I feel like you "supervise" the quadra that is precede your own, while you get "supervised" by the quadra that succeed yours. So Alphas feel supervised by Beta, then Beta by Gamma, Gamma by Delta, Delta by Alpha. And this does not have to do with your actual Supervisor/supervisee existing in their quadra or not.

So for me, it feels like this:

Alpha: I pretty much agree with Alpha quadra values, like constant free-flow of information, "democracy" and making a nice environment. I have no problem or criticism here... Alpha is just like "whatever"... I feel like I'd be "supervising" Alpha. It's like "Come on, hurry up and make something useful, Alphas!"

Beta: The obvious problem with Beta is, authoritarianism, the monarchy, the monolithic state, the evil empire. They are not democratic. It seems to bring the worst of humanity and the basest and crudest desire of mankind, that is the thirst and quest for power and making others subservient. But it can also go the other way, like some Betas, especially the extroverts are usually furiously and hysterically attacking against "injustices" of the world. They are not exactly cowards.

Gamma: I don't really agree with Gamma values at all, except for their "democracy". Gammas are simply put, too greedy. Also, they are very crude, unrefined and unsophisticated. At least the Deltas are more refined and sophisticated. And yet, I feel like I'm "supervised" by Gamma, like their Se is much more powerful than Beta Se. I also feel like Gammas think of Betas as being "whatever".

Delta: I kind of agree with Delta values, like their "egalitarianism", their need for stability, for things to be proper and perfect, for things to just be working more smoothly and efficiently, their perfectionism, their refinement and sophistication. I don't agree with their work ethics, and I don't agree with their pride, their need for moral superiority, lack of dramatic emotional expression. Delta is "look, but don't touch. Admire from afar". I feel neither supervising nor supervised by Delta. Kind of an admiration, kind of an annoyance.