What Powered The Three?

[Belegorn]

I think the Elven Rings were made to arrest time, to bring Aman to Middle-earth as was Sauron's pitch to the Elves. In the First Age the Elves generally left Aman for empire in Middle-earth, to establish themselves there and be the rulers. The cessation of the effects of time may have been more important to those who had lived in the Undying Lands which probably accounts for the Rings coming from that people, the Noldor.

I would say the One ruled the others because of its exceeding power and due to the design taught by Sauron to them. I think this common design was the means by which Sauron could link his Ring to the others. Otherwise it'd have been a seperate type of Ring with the same powers, but the bearer could not extend his will from the One to the others.

Originally Posted by Of the Rings of Power and the Third Age

much of the strength and will of Sauron passed into that One Ring; for the power of the Elven-rings was very great, and that which should govern them must be a thing of surpassing potency;