I live in North Carolina. As many of you know we have had a major problem with gerrymandering both for state and federal districts. For purposes of this question, I am only concerned about state districts.
My proposed solution is to model the federal system and use the nonpartisan districts we already have - our 100 counties. The NC Senate would be easy. Just up the NC Senate to 100 members, and give each county 1 State Senator. However, the NC House would be more complicated. The US House uses the Equal Proportions method to decide how to divide up the 435 static US House seats:
https://www.census.gov/topics/public-sector/congressional-apportionment/about/computing.html
My question is that if we assume each of NC's 100 counties gets at least one NC House member, what is the smallest total number of NC House seats that would be necessary in order to make it somewhat fair? Certainly if it would require 870 members, this might be unworkable. As you can tell some of our larger counties are way larger than our smaller ones:
http://www.us-places.com/North-Carolina/population-by-County.htm
If there is mathematical way to figure out the optimum number of NC House seats under my proposal, I would appreciate hearing it.