What was virtual representation?
Virtual representation is a concept that led to conflict between the colonists and the British government. The concept of virtual representation means that every lawmaker represents not only the people from his or her area but also all the people throughout the country or empire. The colonists were upset because they didn’t have representatives that they elected to Parliament. Thus, they felt their rights were being violated when tax laws were passed, and they didn’t have elected representatives that could speak about and vote on these proposed laws.
The British believed that every representative in Parliament was representing the best interests of the people throughout the country and throughout the empire. The British argued that since virtual representation existed in Great Britain, it should also exist in the British colonies. The British believed that the colonists did have representation in Parliament because virtual representation existed. The colonists disagreed and eventually after a series of events and challenges occurred, they declared their independence from Great Britain when the colonists believed those challenges couldn’t be peacefully resolved.
The concept of virtual representation held that people like the American colonists did not need to be able to elect their own representatives to Parliament. The theory held that the members of Parliament already represented everyone in the British Empire. They did not just represent the people who elected them. Instead, they had the interests of all the people in mind. Therefore, it didn't matter who elected them or where they were from because they would govern in a way that kept everyone's interests in mind, no matter where they lived or whether they could vote. The American colonists rejected this idea, helping to lead to the Revolutionary War.
Virtual representation means that Parliament stood above narrow interests of constituents and considered welfare for all subjects when deciding issues. In other words, the colonists are not being represented because no colonist is a Member of Parliament.
A British historian, David Starky, thinks that the idea of taxation without representation preceeds the Magna Carta in English culture. If he's correct, then the idea of virtual representation must of been basically repugnent to Englishmen.
I don't know why they declined actual representation, but I would speculate that many of them had experience with the corrupt nature of British government, and they did not believe they could have a voice, even if they sent representatives.