People often also submit to simple suggestions and someone just taking charge - because in many (most?) social situations that's the effective and beneficial thing to do instead of requiring preexisting power.

Power can be 'taken' and enforced, but very commonly power is simply given/gifted when a community, small or large, self-organizes.

> A gun, a hostage

Those are direct use of force, not authority or power.

> 51% voting majority

Can still be undermined by civil disobedience, if we're talking about society. Only a small minority in society (the police) use force to get you to submit. The rest submits to the authority of the law. A very small group can undermine the majority through civil disobedience, since they can outnumber the police very quickly.

Force compels submission, which grants authority.