It's worth remembering that congressional districts *must* be a union of census tracts (since otherwise the decennial "population" is undefined). However, the recent mathematical gerrymandering work has, quite rightly, focused on things that courts might plausibly adopt as standard tests. Since Roberts looked at the proposed and quite straightforward "efficiency gap" metric and said in oral arguments that "It may be simply my educational background, but I can only describe it as sociological gobbledygook", I don't think throwing better math at finding boundaries is going to help much. Many wise folks today (Moon Duchin included) are putting their eggs into the approach of sampling from the space of *all possible* districting plans that meet the relevant legal criteria. This space is too large to exhaustively enumerate, but they're trying various techniques to reasonably uniformly sample from it. The goal here is not to say which districting plan is "The Best", but rather to show what the whole distribution of possible plans looks like, so that if one that's proposed is obviously a massive outlier according to some metric (like how partisan it is), it's easy to draw a picture which shows that. This turns the gerrymandering fight from a mathematical one into a *data visualization* exercise, which I think is brilliant. Courts have gone for an "I know it when I see it" standard before, and given all the gamesmanship that any mathematical definition would lead to, this seems to me like a great way to side-step the problem. --Michael On Fri, Apr 6, 2018 at 3:01 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
this is a good resource created (i believe) by moon duchin, a mathematician at tufts who has been energetic organizing the mathematical community to discuss gerrymandering and even prepare mathematicians for expert testimony in legal proceedings. various well-attended math and gerrymandering meetings have already been held in the last 18 months with more upcoming.
https://sites.tufts.edu/gerrymandr/resources/
On Fri, Apr 6, 2018 at 10:44 AM, Henry Baker <hbaker1@pipeline.com> wrote:
I already live/vote in the worst gerrymandered district in California, and perhaps the nation (CA#24).
I agree with Brent that metrical compactness isn't the main problem -- especially in this age of the Internet.
But even if some sort of metric could be defined, I don't believe that the solutions are unique, and would depend substantially on the overall shape of the state.
Suppose that one had a very long thin state which forced all of the districts into *line segments* -- i.e., each person lives "closer" (under the chosen metric) to a state border than to any other person.
If the total state population is less than the number needed for 2 Representatives, then we have only 1 Representative for the entire state and we're done and unique.
Suppose we have enough total state population for 2 Representatives. We need to find the dividing line that separates the population with a difference of at most 1. If the state has an odd number of people, then we have two solutions, so no uniqueness.
If we have enough population for 3 Representatives, then we need to find 2 dividing lines, which provides for 2 sources of non-uniqueness.
Suppose now that our state consists of 2 disconnected pieces -- e.g., Michigan. How does the metric work between the disconnected pieces?
We could even have a dumb-bell-shaped state, or a panhandle state. Do we use a different metric in the panhandle?
If we have a more-or-less compact 2D state, we could start with a Voronoi diagram about each person. But what if the population density was maximal along a lazy river which approximated a space-filling curve through the whole of the state?
At 09:56 PM 4/5/2018, Brent Meeker wrote:
I don't think bad boundaries is the problem.
In many cases geometric proximity isn't a measure of common interests. <snip> On 4/5/2018 7:52 PM, Keith F. Lynch wrote:
It's been nearly four years since we discussed gerrymandering.
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