Which of the following was one british principle of government valued by the american colonists? the potential to have an aristocratic house in the legislature the custom of having a ruling king or queen the right to pay no tax unless it was levied by their own representatives the freedom to wage violent protest if they thought it was necessary

I would say that "the right to pay no tax unless it was levied by their own representatives" is the best choice.

The American colonists were opposed to the whole aristocratic monarchy idea, as evidenced by the US Constitution (ratified later) that made the United States a democratic republic led by the President and three branches (executive, legislative, judicial). Additionally, violent protests were not a hallmark of the colonists during the American Revolution. Boycotts, refusal to comply with the law, and other such strategies allowed the colonists to grow in power. Violence was more typical on the British side, as seen in the Boston Massacre that killed a number of American colonists and sparked outrage across the colonies.