This isn't a serious proposal, but it would make for an interesting map.
I'm think an algorithm something like this:
1. Calculate the center of population for each state. (COPs for current borders are here.)
2. Designate the nearest top 10 city to be the state capital
3. Reassign counties to the state with the nearest state capital.
4. Repeat steps 1-3 with new boundaries.
This should tend to make states more circular, and more equal in area. What is unknown is whether the gradual tendency of states to become larger towards the west will be maintained, with only local equalization, or national equalization.
1. The Census Bureau has COP for counties. It may simplify matters to calculate state COPs from the county COPs, particularly after moving counties.
2. This may cause problems because states define cities differently. It might be simpler to drop this rule entirely, and locate the state capital at the COP. A more complicated rule would use the county seat of COP. It is more likely that a city is populous because it is the capital, rather than it is the capital because it is populous.
3. This is ambiguous. The equidistant line between two points (capitals) is a great circle perpendicular to the great circle between the two points at the midpoint between the two points. This will divide counties. Are counties assigned based on area or population? Do you use majority of area or population, or COP or COA?
The COP for Pennsylvania is north of Harrisburg. This will result in Pennsylvania losing Philadelphia metro to Delaware and New Jersey. This will move the COP for Pennsylvania westward and northward, and for Delaware to the north, which will result in a repetition.
The COP for New York is barely in Sullivan County, but the nearest Top 10 city is either Yonkers or White Plains. That is the reason I suggested the change to Rule 2. But in any event the dividing line between Pennsylvania and New York will have a significant northwest direction, moving Buffalo and perhaps Rochester into Pennsylvania. The COP for Pennsylvania will move further north and west. This might permit Pennsylvania and New York to move to the west, permitting the New England states to expand.
