Kaj Sotala points us to a finding that people ignore info more when they feel powerful.  On a related note, Michael Nielsen, quantum physicist extraordinaire, suggests a "bias toward power":

A form of bias I’m interested in is the great deference we pay to power, often far more than is warranted by the facts. I’m particularly interested in the damage this does to powerful people, since it greatly reduces the incentive they have to perform well …

• People’s early works, when they are unknown, are often better than their later works, after they’ve become famous. See, e.g., Tom Clancy.

• A professor speaking pretty much complete rubbish, and yet being taken seriously by a group of more junior academics. …

• A professor shutting down a grad student in a group, simply by disagreeing with them. People tend to assume that the professor is right 100 percent of the time, and the student 0 percent. A more accurate breakup in my experience is 60/40. …

• A rich or famous person holding forth on pretty much any subject, from things they understand well, through to things they barely understand at all, and having other people pay serious attention.

People relate to power two ways, via deference and defiance.  When we defer to power, we are indeed biased to give it too much inferential weight, but when we defy power, we give it too little inferential weight.  We listen too much to the powers that we feel allied with, and too little to powers we feel allied against.  To think more objectively, become less allied.