Jan. 1 (Bloomberg) -- Most of us acknowledge that some of our most cherished beliefs are based on faith, not facts. Even so, it takes a lot to dislodge those beliefs. When we are confronted by contrary evidence, we may dig in even more deeply. Consider a cautionary tale, exotic to be sure, but helping to explain why evidence-challenged thinking persists in a lot of areas, including politics and business.

Harold Camping, a Christian radio talk-show host, predicted that the world was going to end on May 21, 2011, with the coming of the rapture. He contended that the Earth would be ravaged, that all human beings would be judged, and that believers would ascend to heaven. He said that those who weren’t saved would experience five months of “hell on earth” until the annihilation of creation on Oct. 21, 2011.

Camping’s program could be heard daily on his network, Family Radio, one of the largest Christian broadcasting networks in the U.S., which benefited from a budget of tens of millions of dollars. His prediction was followed by millions of people around the world, and a lot of them seemed to believe it.

But did they, really? Social scientists have offered two different hypotheses about those who appear to hold extreme beliefs.

The first is that they are entirely sincere. They are influenced by figures of authority and also by trusted peers. When they express a belief that the world is ending -- or any other extreme belief that is essentially a matter of faith -- they mean it.

Sincere Belief

The second hypothesis is that people who purport to accept extreme beliefs often lack conviction and are responding to social pressures. If you could somehow get them in private, you would find a lot more skepticism, uncertainty and doubt.

It isn’t easy to test the competing hypotheses. Economist Ned Augenblick of the University of California at Berkeley and his co-authors have now provided such a test. At least for Camping’s followers, the answer is unambiguous: Their belief was entirely sincere.

Here’s how the test went. Four weeks before May 21, 2011, Augenblick and his co-authors asked a number of Camping’s followers: Would you prefer to have $5 today or some greater amount of money after May 21? That greater amount ranged up to $500. The researchers posed exactly the same questions to members of the Seventh-day Adventist Church, who also believe that Judgment Day is coming, but not by a specified date.

The median cutoff answer from the Seventh-day Adventists was $7 -- well within the range of answers given by most people. By contrast, the median cutoff answer from Family Radio members was $500, meaning that they would prefer $5 now to $500 on May 22. As far as the researchers could tell with the payments they offered, there was no amount that Family Radio members would prefer on May 22 to $5 today -- compelling evidence that they sincerely believed that the rapture was coming on May 21.

We know, of course, that the rapture didn’t come on that day. Did Family Radio members conclude that the whole idea was a fraud? Not at all.

Camping himself quickly recovered, insisting that he had been correct, but that the world wasn’t ending for a while, because of a divine decision to delay implementation: “On May 21 Christ did come spiritually to put all of the unsaved throughout the world into judgment. But that universal judgment will not be physically seen until the last day of the five month judgment period, on October 21, 2011.”

This kind of fancy footwork is characteristic of leaders and followers, who often respond by doubling down in the aftermath of false apocalyptic prophecies.

Contrary Evidence

For decades, social psychologists have invoked findings of this sort to support the idea that people seek to avoid “cognitive dissonance” by dismissing evidence that is inconsistent with their deepest beliefs. When people are sincerely committed to the truth of some proposition, they will work hard to hold on to it, even if the facts stand in their way.

Our desire to maintain our deepest convictions may be so intense that contrary evidence doesn’t merely fail to undermine those convictions; on the contrary, and bizarrely, it may fortify them. For example, researchers have found that after hearing about apparently credible evidence to the contrary, many people who believed that Iraq had weapons of mass destruction ended up thinking the same thing they thought before -- only more strongly.

The good news is that in the face of clear contradictory evidence, people eventually find it hard to maintain false beliefs. In May 2012, Camping asked for forgiveness for his mistaken prediction about Judgment Day. “God has humbled us through the events of May 21,” he wrote. “We must also openly acknowledge that we have no new evidence pointing to another date for the end of the world.”

(Cass R. Sunstein, the Felix Frankfurter professor of law at Harvard University, is a Bloomberg View columnist. He is the former administrator of the White House Office of Information and Regulatory Affairs, the co-author of “Nudge” and author of “Simpler: The Future of Government,” forthcoming in 2013. The opinions expressed are his own.)

To contact the writer of this article: Cass R. Sunstein at csunstei@law.harvard.edu.

To contact the editor responsible for this article: Katy Roberts at kroberts29@bloomberg.net.