There are many such examples. When parents think that vaccinations are dangerous, pro-vaccination messages can make them even more wary. And after reading a correction of their original belief that the Affordable Care Act contains death panels, conservatives ended up more strongly committed to that belief. (There is every reason to think corrections can be counterproductive for liberals as well.)
What explains these findings? The first answer is that whenever people have a firm conviction, efforts to correct their errors by invoking the facts might well trigger a negative emotional reaction, intensifying their commitment to what they originally thought. It's not a lot of fun to be told that you're wrong, and your response might be to insist even more strongly that you're right.
The second and subtler answer is that corrections can reinforce the very narrative that led to the original conviction. If liars say they aren't lying, well, isn't that just another lie and so further evidence that they are liars?
Which brings us to Trump. His supporters pride themselves on their independence; many of them are angry, and they are fiercely committed to him. Even more than most people, they don't like anyone who talks down to them. As a former Mitt Romney and current Trump supporter said in the aftermath of Romney's anti-Trump speech: "You're telling me who to vote for and who not to vote for? Please."
In Washington, Republican officeholders appear keenly aware that if they come out against Trump, they might actually help him. He presents himself as an outsider who is leading an insurgent campaign; high-level Republican opposition feeds that narrative. It's further evidence in his favor.
So what might they try instead? For one thing, those who oppose Trump might want to focus on the right messenger even more than the right message. Behavioral research strongly suggests that if you want citizens to shift on a contested topic, such as climate change, you need "surprising validators" people who can be counted as "one of us" rather than "one of them." Because of his close connection with evangelicals, Sen. Ted Cruz has had some success with this strategy (as Sen. Marco Rubio has not).
But the message matters too. If a candidate can be made to appear a bit ridiculous, he's in trouble. In the Republican debates, the most effective anti-Trump line belongs to Cruz: "Count to ten, Donald." Many of Trump's supporters believe that he is strong and tough, a natural leader. Anything that counteracts that impression, and makes him appear more like a cartoon, can be helpful, at least if it does not look high-handed or condescending.
In recent history, the closest analogue to Trump's candidacy is probably that of Ross Perot in 1992. As late as June, Perot led both Bill Clinton and George H.W. Bush with 39 percent of the popular vote. Yet over just a few months, his level of support fell by half. Despite several missteps and controversies, there was no single trigger; millions of former enthusiasts simply came to see him as a kind of self-parody an impressive figure in business to be sure, but ill-suited to be commander-in-chief. In the blink of an eye, Perot suffered from a kind of cascade effect, in which sharply negative impressions spread rapidly from one person to another.
As of now, Trump seems to be a far more formidable candidate than Perot, and this is an angrier and more polarized time. For those who oppose his candidacy, the simplest advice is not to rely on messengers who end up fortifying the narrative of those who are drawn to him and to enlist those that can make that narrative seem preposterous.
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Bloomberg View columnist Cass R. Sunstein, the former administrator of the White House Office of Information and Regulatory Affairs, is a professor at Harvard Law School.