Inequality

The inequality in population is a measure designed to be consistent with the measure of geographic integrity based on chops due to node fragmentation. The correlation between the range and the number of geographic units suggests that the range decreases exponentially with the number of units per apportionment region. The factor from the slope of that relationship gives approximately a decrease in the range by a factor of 10 for every additional 10 geographic units per region.

There are 3143 counties or county equivalents in the US. The New England states were analyzed based on towns instead of counties, and Alaska and Hawaii present other challenges to model so those 8 state are excluded. In addition the independent cities in Virginia that are wholly surrounded by one county are excluded. That leaves 3023 county equivalents for 42 states, or an average of 72 counties per state.

There are 435 congressional districts in the US, but excluding New England, Alaska and Hawaii there are only 412. The remaining 42 states have 76 counties that are larger than a district and would be forced into a region with more than one district. There a total of 124 districts that could be embedded in a county, so the maximum number of regions is 288 for the 42 states. That is an average of just under 7 regions per state.

An average state with 72 counties and 7 regions has 10.3 counties per region on average. For each county that is chopped to reduce the range it decreases the number of regions by one. With one chop the average state would have 6 regions with 12 counties per region. With two chops the average state would have 14.4 counties per region. Each chop correspond to a change of approximately two counties per region. Based on the slope factor described above, there should be a decrease

Inequality Factor

The inequality factor scores the range of a region or district plan. It assigns a score of 0 to an ideal plan with a deviation from the quota by 0 or 1. The score increases by 5 for every factor of 10 increase in the range.

When using the inequality factor on a region plan, it is possible to create an artificially low score by grouping together regions with large deviations in opposite directions. For example suppose there are three districts with deviations of +1000, -800 and -200, and a range of 1800 and inequality factor of . If the first two districts were grouped together there would be two regions with and range of 400 and a decrease in the inequality factor from to . Yet the plan is unchanged with no chops. To prevent this, the inequality factor for any district plan cannot exceed the inequality factor for the region plan.

Inequality Factor	Range
0	0 - 1
1	2
2	3
3	4
4	5 - 6
5	7 - 10
6	11 - 15
7	16 - 25
8	26 - 40
9	41 - 60
10	61 - 100