Hardheadedness seems to be rampant. From the boardroom to politics to everyday interactions, we often encounter people (and may also find ourselves) upholding a stance despite evidence of its inaccuracy. Take the many well-educated and well-intended individuals who, despite overwhelming factual evidence to the contrary, continue to deny climate change or believe that vaccines cause autism. But what do people think of those who refuse to change their minds? How do leaders, in particular, come across when they steadfastly continue to uphold a stance in the face of contradictory evidence? We performed a series of experiments to find out.