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Republicans have largely avoided tea-party rebellions this primary season. Worst-case scenarios for the party — electing people so far to the right in primaries that they would be vulnerable against Democrats — failed to materialize in North Carolina, Georgia, Colorado and Iowa, while incumbent senators prevailed in Mississippi, Kansas, Tennessee and Kentucky.

But there’s still one contest in which Republican primary voters could ruin the establishment’s plans: Alaska, where on Tuesday the state’s GOP voters will choose who will challenge Mark Begich, the incumbent Democratic senator.

Polls suggest that the party establishment will win this final primary, but between the challenges of polling in Alaska and a strange name game, there’s plenty of uncertainty.

The contest is a three-way race between Dan Sullivan, a former state attorney general and natural-resource commissioner; Mead Treadwell, the well-known lieutenant governor; and Joe Miller, a tea party-backed candidate who defeated Lisa Murkowski in the 2010 Republican primary but eventually lost to her write-in candidacy in the general election.

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Sullivan is generally regarded as the favorite. He has raised more money than his opponents and has won the support of a fairly broad group of conservative and business organizations. He also won prominent support from Republican strategist Karl Rove.

Sullivan has led in every poll conducted this year, including four surveys since June 1 in which Sullivan had an advantage of around 10 points. Treadwell has been in second place in every poll, holding around 25 percent of the vote. Miller has languished in third, with around 15 to 20 percent of the vote, so it seems the Republicans will avoid a worst-case scenario in facing Begich.

Nonetheless, doubts about Sullivan’s primary chances remain.

Sullivan has faced millions of dollars in negative advertisements, mostly from Begich and his allies. Sullivan has been attacked as an outsider — he was born in Ohio, moved to Alaska after law school in 1997, left for Washington, D.C., in 2002 and returned to Alaska in 2009. The outsider charge is a serious one in a state separated from the rest of the country by hundreds of miles.

There’s not much evidence, at least in the public polls, that these attacks have dented Sullivan’s support. But his modest lead is not especially convincing because polling errors in primaries are usually larger than those in general elections. That may be especially true in Alaska, a state known for being challenging to poll.

That reputation stems from an uninterrupted string of polling errors going back a decade: In 2004, Murkowski trailed in the only two nonpartisan polls of October, yet won; Begich was thought to have a significant lead in October 2008, but he won by only a point; Barack Obama was thought to trail by perhaps 10 to 15 points in 2008, but he lost by more than 20; Murkowski trailed again in 2010, but her write-in campaign ultimately prevailed.

Explanations for these misfires vary.

The state is at once one of the nation’s most urban — only New York City has a larger share of its state’s residents than Anchorage — and one of the most rural; two-thirds of Alaska’s communities aren’t accessible by road and depend on satellite- and cellular-based telecommunication.

The state’s far-flung populations — including the native people of Alaska, who represent 14 percent of eligible voters — are hard to reach to pose poll questions.

The population of the state is no greater than that of the average congressional district. In today’s era of low response rates, pollsters might find themselves running out of telephone numbers associated with active, registered voters.

There were only 300,000 voters in the 2012 general election.

These challenges are even more acute in low-turnout Republican primaries, which pose problems for pollsters anywhere in the country. Errors edging near 10 points have been fairly common in Republican primaries this year, and Alaska’s Republican primary is more like a congressional primary than a typical Senate contest.

Only 100,000 voters participated in the 2010 Republican Senate primary. The sole pre-election poll four years ago showed Murkowski leading Miller by 32 points, 62 to 30, yet Miller won by 2 points.

The ballot itself poses another, unusual complication: the presence of another Dan Sullivan, who happens to be the mayor of Anchorage.

The question is whether Dan Sullivan — the Senate candidate, to be clear — has been benefiting from sharing the same name as the Anchorage mayor, who’s quite popular among Republicans for taking on unions.

Both Sullivans will appear on the ballot; the Anchorage mayor is pursuing the office of lieutenant governor, vacated by Treadwell. No one knows how voters will react when some of them learn, perhaps even at the ballot box, that there are two Republican Sullivans.

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