[EM] Impractical districting idea, complexity

Forest Simmons forest.simmons21 at gmail.com
Fri Jun 10 21:49:17 PDT 2022


It seems to be easier (in the virtual setting) to save the "district"
center's for last.

Start with a singular value decomposition of the scatter plot to get an
ellipsoidal approximation of the ballot distribution.

Make hyperplane cuts perpendicular to the ellipsoidal axes starting with
the longest axis, in such a way that each region so delineated has the same
number of voters, and that the regions are as compact as possible given the
constraint of cutting only perpendicular to the axes.

Then find the best allocation of candidates to districts. If there is a
district with no candidate interior to it, then the representative will
have to be from outside the district. If a representative cannot be
interior to the district she represents, that's not her fault: the problem
is a substantial void without any voter from that region willing to run.


El vie., 10 de jun. de 2022 3:12 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> On 6/10/22 1:03 AM, Forest Simmons wrote:
> > What would be the best rule to keep bots from overwhelming the
> suggestions?
> It's kind of impractical, but perhaps:
> - You send a request form to the local authority, from your registered
> mailing address (where official documents are sent).
> - The authority gives you a code that identifies you.
> - It then sets the request rate so that it isn't overwhelmed. Say it has
> issued a thousand codes and checking the quality of the solution takes a
> second. Then any given code has to wait 1000 seconds (around 17 minutes)
> before trying again.
> If the authority is hostile or the users' privacy needs to be protected,
> then it gets more complex (the latter requires blind signatures, the
> former is harder still). Not having a registered mailing address (e.g.
> homeless) would be a problem too.
> (I'm not sure if all states have a concept of a registered mailing
> address either, so this scheme would possibly need to be changed to e.g.
> showing up at an office or something similar. I'm far from an expert in
> American law.)
> It's also possible to offload some of the computation to the user. If
> the user submits a set of centers and the (center, inhabitant)
> assignments, then the optimality of the assignment for the given centers
> can be checked in O(kp + p log p) time.
> (Checking optimality prevents the users from submitting a gerrymandered
> assignment and hoping nobody comes up with a better one by the sum of
> squares metric. Not only does the assignment have to be good, but it
> must also be the optimal for the given set of centers.)
> -km
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