Apportionment regions

An apportionment region (or simply a region) is a group of counties or other geographic units that meets criteria for contiguity and population equality within a specified deviation for a whole number of districts. Regions provide a useful tool for grouping counties together either due to the presence of large counties in excess of the population of one district or to reduce erosity. The nearest whole number of districts for that region is its apportioned number of districts.

When a region has a number of apportioned district in excess of one, chops are used to create single districts. In general the number of districts in the state minus the number of regions equals the minimum number of chops for the whole plan. So increasing the number of regions in a plan is equivalent to reducing the number of chops.

The presence of multiple districts in a region allows the deviation for the region to be larger than the deviation for a single district. Ideally the region could have a deviation equal to its number of apportioned districts times the maximum district deviation. In practice this tends to force chops that will split subunits like towns used in a chop. To avoid this yet recognize the ability to have a larger deviation, a region should have a maximum deviation equal to the square root of its number of apportioned districts times the maximum district deviation.