The Mayflower Compact was written for the purpose of establishing a rudimentary form of self-government for the Pilgrims settling in North America, ensuring that they would create a social contract to maintain order and cooperation among the colonists. The Virginia House of Burgesses was established for the purpose of creating a legislative assembly to allow settlers in Virginia to have a voice in governance and to make local laws.
Both of these forms of government demonstrate the principles of self-governance and democratic representation. They are important because they laid the groundwork for future democratic institutions in America, highlighting the early colonists' desire for self-determination and participatory governance, which would eventually influence the development of the United States' democratic system.