Building a house was an attempt for Iron Eye to get his tribe to move forward.
Based on the provided information, the best evidence to support the statement that building a house was an attempt for Iron Eye to get his tribe to move forward is the passage that states, "wealth.
That the chief had no army suggests that he had to govern by reaching consensus with the community's leading male figures and whatever subordinated chiefs may have existed."
This evidence implies that Iron Eye's authority and power lie in his ability to persuade and influence his tribe, rather than by force. Building a house could be seen as an effort to improve communal living conditions and encourage progress within the tribe.