For nearly a month, Alaska’s House of Representatives has been unable to agree on who should lead the body, an impasse that has ground legislative action to a halt even as the state faces tough choices over steep budget cuts.

Republicans control 23 of the 40 seats in the state House. But three of those Republicans, and one independent, have voted against their own party’s candidates for House Speaker, leaving the chamber without a leader for four weeks.

“I think Alaskans pride themselves on our politics being unusual,” said John-Henry Heckendorn, a political strategist in Anchorage.

State Rep. Mark Neuman, the first Republican nominated to be speaker, lost on a 19-20 vote. A week later, on Jan. 22, state Rep. Dave Talerico (R) mustered 20 votes for speaker — but 20 voted against him, too. Last week, Talerico lost again, in another tied 20-20 vote.

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State law requires the Speaker to muster 21 of the 40 votes to win election.

The hold-up comes from state Rep. Gary Knopp (R), who represents the Kenai Peninsula. Knopp said in December he would join two other Republicans to withhold votes from either the Republican or Democratic nominees for speaker in hopes of forming a bipartisan coalition.

“The Republicans were trying to organize around a 21-member majority, which means anybody could hold the caucus hostage,” Heckendorn said. “Gary was looking at it and saying, this is a recipe for failure.”

The House did manage to elect a temporary Speaker, Rep. Neal Foster (D) — though only so that a new member could be sworn in to fill a vacancy.

Foster’s power was so circumscribed by the rest of the House that his powers have been reduced to gaveling the chamber into order, inviting a chaplain to give an invocation and then quickly gaveling the sessions closed.

The delay in selecting a Speaker has now become the longest legislative logjam in Alaska’s history.

Without a speaker, the House cannot form committees to hold hearings on potential legislation. The body cannot vote on bills or conduct most other legislative business.

So while the state Senate plows through legislation and Gov. Michael Dunleavy (R) lays out his first-term agenda, the House stalemate has become a governmentwide stalemate.

The legislature’s daily journal tells the story of stagnation: On Jan. 19, the fifth day of session, House members were on the floor for less than a minute.

On Jan. 25, the 11th day in session, they made it 13 minutes before adjourning. Three days later, the session lasted for two minutes. On Feb. 1, they ended session after 11 minutes.

In the meantime, legislators who travel across the state — in some cases from more than a thousand miles away — are collecting $50,400 salaries, and $275 a day in per diem allowances.

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And the state faces big challenges ahead, as pension and retirement obligations rise. Dunleavy has proposed cutting $1.6 billion in spending on state services.

He has also proposed giving Alaska residents a higher payout from the state’s Permanent Fund, an annual dividend that comes from oil and gas severance taxes.

Dunleavy’s proposal, which is already competing with both more aggressive and more conservative plans in the legislature, would give Alaska residents an extra $3,600 over the next three years.

None of those measures can advance without the House electing a Speaker.

A bipartisan coalition of eight members say they are nearing a power-sharing agreement that could result in a new Speaker — or Speakers, one from each party — based on a bipartisan deal struck in Montana a few years ago.

But others have broached potential solutions as well.

“There’s 40 members, but there’s probably 87 ideas,” state Rep. Lance Pruitt (R), a member of the negotiating coalition, told the Anchorage Daily News

Alaska’s political history is littered with the bizarre.

In 1990, Gov. Wally Hickel — who had served as Richard Nixon’s secretary of the Interior — won election on a secessionist party’s ticket.

In 2009, Gov. Sarah Palin (R) resigned in the midst of her first term, after her failed run for vice president.

The next year, Sen. Lisa Murkowski (R) won a write-in campaign after losing the Republican primary to a conservative upstart.

And in 2014, voters elected Gov. Bill Walker, who became one of just a handful of independents ever to win a governorship.

Coalition governments are nothing new either.

While Republicans controlled 22 of 40 seats in the last legislative session, three of those Republicans joined two independents and 17 Democrats to hand the Speakership to state Rep. Bryce Edgmon, a Democrat.

Edgmon, who represents Dillingham in Bristol Bay, has been nominated as Speaker twice this year. He has declined the nomination both times, and he did not respond to an email seeking comment.