In the theory of humor that I am developing, I argue that there are two fundamental aspects of humor: an incongruity aspect and a social aspect. The social aspect often deals with adjusting status among the members of a social group. The adjustment is often downward, laughing at someone in order to bring that person down a peg, or using self-deprecating humor to deflect envy about one's own high status.
I have been purposefully vague about what status is. When I first started trying to explore the theory of humor, I was well-aware of my own view that humor often adjusts status downward in a group. So I explored the social psychology literature regarding the nature of group status. Two profound facts emerged from what I learned, one, that all groups have emergent status hierarchies and, two, that humans are loyal to groups, even if the group in question is barely a group.
First, from the 1940s onward, Sharif, Harvey, and other social psychologists established that when experimenters place humans together in groups to perform an activity, we will sort ourselves into status hierarchies, often unconsciously. There is basically no such thing as a functioning group that doesn't have at least an implicit status hierarchy. It is also the case that most (perhaps all) social animals exhibit social hierarchies, so the topic is not limited to humans. The term "pecking order" comes from the study of social hierarchy among chickens, who enforce the social structure by pecking each other.
Second, from the work of Henri Tajfel, it has been shown that even the most minimalist groups, groups where the members do not know each other and which have no known shared qualities, exhibit in-group bias and loyalty. So you can never get away from in-group / out-group divisions, no matter how you try to educate people about things like the universal brotherhood of man (to use a particularly gendered version of the idea). Combine these two findings, and we have the conclusion that humans are strongly motivated to belong to groups and to strive for status within those groups.
Within the status literature, one major division is between dominance and power on the one hand and informal social status on the other. Dominance carries a threat of violence, whereby those higher in the pecking order might harm those lower in the order if they do not comply with the rules established by those higher in the group structure.
Social status, on the other hand, might be collectively and unconsciously agreed upon by all group members, and might not carry a threat of violence. All members in the group may confer high status on some members in the genuine belief that those others should have high status, not out of fear. There have been studies of bee hives and other social networks that show that decision-making in groups can come from the bottom-up, not pushed down from powerful members of the group asserting their self-interest. I suspect that the status dynamics within human groups are usually a combination of top-down dominance pecking order and bottom-up hive decision-making.
The difference between hard dominance and a softer social status is also manifest in humor. A social group in which there is the palpable threat of violence often does not feature public humor with the dominant members as targets, but the powerful may ridicule those low in power, and those lower in rank may use humor amongst themselves to lower the stress of being powerless. Indeed, the highest status individuals might take actions which would otherwise invite ridicule, but no one ridicules for fear of punishment. This seems to be supported by the findings of Ruch's 3WD studies, which show that religiously fundamentalist personalities are negatively correlated with appreciating the humorous qualities of jokes. An angry god does not joke around, and certainly not with self-deprecating humor.
For informal social status hierarchies, self-deprecating humor and teasing are not uncommon. Those high in status signal to others, "Hey, I am just one member of the group, even though I have had this status conferred upon me." The status is deserved, it is not maintained by fear. Those high in status are not threatened by criticism of their shortcomings. They deserved their places.
The contrast between power dominance and softer social status may not be a dichotomy. It may be a spectrum, or it may be multi-dimensional. I am not convinced by my modest investigation of the literature that the issue is settled. For example, a military leader may inspire others to follow because that person displays qualities that confer status; however, because the leader has followers, the leader can use that structure to exercise dominance and power.
I suspect that the phenomenon of social status hierarchies is not studied as much as it might warrant is because the idea that social groups are always structured goes against the political ideals of our culture. Also, one way to motivate those lower in the status hierarchy to work hard is to claim that there is no hierarchy, so those high in status in our culture who control the funds for studying social behavior may have a disincentive to prioritize the study of status hierarchies. The claim that there is no hierarchy can come in the form of claiming we are all equally children of God (some traditional religions), or claiming that we all have the liberty to pursue happiness (secular liberalism), or claiming that the dictatorship of the proletariat has transformed us (communism). Take your pick.
Nevertheless, humor does function within this world. Ridicule especially is a powerful tool for social modification of behavior. A group where those who are high in status tolerate or encourage humor at their own expense generally is a stable group which is not maintained by threats of violence.