Olmec buildings and artwork show us that their society's government was probably a

Answer: Centralized monarchy.

Explanation:

The colossal heads that are most likely to represent the rulers of this nation create the assumption that the government of this society was most likely a centralized monarchy.

A stable central government could have influenced these ancient artists to represent and glorify their rulers in this way. The Olmecs were among the first Mesoamerican societies. With their actions they left a lot of influence on the later Mesoamerican civilization.