The Alaska Senate race with two Dan Sullivans is at the epicenter of the political world—and could determine whether Democrats take control of the chamber.

Republicans, seeking to protect incumbent Sen. Dan S. Sullivan, have fought and failed for weeks to keep a spoiler—fishing village retiree Dan J. Sullivan—off the ballot. Now the matter is the subject of several legal inquiries that have put the Democratic candidate, Mary Peltola, and the party itself on the defensive. Here is what we know.

The state and the Justice Department each have opened investigations into whether anyone broke the law in their attempt to get the second Sullivan on the ballot. But even fast-moving probes take time, and it is difficult to charge people overnight.

Alaska Republican Gov. Mike Dunleavy ordered the state investigation after the New York Times reported that there was an organized Democrat effort to recruit the spoiler candidate. The governor promised a “thorough and by the book” probe, but said it may not be wrapped up before Election Day.

The Justice Department is moving full steam on its efforts, sending out a new batch of subpoenas on Thursday. It is exploring a theory that people involved in the effort willfully violated the civil rights of voters by confusing them, officials familiar with the probe said. Investigators could rely on a statute, historically used to prosecute police officers for using excessive force, that targets rights-violations by people acting in their official capacities.

Some legal observers are dubious of the Justice Department strategy. A criminal case could be more straightforward if investigators find that someone involved in the alleged scheme lied in official documents or in response to law enforcement inquiries.

There are no federal laws that bar the practice of ballot stacking in general, said Northwestern University law professor Michael Kang. If all Democrats did was seek spoiler candidates, even ones with the same name as an incumbent, “I don’t really see any kind of violation of law there,” he said.

State laws governing election behavior are also unlikely to come into play, said University of Washington law professor Jeff Feldman. “It’s less than clear that the conduct that has been reported would violate any provision of Alaska law,” he said.

The Alaska Republican Party unsuccessfully tried to get Dan J. Sullivan off the ballot in the primary. The Alaska Supreme Court ruled both Sullivans could appear. Both candidates are listed with middle initials, and the incumbent senator’s party affiliation appears next to his name.

Politics is a rough and tumble sport, and both parties have tried to leverage naming confusion to their advantage.

In a 1998 U.S. House race in Georgia, Republicans ran a man named John H. Lewis Sr. against U.S. Rep. John Lewis, the civil-rights leader and longtime Democratic lawmaker. The incumbent congressman won in a landslide. Pennsylvania voters faced a similar name confusion in 2022, when a Republican candidate named Mike Doyle ran for the seat that Democratic congressman Mike Doyle was retiring from. The new Doyle lost to the current incumbent, Rep. Summer Lee.

Sometimes shenanigans have led to legal trouble. In a 1930 Nebraska Republican primary race, some in the party wanted to recruit a spoiler to weaken incumbent Sen. George W. Norris. They landed on a grocer named George W. Norris. The second Norris ultimately didn’t make it onto the ballot. He was later sentenced to three months in prison and fined $100 for perjury after lying to a U.S. Senate committee about who funded his campaign.

The Justice Department had already sued Alaska state officials on Oct. 22 to block them from certifying election results if Sen. Sullivan loses his re-election bid and the votes cast for Dan J. Sullivan Jr. are sufficient to potentially change the outcome.

The Peltola campaign, Democratic Senatorial Campaign Committee and voting-rights groups have intervened in the litigation to seek dismissal of the Trump administration’s effort. Each of them is arguing the administration has no constitutional authority to interfere with how the state runs its election.

The litigation is moving quickly. On Thursday the Trump administration filed an amended complaint referencing the New York Times report, but with broadly similar legal arguments. U.S. District Judge Sharon Gleason, an appointee of President Obama, could issue a ruling in the next few days. Dan J. Sullivan has told The Wall Street Journal that nobody put him up to running.

Peltola on Thursday denied that she knew about an effort to put a second Dan Sullivan on the ballot, the Associated Press reported. “I am not interested in tricking voters,” Peltola said during remarks in a bar in Juneau.

The Democratic Senatorial Campaign Committee said it wasn’t involved with the second Sullivan’s candidacy. “Republicans have a long history of recruiting and propping up candidates in an attempt to boost their own campaigns,” the group said.

In court, its lawyers are arguing that the Justice Department is using the controversy to distract from its own “open effort to interfere with the certification of a potential loss by the president’s favored U.S. Senate candidate.”Republicans who run elections in Alaska are fighting the Justice Department’s lawsuit, signaling they want to certify the Senate results based on the final vote tallies.

But Dunleavy, the Alaska governor, has suggested he may not go along. In a NewsNation interview Thursday, he said, “If we conclude that there were things that should not have happened, let me put it that way, that are illegal, we will act on that. And that may, in fact, impact whether somebody is seated in the U.S. Senate.”If Dunleavy were to refuse to sign off on the certification, a court could order him to do so or allow someone else to his place, said Derek Muller, a Notre Dame law professor.

Peltola would then have a certificate of election to take to Washington “that’s treated like an admission ticket,” Muller said. If U.S. Senate Republicans then attempted to refuse her admission, it could set off a complicated fight with little modern precedent.