“It’s nearly three years since I, along with 17. 4 million other Britons, voted for Brexit. Today I have to admit that the Brexit project has gone sour.” So began the Daily Mail columnist Peter Oborne’s widely shared piece on why he changed his mind about Brexit. The article stood out because it was a rare example of someone changing their mind and admitting to it in public.

All too often we get locked into our beliefs. We seem incapable of changing our mind, no matter how compelling the evidence is that we are wrong. An extreme example of this was uncovered in 1956, by the American social psychologist Leon Festinger and his colleagues. They studied a cult that believed planet Earth would be destroyed by a great flood on 21 December 1954. Its followers also believed a select group of true believers would be saved when an alien spaceship arrived to collect them. At midnight on the allocated date, the members of the cult gathered and prepared to be saved by aliens. When the end of the world didn’t come, and the aliens didn’t arrive, they were stunned. Instead of dropping their precious beliefs they revised them. Their leader told them that the god of Earth had decided to give Earth a second chance. These cult members show us the lengths people will go to preserve their beliefs when faced with overwhelming evidence to the contrary.

If we’re faced with a steady stream of facts that cut against our beliefs, we can start to feel uncomfortable

Since Festinger, many psychologists have observed that when we are faced with data that undermines our beliefs, we stick with our beliefs and ignore the data. Even so, while we are remarkably wedded to our beliefs, we sometimes do change our mind. The big question is why.

One reason is facts. We tend to ignore facts that don’t fit with our beliefs, but we’re not entirely deaf to disturbing data. If we’re faced with a steady stream of facts that cut against our beliefs, we can start to feel uncomfortable. As our anxiety builds we approach a tipping point, when our beliefs suddenly shift. For instance, the steady stream of data about school shootings has eventually led some US gun owners to change their mind about gun control.

We are also more likely to change our mind when we talk to members of our community who have done so. One analysis of changing attitudes to same-sex marriage in the United States found the number one factor that explained why a person changed their mind was contact with someone like them who had changed their opinion. These one-to-one conversations helped shift public opinion in the US from being 68% against same-sex marriage in 1996 to 67% for same-sex marriage by 2018.

The way an argument is presented can help to change our mind. If we hear an argument that appeals to values that aren’t our own, we’re likely to ignore it. But if the same point is made by appealing to values we hold dear, we’re much more likely to listen.

For instance, if you tell a conservative that a small tax rise for wealthiest 1% will get rid of social injustice, they’re unlikely to listen to you. If you tell them the same policies will help to preserve families, they may prick up their ears. That’s because by making arguments about social justice, you’re referencing values that inspire people on the left but which conservatives are less attached to. But by talking about family, you’re appealing to core conservative values.

Another reason we change our mind is because our behaviour has changed. The 17th-century French philosopher Blaise Pascal captured this perfectly when he pointed out that if you wanted to believe in God, the best thing to do was to kneel down, begin to pray, and then you will begin to believe. Centuries later, psychologists began to catch up. For instance, one classic study found that people who were given a boring task with meagre rewards tended to tell others the task was actually interesting and rewarding. By changing their mind about the task, they were able to feel better about what they had been doing.

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Changes in the world around us can also push us to change our mind. When big changes are introduced that cut against our beliefs, we have a remarkable capacity to simply accept the change. For instance, when a ban on bottled water was announced in San Francisco, many residents accepted it and changed their attitude to bottled water. What was once seen as a necessity became a pointless pollutant.

Finally, when we experience a significant event that has direct personal impact on us, we are also more likely to change our mind. For instance, after the devastation of Hurricane Irene and Sandy, residents of coastal New Jersey who were generally against environmental policies changed their views and embraced green politics after the storm. The shift was particularly stark among residents who had suffered significant personal losses due to the hurricanes.

Changing our mind can be a difficult thing to do. But it is possible. What’s so surprising is that when we do actually change our minds, we often start to think that we thought this way all along.

• André Spicer is professor of organisational behaviour at the Cass Business School at City, University of London