Your analogy doesn't hold at all. In no way is consent of the governed impossible or analogous to agreeing to be raped, either semantically or logically. Maybe you skipped history lessons, but the whole point of the DoI was to outline the acceptable methods of government to the colonists and to justify the reasons they were declaring independence. The DoI doesn't grant any authority, you misunderstood what I said. The DoI explains the rationale by which the government later granted itself authority by claiming it was acting with the consent of the governed. By living here, you are consenting to the jurisdiction and authority of the government, because you're free to leave. However, you're not free to ignore the edicts of the government, that is "the Will of the People." (Said semi-sarcastically)

Don't misread me. I'm sympathetic to voluntaryists. I'm merely explaining the rationale behind the system of government, not defending it. I think democracy is a rather dreadful thing, as the majority forces its will on the minority with impunity. However, I've never become convinced a completely voluntary society would work, for many reasons which are not the point of this thread.

The short of it is that the DoI does not do the vesting of authority. It explains how and why the vesting of authority is legitimate. The actual vesting of the authority comes from the Constitution.