Which State...

[muon2]

Ever gotten any districts with no county breaks?

I've gotten a few in Indiana and one in Wisconsin I think.

I did a series of threads on this a while ago (2012). The first was on states using whole counties only. Then I did it for the New England states using whole towns. Finally I did one with states where the only splits were for counties larger than one CD.

The result was a general mathematical relationship where one could predict how close the district populations should be to the ideal depending on the average number of counties per district. Note how most states sit below the green line in the graph below (reproduced from the third thread mentioned above).

[muon2]

It says that if you tell me how many counties, large counties, and districts in a state, I can tell you how small the range (or deviation) should be in a plan using whole counties. If it isn't about that number or smaller than that, then you probably didn't work hard enough, or were trying to preserve other elements in a plan like low erosity or UCCs (This graph from 2012 was the original basis of my Pareto model of trade offs). It also applies to any other building block used to form districts as long as their populations are distributed like the counties in a typical state. The fascinating thing is that it shows that the states are quite similar in this regard, and New England towns distribute themselves in population like counties in other states.

[muon2]

The log effect means that the relationship is a decaying exponential like radioactive half life. Roughly, for each additional 10 counties (or other unit) per district available the range should drop by a factor of 10. 20 additional counties per district would decrease the range by a factor of 100.

To read the graph take the number of counties per CD and look at the vertical axis value. Take that number as an exponent for a power of 10 to get the range. For example, IA has 99 counties and 4 CDs for an average of 24.75. For that value the green line is at about 2.2. 10 raised to the 2.2 Is just about 158, so any IA whole county plan would be expected to have a range of less than 158.