[EM] A computationally feasible method (algorithmic redistricting)

[Raph Frank]

On 9/1/08, Michael Rouse <mrouse1 at mrouse.com> wrote:
>
>  There was a discussion of district-drawing algorithms on the
> election-methods list a few years back. I've always thought that taking
> centroidal Voronoi cells with equal populations was an elegant way to do it.
> Here's an example of standard Voronoi cells and the centroidal version I
> pulled off of Google:
> http://www.mrl.nyu.edu/~ajsecord/npar2002/html/stipples-node2.html

Is there an algorithm to take a discrete set of points (residents) and
find the set of district centres?

>  The other possibility I liked was allowing voters to vote for the districts
> they wanted -- either for the next election, or more entertainingly, the
> current one.

It might be possible to achieve moderate PR with this method.

In principle, if each voter could decide what district he was in, no
voter would join a district where he was part of the weak minority.
Likewise, there is little point in joining a district where you are
part of a strong majority.

The effect should be competitive districts and then a few 'overflow'
ones which the party with a majority wins.

I wonder would non-geographic districts be allowed by the
constitution.  Each voter would register for a numbered district and
could vote at any polling station.  Once registered, a voter wouldn't
be allowed to change registeration unless moving to a district with a
lower population.

The polling stations would then announce the counts for each district,
which would be tallied centrally.

This might allow perfect gerrymandering though.  If you had 55% of the
State population, your supporters might spread out evenly.  Tactics
might be interesting, a minority might try to flood a district, so
that they get a majority and then the district can take no more new
people.

Even with perfect gerrymandering for the majority, what it would
prevent is a minority party using gerrymandering to maintain its
majority in the legislature (possible in theory even if they are only
supported by 26% of the populaton).

Also, it could be somewhat considered to break the secret ballot, as
part of your vote is in effect picking what district to stand in.

Another option is that each voter picks a party, and the algorithm
tries to create districts that will give PR (assuming that the party
support of the voters who just voted reflect actual party support).
Ofc, it would probably not be able to give any seats to a 3rd party.

They would have to focus on a specific area and build up their
popularity there.  However, once they did that, they would get a
district centered on that location for as long as they managed 1 seats
worth of votes statewide and maintained sufficient support at that
location.

> You could have all qualifying parties submit
> a map, as well as any group that gets above a certain number of signatures
> in a petition.

That's another perhaps easier option.  It is less likely that the
algorithm would go crazy.

I wonder if the voters would gerrymander.  The voters might
effectively be given the option of a Republican or a Democrat
controlled House and then the actual election would just be a
rubberstamp.

Ofc, it is also possible that both parties would agree on a compromise
house that doesn't favour either party.