# [EM] Even simplier anti-gerrymandering rule

Brian Olson bql at bolson.org
Wed Nov 8 18:50:39 PST 2006

```On Nov 7, 2006, at 5:48 AM, raphfrk at netscape.net wrote:

> From: bolson at bolson.org
>
> > Since that grows all the districts in parallel, but approximately
> doubling districts at each step, at the end
> > you'll have some districts with about double the population of
> other districts.
>
>
> Yea, I sorta said that at the end.
>
> I think that breaking the country up into simple blocks could allow
> similar algorithms though.

Such data is available.
http://ftp2.census.gov/census_2000/datasets/Summary_File_1/

For example, California is split up into 533163 little blocks. Only
about 330,000 of them are actually populated. They cut the map into
lots of little pieces.

> Each of these blocks would have a population that is less than the
> maximum
> allowable error.  This allows the algorithm to operate on those
> blocks rather
> than complex geo data from the census.

Supposedly the Census has no error. Every block has an official count.

As for the file format, yeah, it's nasty. If someone were really
interested I could clean up the code I wrote for http://bolson.org/
dist/ and give that out, or even digested forms of the Census data in
a more applicable format for redistricting research.

> New Plan for single seater districts based on the split line
> algorithm:
>
> The total population of the country is divided by the number of
> seats to be filled.
>
> This shall be the target population per seat.
>
> The maximum and minimum shall be 5% above and below this target.

0.5% is readily achievable by my solver. A US House district is
300000000/435 = 689655 people. 1% of that is of course a 6897 person
variability from district to district. I think people might whine
about this; it affects the degree to which they are represented. It
won't necessarily be a logical argument.

Also the wider the margin the greater possibility for distortion to
malicious ends (depending on the exact method of picking within the
constraint). Of course current districts are equal population to
within 100 people according to Census data and are still distorted in
some extreme ways.

> Each county shall be split into sub-county regions.  <insert hard
> to change rule>
> (Max population = (2%)? of the target)

Census blocks average 100 people, and I don't think any are bigger
than about 1000.

> The country shall be split using the following algorithm
> recursively with the entire
> country being the top level region.  Recursion shall stop for
> regions which have only
> one seat allocated to them.
>
> The region shall be divided in two by the shortest boundary that
> divides the region in 2 such that
>
> - the boundary must follow county boundaries
> - seats can be allocated between the 2 sub-regions such that the
> sub-region population per seat assigned
> ... is within the max and minimum permitted
> - the 2 sub-regions are contiguous
>
> Seats shall be allocated between the 2 sub-regions using the
> allocation that is closest to the
> correct proportions as based on the 2 sub-regions' population.
>
> If no such  boundary is possible, the same procedure is applied,
> but boundaries can
> follow sub-county regions.

Automatic affinity to existing divisions is interesting and tricky.
The ability to pick which boundaries count may allow for some back
door tweaking of the districts that get picked. Also, it's hard to
program - mostly because the file formats are nasty and that data
wasn't immediately apparent to me though I'm sure it's in there.

I came at the problem from the other end when I wrote my
redistricter. I started with a definition of what a good district is
and wrote a solver to find the best set of districts. Defining a
forward process is good too, it just has to prove that every step is
fair and that therefore the end result is fair.

Brian Olson
http://bolson.org/

```

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