There are relationships where one has authority over the other. A judge is expected to be fair to every citizen so on the level of fairness he is expected to be friendly. There is also a certain expectation of civility and respect we are to give to our fellow man and other people regardless how uncivil they may seem. We also expect a judge or politician to be honorable and we give honor due in exchange for a certain level of respect and submission to them. Submission is considered a bad word for our free society but it simply means that we obey rulings and laws. But this is contingent on justice. If a person in authority becomes self seeking, we call them a tyrant. Free people are expected to submit only as long as the agreement for both freedom and security is being honored. Government and citizens stay friends as long as there is justice.
We have examined the three grounds for friendships, utility, pleasure and commonality. There are also two types of these; ranging from those based in superiority to those based in equality. We can start with the most authoritative type with a single person in charge. This works well if that single person is good and is interested in the good of those beneath him. A father figure would be an example; department heads; presidents all the way to a monarchy. But this type of authority can also go wrong badly if the head becomes a tyrant. A tyrant has self interest at heart and is out to use and abuse everyone else.
The next kind of authority would be a type of a board. More than one person is in charge and we choose those who are the most competent to run things. Interestingly, Aristotle considered a marriage one of these where a husband and wife are competent to run their particular area of an estate. They take care of the children in the same way. This seems to be contrary to what I read by others on Greek society. Injustice can come from the board system if they become self absorbed and give favors to those who cater to them while abusing those who don't. We call them aristocrats or elitists on a large scale and some countries have even made permanent classes according to family and influence. Parents can show favoritism while a company can have those who must be appeased for advancement. A board authority isn't a bad thing as long is the group stays focused on helping others and being just.
Lastly there is equal authority where everyone has an equal say. This bears the closest resemblance to a true friendship. Brothers in a family; soldiers on a battlefield; room mates; all have a commonality and want what is best for each other. This also applies to fellow citizens. Where this can go wrong is when a few have self interests they want imposed on everyone. If they influence the majority, the minority is forced to obey their will. Sometimes belonging to a group is hard when the majority gangs up on others. We call this peer pressure in schools but it can be the same in a work environment. Sometimes we have to separate ourselves from a group because they always mean trouble. We might enjoy hanging out with them but the mob can get us in trouble. The equal authority friendship is the worst for getting things done since a consensus is hard to come by; but is rewarding as long as the group as a whole is good.
Each kind of authority has good points but can go bad when people go overboard on their own interests. We aren't talking about altruism. Everyone has a certain amount of self interest in what they do. To say differently is dishonest. But there is a right amount to everything and we are going to look at what this right amount is.