's system, Palin must face a second round of voting that includes the top four finishers from the first round. One of the top four in the June vote has dropped out, but Palin is still battling two second-round rivals on Tuesday, including another Republican. He is Nick Begich III, the grandson of the last person to hold this seat before Young. His grandfather was a Democrat who was lost in a plane crash in the Alaska wilderness in 1972; his uncle Mark, also a Democrat, was a one-term U.S. senator.

The third candidate this Tuesday is Mary Peltola, a former state legislator who is a daughter of a Yup'ik Eskimo. A Democrat who has emerged as a factor in her own right, she could even win a plurality of first-place votes on Tuesday. But that would not be the end of the story, because a first-place plurality is not enough.

Alaska has just installed a new ranked-choice system, like the one used in Maine and New York City and elsewhere. It allows each voter to vote for more than one candidate, ranking them by order of preference.

If no one gets over 50% on first count, the two with the most first-place votes proceed to an "instant runoff" — a tally of their respective second-place votes. If a candidate has enough of an advantage in the second tally it can overcome a deficit in the first.

Because third-place votes at this point may be the kiss of death, the contest becomes less a popularity contest than an unpopularity contest. The candidate liked best by some but liked least by too many others is not going to win.

Negatives can weigh heavily

One of the arguments for the ranked-choice system has been that it encourages candidates to be more congenial and supposedly discourages negative campaigning.

But Begich's ads have been tough on Palin. One says "she left Alaska to be a celebrity." A voice in another says "vote smart, not Sarah." It was widely noted that she missed a candidate debate this summer for a fundraiser in Minnesota.

And while she was a charismatic force in the 2008 presidential campaign, she has not faced any voters since quitting midway through her one term as governor in 2009. Some Republicans have still not forgotten how she won that term, challenging an incumbent Republican. A recent poll by Alaska Survey Research showed her to be viewed unfavorably by 60% of Alaskans, far more than either Begich or Peltola.

Surveys have shown voters in other places have found the system reasonably easy to use and like the chance to make more than one choice. Trump, for his part, has weighed in calling the system "crap."

He might be even less enamored of it if it frustrates Palin on Tuesday. She was among the first famous Republicans to support him in his presidential quest, and he was pleased to return the favor.

But he will likely console himself by thinking about Wyoming.

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