[EM] Maps on which to draw rectangular districts

[Ernest Prabhakar]

Hi Mike,

On Jan 8, 2004, at 1:37 AM, MIKE OSSIPOFF wrote:

> Hexagons sounds good, till you consider that they won't work at the 
> borders of the state being districted. Since district shapes can't be 
> hexagons at the state's borders, why bother making hexagons in the 
> interior?

For the record, I wasn't suggesting an explicit mandate of hexagons.  I 
was just pointing out that a circumference-minimizing criteria would 
tend towards circles, which as a practical matter would generally lead 
to something that look like hexagons (since you can't cleanly pack 
circles together).

I do tend to agree with your argument that simpler is better, so I can 
see some advantages to rectangles.

On Jan 8, 2004, at 3:12 AM, MIKE OSSIPOFF wrote:

> There are obvious ways to write a simple rectangular mapping formula. 
> If the state is L times as long north-south as east-west, and N is the 
> number of districts, then, divide the state into sqr(NL) bands of 
> east-west extent. Divide each band into rectangles containing 
> population equal to the state's population divided by N. The band will 
> end with a fractional-size district. Adjust the north-south dimension 
> of the band to make an integer number of whole districts of the 
> desired equal population.

> Obviously, adjust to a larger north-south dimension, to add a district 
> to the band, if the fractional district is more than half of the 
> desired population. Adjust to a smaller north-south dimension, to 
> subtract a district from the band, if the fractional district is less 
> than half of the desired equal population.

Interesting.   That does seem simple enough that it could be explained 
to both people and politicians, which might outweigh locality concerns. 
  Although, philosophically I like the edge-weighted approach better, to 
preserve locality of association. Otherwise, why not just go with some 
non-geographic weighting, as discussed earlier?

I also agree with you that for anything the size of a state or less, it 
doesn't much matter what kind of map you use.  However, if the goal is 
rectangular districts, I'd suggest an equal-angle projection, rather 
than equal-area (which is irrelevant for our purposes) or Mercator 
(which wouldn't work well for, say, Alaska or northern countries).

> As I said, simplicity is the most important consideration for the 
> district-drawing formula. Rectangular districts, drawn on some 
> specified map, by a simple formula such as I've described, are the way 
> to draw the districts.

I did have a couple of questions about your algorithm.    Specifically:

a) Will it give the same answer whether you go from North to South, or 
East to West, or backwards?

b) This should be easy to visualize for most U.S. states, which have 
roughly rectangular form matching latitude and longitude.   However, 
would it be awkward to apply it to more unusually shaped regions?   Or 
do we just choose a projection (and orientation) to make things looks 
rectangular?

-enp