Final answer:
The term used to describe leaders with supporters in several villages whose power is based on generosity in the South Pacific is 'big man'. This role is distinguished by social influence gained through wealth distribution and community service, rather than formal authority like a chief.
Step-by-step explanation:
The term used to describe political leaders in many societies in the South Pacific who have supporters in several villages and whose power and position is related to their generosity and reciprocity is big man. The big man is an informal leader who has gained power through the accumulation of wealth, sponsoring feasts, and helping young men pay bride wealth. Unlike a chief, who holds a formal, inherited position of leadership within centralized societies, the big man's power is persuasive and based on his ability to manage wealth and his service to the community. The big man sets an example by distributing wealth equitably and organizing community activities, earning respect and authority.