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).
I reply:
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 reply:
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.
I reply:
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)
I reply:
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).
I reply:
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:
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?
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?
I reply:
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 reply:
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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