The Impact of Zeroing Out


The picture above shows part of the line dividing Nevada’s 1st (north) and 3rd (south) congressional districts. The line follows East Russell Road for this stretch almost perfectly, but juts upward for a block and comes back down. What is so special about the 13 residents that live there that warrants a change in an otherwise smooth line? Why not the block next to it? Why a jut at all?

It’s worth noting that that deviation from the line represents a single Census block, which is the smallest unit of geography that the Census reports population counts for. What this means for mapmakers is that the lines of a state’s Census blocks represent the possible lines for their districts: they can’t split a block, since they won’t know how many people are in either division.

I can’t guarantee it, but I would bet good money that there isn’t anything special about these 13 people, other than the fact that there were 13 of them. Congressional districts, unlike state legislative districts, are held to an especially strict standard when it comes to population equality. While tiny deviations are allowed when justified on neutral grounds, the majority of states err on the safe side and draw districts that vary by just one person. Nevada, for instance, has 3 districts with 675,138 residents (at the time of the 2010 Census), and one with 675,137.

What does this mean for the actual mapmaking process? Quite likely, the rough draft of this Nevada map followed Russell Road perfectly on this stretch, but District 1 was overpopulated by some small amount – say, a few hundred to a few thousand people. When the mapmaker was then satisfied by the rough draft, though, it came time to “zero out” the districts, or hit perfect equality. At that point, they may have picked bigger chunks than the Russell Road block to inch themselves closer to that point of equality – the image below seems like it may have been part of that stage, where district 1 is the southwestern part of the image.


It’s possible that the line originally went out to the intersection of Lake Mead and Hollywood, but to get down closer to the ideal population, they shifted inward.

You may get lucky and be able to find a district boundary that makes it to perfect equality by following lines that look relatively straight and smooth everywhere, but chances are good you’ll find yourself somewhere within 100 people of your goal and no options of that kind left.  At that point, the mapmaking process can devolve into searching around the border of your existing lines, looking for one or a combination of blocks that have the exact population you need to shift.

Put another way, the answer to the question of “why this block, not the one next to it?” is probably nothing more noteworthy than that they needed to shed exactly 13 people from district 1, and this block fit the bill.

I’m not picking on Nevada in particular; you can find these odd choices in plenty of other states.


However, it does raise a couple of questions. The obvious one is whether perfect population equality is worth this sort of line drawing. The populations will no longer be perfectly accurate almost immediately after the Census count, much less a year or two later when the maps are drawn, if they were ever perfectly accurate to begin with (there is certainly some error involved in the Census’s results), so striving for perfection seems like an artificial standard. Even if you do grant that the populations for each block are correct, are these sorts of neighborhood splits worse than a deviation of a few hundred people between districts (i.e., a tenth of a percent or less)?

This is partly a legal question, though, and it’s understandable that states want to avoid having their districts rejected in court over something relatively trivial like this. The second question, though, is whether the issue is more likely to affect certain people than others.

Which Blocks are Chosen?

I haven’t done any systematic analysis on this, it’s based on observations I’ve had while poking around, so take it with a grain of salt.

The first thing is that the block has to be on a district boundary. I would suggest that this is less likely to happen in a rural county than a more urbanized one. Because of their lower population, they’re more likely to be added to a district in the drawing process as a whole unit. Going back in and taking out just a small chunk of that county during the zeroing out process is less appealing than changing the boundary within a county that is already split, both for appearance’s sake, and depending on your state’s guidelines regarding minimizing county splits, possibly for legality’s sake.

The second tendency is that the block shouldn’t have “holes”. To see what I mean, here’s a block map of a portion of Florida.


In the center of the image is a small town, made up of nice rectangles, but around it are large, rural blocks, some of which completely surround other blocks. If you add the large, light blue block in the northeast to a district, then, you have to include all the tiny flecks within it, or end up with a non-contiguous map. In some cases, these flecks represent things like lakes which won’t have population (the two blocks within the darker green block in the northwest are a case of this), but not always.

Even if a block doesn’t have holes, one that is especially non-compact might not be attractive – all things equal, a mapmaker will want to disturb the smoothness of the line as little as possible. Cities tend to be great for this, as they often have nice grid-pattern streets and rectangular Census blocks. The opposite side of the spectrum is a certain type of suburb, the ones with winding streets and cul-de-sacs. This is another portion of Florida.


Attempting to draw anything resembling a straight line through here is impossible, and even drawing a smooth line often requires picking up multiple blocks. In some areas, the Census makes it even worse by drawing a neighborhood as blocks that make holes in a larger, enveloping block.

Finally, low-population blocks are especially prone to being chosen, since they’re more likely to get a mapmaker to the exact population needed in a district. Some blocks have have hundreds or even thousands of people, such as blocks with high-rise apartments or the enveloping blocks of large suburban neighborhoods, which don’t help much; the ones in the 1-20 people range are more useful.

If you add all of these factors together, it seems reasonable to guess that lower-density, non-suburban residential areas in larger counties are the most likely to be subject to these sorts of maneuvers. Granted, this effect is small and might not even apply in a state that’s engaging in gerrymandering. Furthermore, I’m not convinced the average person is even aware of where his district lines fall, even if it’s on the street outside his house, so compared to the more global shape of a district, it might not be important.

Still, though, the fact that someone trying to draw a good district map has to resort to this strategy brings me back to my first question: is perfect population equality worth it?


Leave a Reply

Your email address will not be published. Required fields are marked *