Now, with less than a week until the Iowa caucuses and with Bernie Sanders advancing in the polls, Hillary Clinton still hasn't been able to clear away the accusations of dishonesty that have clouded her campaign. At the Democratic presidential town hall on Monday, a Sanders supporter noted that it's a reason Clinton has struggled to attract young voters: "I've heard from quite a few people my age that they think you're dishonest," he said.

Here's the thing, though: There was no cherry tree. Washington's biographer apparently fabricated it. "The great founding myth of American political integrity, chopping down the cherry tree, is, in fact, itself a lie," said Martin Jay, a historian at the University of California at Berkeley and author of a book called "The Virtues of Mendacity."

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That's the real lesson of the tale of Washington's cherry tree: Americans might just be overly attached to the ideal of a scrupulously honest president. Especially at a time of intense polarization in Congress, recent experience suggests that the direction of public policy will have little to do with whether the Oval Office's next occupant really believes what he or she says on the campaign trail.

"It's necessary, in politics, to have a certain willingness to bend the truth," Jay said. "You're not electing the pope."

'Say anything to get elected'

A plurality of Democratic voters and those inclined to vote for Democrats say Clinton is not as trustworthy as Sanders, according to a poll by The Washington Post and ABC News released Wednesday.

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For Democratic primary voters, those figures raise the question of whether she can be trusted to advocate for the progressive agenda she has espoused during her candidacy, if she wins.

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Clinton was pushed to address that question during a debate in October: "You were against same-sex marriage. Now you're for it," CNN's Anderson Cooper said to her. "You defended President Obama's immigration policies. Now you say they're too harsh. You supported his trade deal dozens of times. You even called it the 'gold standard.' Now, suddenly, last week, you're against it. Will you say anything to get elected?"

"I have been very consistent. Over the course of my entire life, I have always fought for the same values and principles," the former secretary of state replied. "I do absorb new information. I do look at what's happening in the world."

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That willingness to consider the evidence and to reconsider one's opinions is the kind of trait you might value in an employee or a colleague, said psychologist David Rand of Yale University. Yet voters don't like to see it in politicians.

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Rand and his colleagues have argued that's because, as a result of eons of human evolution, keeping our promises has become intuitive. We often act honestly and unselfishly without even thinking about it. As a result, Rand argues, we feel that people who seem to act on emotion and impulse are more trustworthy.

Reasoning logically, assessing arguments and evidence — those things don't come naturally. Consequently, in Rand's view, there's something unsettling about watching the cogs turn in someone's head. We tend to trust people who make decisions with their guts instead of their brains — even if those decisions are ultimately the same.

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That goes for politicians, as well. What Rand sees as Clinton's sober and deliberative demeanor could be exactly what voters distrust.

'The essence of democracy'

The democratic process, however, is not conducive to this kind of intuitive decision-making. Politicians must deal with their ideological adversaries, making calculations about which of their priorities are most important to them and on which points they can compromise.

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"Picking candidates that don’t compromise is not good for democracy," Rand said, "because the essence of democracy is compromise."

Often, when candidates whom voters perceive as making decisions based on emotion and intuition win office and begin to compromise with their opponents, their supporters feel betrayed.

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Followers of Sanders should be prepared to experience that frustration, argued John Hudak, a political scientist at the Brookings Institution.

"Republicans in Congress are not going to raise everyone’s taxes," he said. "Republicans in Congress are not going to approve a health-care reform package that makes Obamacare look capitalist, which it is. Republicans in Congress are not going to provide free college education to every student."

If the senator from Vermont were to win the general election, he would have to compromise with Congress on many of his democratic-socialist objectives.

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"You’ll see his supporters also becoming disaffected and discouraged by the realities of politics and the realities of governing," Hudak said.

'Sticking points'

For progressive voters looking for the candidate who could best advance their goals in the White House, personal traits other than honesty might be more relevant: skill in negotiation, say, or in managing the bureaucracy or the press.

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These traits aren't incompatible with honesty, but it might be difficult psychologically for a candidate to convince voters that she is both trustworthy and a savvy negotiator.

Both Sanders and Clinton could make compelling arguments to voters on these grounds. Despite his revolutionary rhetoric, Sanders has a record of successful bipartisan negotiation in his 25 years in Congress.

The two leading Democratic candidates are "two serious individuals running for the nomination who have a lot of experience dealing with Republicans," Hudak said. "They know the people involved. They know the procedures. They know the sticking points and the places where agreement might be found." And Martin O'Malley, the third contender, can appeal to voters on the basis of his experience as a former governor of Maryland.

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A case in point is the presidency of Clinton's husband. By the end of his tenure, amid a scandal surrounding his personal life and impeachment proceedings in Congress, President Bill Clinton was widely distrusted. Only 39 percent of respondents called him honest and trustworthy in a poll conducted by CNN just before he left office in 2001.

Yet the vast majority of Americans thought he was a good president. In a poll conducted by Gallup immediately after the president's impeachment in 1998, no fewer than 73 percent of Americans said they approved of Clinton's handling of the job.

"I don't think that honesty and effectiveness necessarily go hand in hand," Hudak said. "At the end of the day, if she's [Hillary Clinton] elected president and she's effective, people aren’t going to care too much."