Is the selection by females the cause or the consequence of competition between males?

It is the cause. I make a comparison, which may seem bizarre, with chimpanzees to explain why that is the case.

Female chimpanzees are not selective. When they are in heat they are willing to mate with any male around.

It is the stronger, dominant males that chase away the weaker ones, keeping the females for themselves and making sure to reproduce.

In this case, there is no selection on the part of the females. The filter that selects the male chimpanzees that manage to mate is the natural and constant competition between the members of this species (chimpanzees are very aggressive).

I have just shown an example of a species where competition between males is the cause of selective mating with females.

It seems obvious, then, that for humans it is exactly the opposite. Here, females are the selecting agent, the cause. The competition between men, the hierarchy, the struggle for status that emerge are but a few of the many ways that men come up with to attract the attention of women and impress them, in the hope of being chosen.