Final answer:
The assembly established by the Virginia Company in 1619 where colonists elected representatives called Burgesses is known as the House of Burgesses.
Step-by-step explanation:
In 1619, the Virginia Company allowed colonists in Virginia to establish a legislative assembly that would give the colonists a certain degree of self-governance. The assembly established by the Virginia Company in 1619 where colonists elected representatives called Burgesses is known as the House of Burgesses.
This assembly, where each settlement area could elect two representatives known as Burgesses, became the first of its kind in the English colonies. The correct phrase to complete the excerpt in the question is the House of Burgesses, which served as a prototype for the representative assemblies that would later become a common feature of governance in the other English colonies in America, influencing the democratic traditions of the future United States.