What is Authority?
This principle states that people are more likely to follow the lead of knowledgeable experts. For example, Physiotherapists can get more of their patients to stick to recommended exercise programs if they display their medical diplomas on the walls of their therapy rooms.
When designing experiences, we need to signal to potential customers and users what makes you a credible authority, which will in turn make you more persuasive.
Authority in the Real World
Consider one of the most famous examples of people being persuaded by a percieved authority - the Milgram experiment.
Researchers at Stanford University measured the willingness of participants to obey an authority figure. This person instructed them to perform acts that conflicted with their moral code.
Study participants were told (falsely) they were recruited to help run an unrelated experiment, in which they were instructed to give electric shocks to a "learner." These shocks were fake, but the participant was led to believe that they were real. The shocks were gradually increased to a level that would have been fatal (if real).
The experiment found that most people would obey an authority's instructions to administer painful shocks. This is due to the persuasive power of perceived authorities (like doctors and professors).