I am trying to create five regions in the state of Colorado. These regions are each based on a central point. I would like to create polygons based on that central point of equal population size. This is somewhat like Theissen polygons but instead of making the polygon based on its proximity to another point in is based on population values. The polygons do not need to be quadrilaterals either. They can be irregular shapes.
When you say the regions are based around a central point, do you mean that the point has to be the centroid of the region or simply that the point has to be within the region?
I don't think there is one configuration of regions that is "the" correct configuration as is the case with Thiessen polygons. Gerrymandering comes to mind as evidence for there being many/infinite possible configurations.
However thinking about this as a volume problem and not a population problem may help. Or maybe not. This is based on some distant memory of integral calculus on surfaces, so take it or leave it. (If nothing else maybe you'll get an idea for new search keywords.) Imagine a raster of Colorado where the cell values represent population instead of elevation. The cities are peaks and the rural towns are valleys. Then the problem is seeking region boundaries to yield five areas of equal "volume." I'm sure integral calculus has provided a way to do that by starting at your five points and integrating outwards until they meet each other. That would yield boundaries with the smallest perimeter...or...something like that. Whether ESRI has provided that tool, I couldn't say.