What is the relationship between the sexes in the world state in Brave New World?
The world state encourages promiscuity because the belief was that committed monogamous relationships would lead to jealousy, conflict. Adults would use "soma" the drug to dull their passions. These practices are utilized by the state to distract, pacify and condition the citizens; to prevent them from challenging the system or engaging in intellectual or critical thought. So, the interaction between the sexes, and all people in general (with the exception of the Savage and the Controllers), is a conditioned interaction; relationships are functionary, not based on emotional or intellectual connection.
The ten Controllers have the most power and are the most free. Everyone else, from the Alphas to the Epsilons, essentially have no power because they've been so conditioned that they lack the ability or the will to have free thought, free will or the ability to choose.
But, Alphas do have a bit more freedom because they are intelligent enough to not completely bend to the laws of state. The Controllers allow some of the Alphas to travel to the Indian reservation for two reasons: the freedom to travel is a way to placate them and it also was supposed to show them how primitive societies function:to make them appreciate the civility of the World State. The idea of power is associated with free will. From the Epsilons up to the Alphas, the more intelligent the caste is, the more ability for critical thought and thus, the more free will they have, the more power they potentially have.
Ironically, although the Controllers have the most power/most free will, their lives are based on a choice among only two options: become an oppressive controller or an outcast. The Controllers, who have the most free will, have the most power because they deny it to everyone else.