# [EM] Districting maps

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Jan 10 22:44:01 PST 2004

```Ernie--

I'd said:

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?

You wrote:

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).

But what could it be? If it isn't hexagons (and it can't be, because tiling
hexagons have to be the same size), then what other shape is there that's
convex and fits together, even if different districts are different sizes?
It seems to me that it would have to be triangles or rectangles. I don't
know how well triangles would work, but it seems haphazard and would require
a more complicated formula than rectangles would.

I posted an improved and better-written version of the rectangle districting
formula, entitled "Better wording of rectangular districting formula"

You continued:

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 missed the earlier discussion. I must go back to the archives and check it
out. I don't know what edge-weighting or non-geographical weighting is. I
didn't realize how much of the discussion I'd missed.

Modifying the districts to keep municipalities intact would make it
impossible to make the district populations equal. What then? Give different
district representatives different votinlg power? Fractional voting power
for legislators? Districts that differ in population by the amount that
intact municipalities would cause is unacceptable if we want fairness to
voters in all the districts.

And if the districting involves someone deciding which areas are communities
that should be kept intact, then that's just the human decisionmaking that
we want to get away from. To keep the districting honest, it's got to have
nothing to do with social considerations.

And how important are municipalilty lines, or other lines on the map, for
defining community? The disticts that I suggest are rectangles with some
effort toward making them square, at least on the average. None of them are
much longer north-south than the side of the typical square district. The
municipal areas would have districts that are skinnier east-west, but which
are smaller than the rural districts. Their smaller size is more important
than their skinnier shape, for determining how much their inhabitants have
in common. Whether or not a distirct is based on municipalities, the people
living within a district boundary have something in common: They all live in
the same area.

Residents of cilties are notiously diverse in their political beliefs and
position. To deal with city matters, that's what city government is for. It
isn't important for the especially diverse population in a city to share a
district. In fact, don't cities tend to be more progressive than rural areas
(because progressives are part of urban diversity)? Making sure to district
all those progressives together, wouldn't that often have some sort of
effect on the composition of the legislature? That's why I prefer a formula
that completely ignores cities, counties, etc.

You continued:

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.

Or even for a whole country. Countries of all sizes have for a long time
typically been mapped with the simple conic projection. Anyway, even if the
gnomonic would show noticible scale variation when mapping a large country,
that's no problem. The map isn't supposed to be aesthetic--it's only used as
something to define rectangular districts with respect to. With the
gnomonic, the district lines would all be straight lines on the ground.

My favorite proposals are: 1) using latitude/longitude lines, or  2) using
rectangles on a gnomonic projection, to give straight district boundaries.
Straight as seen on a state map, that is, not counting the little jogs
needed at the street or house level.

You continued:

However, if the goal is rectangular districts, I'd suggest an equal-angle
projection, rather than equal-area (which is irrelevant for our purposes)

Sure, equal-area serves no important purpose for the district map. The exact
size relation of the districts isn't important.

Yes, a conformal projection would give the districts exactly right-angle
corners on the ground. But the gnomonic would give them straight sides. (All
this disregarding the little jogs). I personally like straight district
boundaries more than exact right-angle corners.

Also, latitude/longitude lines have familiarity and simplicity appeal.

You continued:

or Mercator (which wouldn't work well for, say, Alaska or northern
countries).

Yes, the Mercator combines the large scale-variation of an equator-centered
map (as opposed to a locally-centered map) with the especially great
departures from equal-area that happen on a conformal map.

Using latitude/longitude lines amounts to drawing rectangular districts on a
cylindrical projection map.
If it were done via a map, it would best be cylindrical equidistant, with
north-south & east-west scales in a proportion that gives the rectangles, as
near as possible, the same shape they have on the ground.

Yoiu continued:

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

Sure, when drawing rectangles on a map, it shouldn't make any difference the
orientation of the map. (Of course the latitude/longitude line districts are
only defined for one orientation).

In fact the gnomonic is an azimuthal map that can't really be said to  have
"orientation" unless it's centered on a pole, which these of course wouldn't
be.

But it's more orderly, convenient, and clearer to work with respect to
north-south and east-west.

By the way, I said that, on the map, "north-south" means parallel to the
state's central meridian. The cylindrical, gnomonic, and conic maps have
straight meridians. But if one wanted to use a map that has curved meridians
then "north-south" could be defined as parallel to a straight line on the
map connecting the northernmost and southernmost points where the state's
central meridian intersects the state's border.

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?

No, it wouldn't complicate the procedure to have wavy borders. But Colorado
would certainly be the neatest rectangualr district system. There, there'd
be a great incentive to use latitude/longitude lines, for a perfect
rectangular fit.

You continued:

Or do we just choose a projection (and orientation) to make things looks
rectangular?

I wouldn't depart from north-south, east-west orientation for the
rectangular district system, because it's familiar and convenient. The
rectangular states or countries are north-south, east-west oriented anyway.

It would always look rectangular on the map on which it's based. Districting
a big country, the U.S., China, Russia, Brazil, districts that are
rectangles on a gnomonic map might look noticibly unrectangular on a
national map drawn on a different projection. Whatever projection the
rectangles are based on, they of course won't be exactly rectangular on
other projections, except that the cylindrical projections show eachother's
rectangles as rectangles. For looks it would be best to display the
districts on the projection on which they're based.  The longitude/latitude
line districts would look fine on any map. But because they're oriented
roughly north & south, the rectamg;es would look ok on any map.

But these considerations aren't a serious problem. The important thing is a
simple shape, free of human tampering with the distirct lines.

The rectangular district system would look great on the state or national
map, neat as a brick wall. Based on a simple syatem that obviously has no
human input, no meandering, wavy, concave, funny-shaped districts.
Districting is not the place for creativity or artistic expression.

By the way, speaking of administrative boundaries, consider the diagonal
line part of Nevada's border: Is that diagonal a great circle (straight line
on the ground) or a rhume line (constant compass direction line)?

Mike Ossipoff

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