A powerful/vulnerable binary (sometimes written as powerful-vulnerable binary or powerful-powerless binary) is the generic form of a binary power relationship in which one entity is omnipotent and another entity is totally powerless. Although such binaries cannot actually exist in absolute terms, the ways in which people relate to one another and to their own power or vulnerability as part of their interpersonal relationships is often constrained by the perception that such a binary does, in fact, exist in absolute terms. Powerful/Vulnerable binaries are a common form of role relationships that have abusive elements, such as in the man/woman or gender binary (which results in sexism), the dominant/submissive binary (which results in domism), or the straight-gay binary (which results in homophobia).
In many ways, those interested in having power over other people like to pretend that powerful/vulnerable binaries are the only possible relationships. They pretend that power over others is the only way to have power, ignoring both collaborative power (like the ability to lift something heavy together) and collaborative vulnerability (like sharing painful experiences to heal together), as well as reducing the reality of a power hierarchy that is not absolute back into binary terms. By presenting power and vulnerability as an all-or-nothing game they make inequitable and, by extension, unjust situations seem like the only possible option available. Closely related to this tendency of presenting power relationships as an “all-or-nothing” ultimatum is the idea of a zero-sum game, in which powerful people assert that any power-over others they lose is a power-over them that the other gains.
Most people don’t like power. Because power brings responsibility and if you have a conscience, as most people do, that makes power terrfying. Power does have one benefit though: power feels like the absense of vulnerability and for some vulnerability is terrifying. For others vulnerability is the most beautiful magical thing in the world.
—notfuckingcishet, "I don’t think most people like having power."
Maymay argues that the powerful/vulnerable binary is a kind of magical thinking used by people who seek power to calm their fears of powerlessness or to flee from acknowledging vulnerabilities. Applying this to the realm of sex, they write:
The abuse inherent in BDSM intentionally confuses Dominants about the difference between safety and power. I’m guessing that D-types are taught to believe that having power over others is a way to make themselves feel safer in interactions with them. And I don’t doubt that there’s probably some tiny kernel of truth in that, somewhere. At the very least, it’s arguably “safer” to have sex in which you’re not physically bound than to have sex in which you are. But I think that’s a very narrow definition of “safety,” and I don’t think it’s one that’s particularly useful.
—maymay, "Power cannot exist in a vacuum"
The same magical thinking in this realm of BDSM sex informs the ways in which "switching" is believed to be different from D/s binarism, when in fact it is not; switching is the ultimate sexual expression of the (rather silly) zero-sum game idea applied to a powerful/vulnerable binary.