Authority
Respect for authority is built into our moral foundations as a key evolutionary mechanism for facilitating group dynamics, leadership, and sexual selection.
Hierarchical social organization is closely related to authority. Some philosophers and authoritarians over-emphasize the importance of hierarchy, using the debunked [1][2] pseudoscientific concept of the alpha male to justify acting like an asshole. Social media has turned this into a phenomenon called the manosphere. Jordan Peterson is a psychologist and philosopher popular with these men because he reinforces the importance of dominance hierarchies on the premise that they are "natural" and therefore good.
Jonathan Haidt points out that progressives generally fail to make appeals to our instinct for authority, preferring to focus on justice, and see hierarchy as inherently oppressive. This puts them at a disadvantage when it comes to persuasion, since a large portion of the public still responds strongly to projection of authority. This has helped allow things like alt-right neo-fascism and the manosphere to proliferate.
How can we make progressive appeals to authority that fit with our equal justice ideals?
Authority of Expertise
This will take a lot of restoration of trust in institutions, but the authority of expertise is the only real authority we truly have in an age of extreme complexity and specialization. We must be able to trust experts, and their education and experience needs to command authority within their domain.
Authority of Experience
Age has often been used as an excuse to command unearned respect outside of one's domain of expertise. Many young people have been burned when they were told to "respect their elders" but found their elders' expertise lacking. This is especially true in an age of technology, where the young have a significant advantage over the old when it comes to learning and adopting new tech. It is no longer the case that old people are wiser about things generally, when so many relevant things arrived long after their critical periods had closed.
A new model is needed, where we can respect the wisdom of experience, but acknowledge that with age does not necessarily come expertise. What matters is how long you have been working in the domain in question.
While we should still respect our elders in terms of care and dignity, when it comes to advice we should respect experience. Reinforcing this notion through education and ritual the way that "respect your elders" used to be will help solve the kinds of problems we are seeing with younger generations joining the workforce and not being able to take orders and advice.
Official Types of Authority
Sociology has mapped the types of authority and leadership styles. This article outlines them.