Inequality correlation
For any given state there is a plan which has the minimum possible range of population. In this exercise the state is divided into districts based on the 2010 congressional apportionment. The districts must be made of whole geographic units which are either counties or towns.
Counties that are greater than the population quota have the population divided by the quota. The population of that county is reduced to the remainder, and the number of districts in that state is reduced by the quotient.
A heuristic approach has been taken to identify those plans for each state. The districts must satisfy contiguity (not including point contiguity) and population equality not exceeding a maximum deviation of 0.5%. A graph of the data showing the range as a function of the mean number of geographic units is presented below. The graph suggests a natural range measure for comparing the relative population equality of two plans. Results for the 43 states which have more than one district are included at the end.
State Data
Alabama (7 CDs, 67 counties): deviations +1750/+1523/+228/-1974/+200/-1438/-286; av dev 1057; range 3924. Arkansas (4 CDs, 75 counties): deviations -136/+137/+138/-139; av dev 153; range 337. Idaho (2 CDs, 44 counties): deviations +1/-1; av dev 1; range 2. Iowa (4 CDs, 99 counties): deviations -41/+35/+23/-18; av dev 29.25; range 76. Kansas (4 CDs, 105 counties): deviations -22/+3/+37/-17; av dev 19.75; range 59. Louisiana (6 CDs, 64 parishes); deviations +1475/-1243/-226/+106/-909/+917; av dev 509.67; range 2718. Mississippi (4 CDs, 82 counties); deviations +176/-152/-68/+45; av dev 110.25; range 328. Nebraska (3 CDs, 93 counties); deviations -8/+12/-3; av dev 7.67; range 20. New Mexico (3 CDs, 33 counties); deviations -737/+234/+503; av dev 491.33; range 1242. Oklahoma (5 CDs, 77 counties); deviations -2/-557/-849/-1227/+2636; av dev 1054.2; range 3863. West Virginia (3 CDs, 55 counties): deviations +113/+2/-116; average deviation 77; range 229.
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