Final answer:
The Inca Empire did not grant autonomy to local chieftains as a method of administration. Instead, they controlled their empire through a centralized government, utilizing record-keeping with quipus, hostage taking, and relocating loyalists.
Step-by-step explanation:
The method by which the Inca administrated their empire that was NOT used was granting autonomy to local chieftains. The Inca Empire held a tight control over its vast territory with a strong central government, and although they incorporated local elites and respected local traditions, the overall administration was highly standardized and governed by loyal Inca administrators.
They maintained control through several effective methods such as a complex system of record keeping using a knotted cord system called a quipu, taking hostages from ruling families of conquered peoples to ensure loyalty, and relocating loyal colonists to troublesome territories to tighten their grip on local populations.