Final answer:
The 1922 deal refers to the Colorado River Compact, which divided water from the Colorado River among seven states and was based on overestimations of the river's flow. The Hoover Dam, a later development, was constructed to help manage these water resources.
Step-by-step explanation:
The 1922 deal that overestimated the flow of water from a western US river, affecting the division between seven states, pertains to the Colorado River.
In 1922, representatives from seven states—Arizona, Colorado, California, Nevada, New Mexico, Utah, and Wyoming—negotiated the Colorado River Compact. The agreement was shaped by an overestimation of the river's annual flow, which led to allocations of water that the river could not always sustain.
The Hoover Dam was a significant engineering project on the Colorado River, constructed to manage the inconsistent flow from floods and droughts and to provide reliable water supply and power generation. Despite the well-meaning intent to domesticate the river and its resources, the miscalculation has had lasting effects on water management and distribution in the region.