Final answer:
The principle that had the most significant influence on the conflict between the American colonists and the British government was 'No taxation without representation.' The colonists argued that since they were not represented in Parliament, they should not be subject to the laws and taxes created by that body.
Step-by-step explanation:
The principle that had the most significant influence on the conflict between the American colonists and the British government was No taxation without representation. The colonists argued that since they were not represented in Parliament, they should not be subject to the laws and taxes created by that body. This principle was a key factor in sparking the American Revolution.