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Several US politicians could win re-election despite facing highly-publicised accusations of impropriety. What does it take to get voted out of office?

There's the married Christian who was filmed kissing a staffer. The law-and-order congressman accused of a $1 million tax fraud. The anti-abortion conservative who once asked a mistress to terminate a pregnancy.

Each is a sitting congressman. Each is on the ballot for the 4 November US elections, and each believes they can win.

Take Michael Grimm. In April the New York Republican was indicted on 20 criminal charges, all of which he denies. Prosecutors accused him of concealing more than $1m.

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Grimm - who in January apologised after threatening to throw a reporter off a balcony - is the front-runner in the race for his district. A recent poll showed him leading his Democratic challenger by 44% to 40%.

In Tennessee, pro-life doctor Scott DesJarlais was recorded pressuring a former patient with whom he had an affair to terminate her pregnancy. He was accused of asking other women to seek abortions and reprimanded by the Tennessee Board of Medical Examiners for affairs with patients. His ex-wife said he had shown "violent and threatening" behaviour towards her.

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The allegations emerged just before the last congressional elections in 2012, and it was widely predicted DesJarlais's career would be over this year. But he won the Republican primary in his district by 37 votes, and local media have described him as the "odds-on favourite" to prevail on 4 November.

Then there's Vance McAllister, who was filmed embracing an aide who happened not to be his wife. Recent surveys have suggested he is likely to take the race in his Louisiana district to a run-off.

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You might expect that in an era of relentless 24-hour media coverage and vicious negative campaigning, stories of this kind would be career-ending.

But in a post-Watergate, post-Lewinsky age, the public have become inured to the notion that politicians are flawed, says Alison Dagnes, professor of political science at Shippensburg University.

We shift our attentions really quickly. The next scandal comes along Alison Dagnes, Shippensburg University

"There's so much to pay attention to. We shift our attentions really quickly. The next scandal comes along," adds Dagnes, who co-edited Sex Scandals in American Politics.

These days, says Dagnes, for a sex scandal to shock anyone "there had better be a llama involved". At the same time, a softening of public attitudes towards divorce, homosexuality and drug-taking mean each no longer spells career doom in Washington.

Plenty of current members of Congress have successfully put embarrassing revelations behind them.

New York Democrat Charlie Rangelwas censured by the House of Representatives in 2010 for 11 violations of ethics rules, including failing to pay income tax. He was re-elected in 2012 with 91% of the vote.

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There's also Mark Sanford of South Carolina. As state governor he claimed he had gone on a walking holiday. Instead, he was in Buenos Aires with his Argentine mistress. The incident cost Sanford his marriage and ensured "hiking the Appalachian Trail" became a euphemism for infidelity.

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But it didn't prevent him winning a special election for his old House seat in 2013, backed by 54% of voters. This year he is running unopposed.

In Florida's gubernatorial race, the fact Republican incumbent Rick Scott ran a healthcare company that was fined $1.7 billion for Medicare fraud has been an issue. Scott insists he knew nothing of illegal practices.

They usually can survive if they are in a safe seat Brendan Nyhan, Dartmouth College

A 2012 academic study of over 250 House of Representatives hit by scandals since Watergate found that the careers of around 40% did not survive. Almost three quarters ran in the following election and roughly four-fifths were re-elected, but on average they lost more than 5% of their vote.

Given the decline in the number of swing districts, this margin can be sustained by most congressmen and women, especially in the US system where incumbents enjoy a strong advantage.

Enough partisans can usually be found to rally behind the cause, whatever the candidate has done.

"They can usually survive if they are in a safe seat," says Brendan Nyhan of Dartmouth College's department of government. "We [as voters] have amazing powers of rationalisation,"

Famous American scandals

Image copyright Getty Images Image caption Richard Nixon resigns in 1974

Watergate : The cover-up of a bungled break-in at the Democratic party headquarters led to President Richard Nixon's resignation in 1974

: The cover-up of a bungled break-in at the Democratic party headquarters led to President Richard Nixon's resignation in 1974 Bill Clinton and Monica Lewinsky : The 42nd president was tried by the US Senate over his relationship with a White House intern

: The 42nd president was tried by the US Senate over his relationship with a White House intern Iran-Contra : Revelation that the US sold arms illegally to Iran in order to fund Nicaraguan guerrillas shook the Reagan administration

: Revelation that the US sold arms illegally to Iran in order to fund Nicaraguan guerrillas shook the Reagan administration Chappaquiddick : Senator Edward Kennedy was involved in a 1969 car accident on Chappaquiddick Island in which a young woman died. Around 10 hours elapsed before the police were notified

: Senator Edward Kennedy was involved in a 1969 car accident on Chappaquiddick Island in which a young woman died. Around 10 hours elapsed before the police were notified Teapot Dome: Albert B Fall, Warren G Harding's interior secretary, jailed in 1929 for accepting bribes after petroleum reserves were leased to oil companies at low prices

Grimm's 11th congressional district, for instance, is the most Republican-leaning seat in New York city.

Those not found guilty of any offence, like Grimm or Scott, can protest their innocence.

The public will forgive everything except a lie Michael Bronstein, Political consultant

For those who have been caught bang to rights, there's another strategy. Say sorry.

On the campaign trail, McAllister has repeatedly owned up to his "personal mistake". DesJarlais admitted his "personal shortcomings" and asked forgiveness from his "fellow Christians".

"The first rule is to tell the truth at all costs," says political consultant Michael Bronstein. "The public will forgive everything except a lie."

McAllister and DesJarlias have clung on in conservative red states, where biblical teachings about forgiveness and mercy are taken seriously.

By contrast, Anthony Weiner and Eliot Spitzer were brought down by sex scandals in liberal New York.

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Weiner apologised profusely and resigned his House seat after he was exposed for sending explicit messages on social media.

The public sympathy this engendered looked enough to propel him to the city's mayoralty - until he was caught sexting a woman who was not his wife a second time.

It shows there's a limit to the public's reserves of sympathy, says Dagnes. "You only get one bite of the forgiveness apple."