Question

How were the mayflower compact and house of burgesses important to self government?

Answer 1

Virginia company struggled to attract settlers but its population grew dramatically so in 1619 the house of burgesses became America’s first legislative, or law-making body.
When the pilgrims decided to set sail for America in September 1620, 2 months later they reached land and the pilgrims signed the mayflower contract agreeing to make laws to protect the general good.
So to answer your questions, I believe these two occasions are important to self-government because the colonies are learning to be sufficient.