The legend of Steve Jobs is that he transformed our lives with the strength of his convictions. The key to his greatness, the story goes, was his ability to bend the world to his vision. The reality is that much of Apple’s success came from his team’s pushing him to rethink his positions. If Jobs hadn’t surrounded himself with people who knew how to change his mind, he might not have changed the world.

For years Jobs insisted he would never make a phone. After his team finally persuaded him to reconsider, he banned outside apps; it took another year to get him to reverse that stance. Within nine months the App Store had a billion downloads, and a decade later the iPhone had generated more than $1 trillion in revenue.

Almost every leader has studied the genius of Jobs, but surprisingly few have studied the genius of those who managed to influence him. As an organizational psychologist, I’ve spent time with a number of people who succeeded in motivating him to think again, and I’ve analyzed the science behind their techniques. The bad news is that plenty of leaders are so sure of themselves that they reject worthy opinions and ideas from others and refuse to abandon their own bad ones. The good news is that it is possible to get even the most overconfident, stubborn, narcissistic, and disagreeable people to open their minds.

A growing body of evidence shows that personality traits aren’t necessarily consistent from one situation to the next. Think of the dominant manager who is occasionally submissive, the hypercompetitive colleague who sporadically becomes cooperative, or the chronic procrastinator who finishes some projects early. Every leader has an if…then profile: a pattern of responding to particular scenarios in certain ways. If the dominant manager is interacting with a superior…then she becomes submissive. If the competitive colleague is dealing with an important client…then he shifts into cooperative mode. If the procrastinator has a crucial deadline coming up…then she gets her act together.

Computer code is a string of if…then commands. Humans are a lot messier, but we too have predictable if…then responses. Even the most rigid people flex at times, and even the most open-minded have moments when they shut down. So if you want to reason with people who seem unreasonable, pay attention to instances when they—or others like them—change their minds. Here are some approaches that can help you encourage a know-it-all to recognize when there’s something to be learned, a stubborn colleague to make a U-turn, a narcissist to show humility, and a disagreeable boss to agree with you.