The Iroquois Confederacy is also similar to the United States government in the sense that we each "elaborately ritualized systems for choosing leaders and making important decisions" (quote taken from the linked source below).
For the US, that "ritual" is our voting system. We poll the citizens of the country on important issues—at the local, state, and federal levels of government—as well as polling and running campaigns for a new president every four years.
The Iroquois ritual systems were often used in their own decisions, as well as joint negotiations with the colonial governments; however, the Iroquois Confederacy didn't have the same control that the US government has (i.e., a federal government overseeing the state governments that oversee local governments), but the same basic concept of having representatives from each of the five (and then six in 1772) was prevalent.
The Iroquois tactics most closely resembled our voting system, with decisions based on the consensus of the community. The US state houses have representatives, and the federal government then has state representatives. Decisions are made based on what we believe is good for the people and, though the process to getting to that decision may be different, that's how the Iroquois Confederacy operated.