What was the authority behind both the mayflower compact and the declaration of independence?

The Declaration of Independence was issued "by authority of the good people of these colonies." It was a revolution, you know.

The Pilgrims did not cite any specific authority for the Mayflower Compact. However, they declared themselves to be loyal subjects of the king of Great Britain. The Compact was based on their experience in organizing dissenting churches in England and, I suppose, in the Netherlands, where they had sought shelter from persecution. In some ways it was in keeping with the English common law, which dealt with problems and controversies as they arose, rather than waiting for the government to settle them. But in some ways it was a revolutionary, democratic statement, asserting the colonists' right to make their own laws.