With great power comes great responsibility. (AP Photo/Carolyn Kaster, File)

Let's get back to basics for a minute: How does democracy work? The classic understanding is that citizens form opinions on various issues, and then elect representatives who share those opinions. Moreover, when politicians deviate from the will of their constituents while in office, voters can simply vote them out of office in favor of a candidate more closely aligned with their views. Government by the people, for the people, and reflecting the will of the people.

As you might imagine, political scientists' understanding of this relationship between public opinion and politician behavior has grown more complicated in recent decades. Some argue that politicians shape public opinion by showing that their positions are consistent with voters' underlying values. Other research suggests that voters often support policies simply because their favorite political leaders do.

Now, a paper by political scientists at UC Berkeley and the Washington University in St. Louis reports on the results of a novel real-world experiment. The study finds that contrary to classic theories of democracy, voters did not view politicians more negatively when the politicians took positions voters opposed. Not only that, voters often adopted these positions themselves, even when politicians offered little or no justification for them.

These results "leave open the possibility that politicians think the constraints public opinion places on them are stronger than they are," the authors conclude, and they suggest that "politicians can enjoy broad latitude to shape public opinion."

Here's how the experiment worked: The researchers recruited 7 Democratic state lawmakers in an unnamed midwestern state. In the spring of 2014, the researchers surveyed registered voters in the lawmakers' districts to determine which issue positions had the least public support. The issues included everything from immigration to taxation to marijuana policy.

The legislators then sent official letters to registered voters of both political parties in their respective districts. The letters were targeted toward voters who had expressed opinions that were at odds with the lawmakers' own stances. The voters were randomly assigned to receive one of three letters. From the report:

(i) a “control” letter where the legislator introduced themselves, described the services their office could conduct for constituents, and described a few locally oriented achievements (e.g., designating a building downtown a historic place),

(ii) a “direct” policy letter that added language in which the legislators took a position the recipient had not agreed with previously and made only the briefest justification for their position, and

(iii) an “arguments” policy letter that added extensive arguments for this position designed to appeal to citizens’ values

Finally, they performed a follow-up survey of the constituents to see how their opinions of both the issues and the politicians had changed, if at all. As it turns out, the positions staked out by the legislators had a significant effect on their constituents views: "The constituents who were sent letters with the legislators’ positions were about 5 percentage points less likely to disagree with the legislator and about 5 percentage points more likely to agree with the legislator."

More surprisingly, it didn't make a difference whether politicians provided good arguments for their positions or not: "We find little evidence that legislators’ arguments were responsible for their persuasive impact. Legislators appeared able to move constituents’ opinions by stating their own positions with minimal justification; adding additional arguments did not make them more persuasive."

Finally, lawmaker favorability was completely unaffected by knowledge of their policy stances. "We find no evidence that legislators suffered electoral costs by taking positions constituents disagreed with; citizens who received letters from their legislators taking positions they had disagreed with previously evaluated their legislators no less favorably."

"We were surprised by the fact that there wasn't any pushback from the constituents in terms of disapproval," co-author Dan Butler said in an interview. Since voters tend to not know a lot about their state legislators, the expectation was that finding out about a disagreement would lead voters to perceive them more negatively.

"It seems like a lot of people are predisposed to trust their legislators, even on policies we think of as inspiring a lot of controversy," co-author David Broockman said. "Most legislators really do care about advancing the public interest. What's exciting here, and the reason why the lawmakers were interested in participating in the study, is that it gives them insight into whether they can help advance those causes further."

We tend to think of voters' political views as fixed and immobile, particularly in the current environment of polarization and partisanship. But these results suggest that politicians do have some latitude to sway voters' views.

Moreover, it doesn't seem likely that voters changed their views due to raw political tribalism. The letters from the lawmakers didn't include information on party affiliation at all. "What this points toward is a world where politicians actually have special responsibility to inform the public because they are afforded special trust," Broockman said. "The costs associated with doing the right thing according to their values are not as significant as they think."

That "special responsibility to inform" is a key point. The optimistic takeaway here is that legislators with sincerely-held beliefs have some power to bring constituents over to their side. But the flipside is that demagoguery may be more politically potent than previously assumed. For instance, Sarah Palin sold many voters on the false notion of Obamacare "death panels" as far back as 2009. Five years later, 34 percent of voters still believe in them.