Consider a network where the nodes represent individual membership in a
district and the edges connect any two individuals that could possibly be
considered as being in the same area. An edge has a weight of -1 if the
neighbors are in opposing political parties and 1 if they are the same. A
node has the value of 1 if it is in a district and -1 if it is not in that
district. Districts are mutually exclusive, so all of the nodes associated
with an individual, when considered as binary values, must sum to one.
Specifically suppose there are two districts, and node(A,D) is defined as
individual’s A participation in district D. Then
(node(A,0)+1)/2+(node(A,1)+1)/2 = 1. Constraints like this can be converted
into penalties by moving the RHS to the LHS, negating the value, and then
squaring the LHS. An energy for the whole network can be written as a sum of
all of the network’s interactions.
sum(edge_weight(i,j)*node(i,d)*node(j,d)) where i < j for i,j from the set
of nodes and d from the set of districts
+ K*(all mutual-exclusion penalties as above) where K is a large number
Now minimize this energy using a system that can find the ground states of a
high dimensional Ising model, such as a quantum annealer. This function will
be minimal when each district has neighbors that tend to be in different
parties.
From: Friam <[email protected]> on behalf of Tom Johnson
<[email protected]>
Reply-To: The Friday Morning Applied Complexity Coffee Group <[email protected]>
Date: Saturday, November 3, 2018 at 4:55 PM
To: "Friam@redfish. com" <[email protected]>
Subject: Re: [FRIAM] gerrymandering algorithm question
First, we would have to agree on whether there will be objectives related to
the demography of any district? I prefer only counting the number of current
population 18 and over. Or some would argue for the total population of any
age. But given either choice, there will be serious suggestions that doing so
would work hardship on racial, ethnic or other groups. Could be, but it could
also mean that anyone running for office would probably have to find a way to
appeal to ALL voters.
Second, let's say we're creating Congressional districts. Overlay a state with
a grid of hexagons of X diameter; could be 100 yards or 1000. I don't know,
but perhaps something like Netlogo could give us a scalable system to run tests.
Third, given a known population of potential voters, we know how many
Congressional districts a state would have. Randomly distribute that number of
hexagons across the state with the objective of maximizing the centroid
distances of all the hexagons.
Fourth, expand out from each hexagon one additional hexagon at a time in a
circular fashion with all expansions starting on the same side of the original
hexagon. Total the number of potential voters. If there are no potential
voters in a hexagon, advance one more in the rotation. Then repeat the same
expansion, total the voters and do it again until the desired district
population is reached.
There are obvious problems here: e.g. what happens when a district encounters a
state boundary or another district's hexagon early on? I don't have a solution
(yet). But I think this simulation could be easily tested without a lot of CPU
overhead. And after the districts are created, we could start to look at the
demographics of the potential voters.
TJ
============================================
Tom Johnson
Institute for Analytic Journalism -- Santa Fe, NM USA
505.577.6482(c) 505.473.9646(h)
NM Foundation for Open Government<http://nmfog.org>
Check out It's The People's
Data<https://www.facebook.com/pages/Its-The-Peoples-Data/1599854626919671>
http://www.jtjohnson.com<http://www.jtjohnson.com/>
[email protected]<mailto:[email protected]>
============================================
On Sat, Nov 3, 2018 at 4:14 PM Nick Thompson
<[email protected]<mailto:[email protected]>> wrote:
Oh, I absolutely agree that we could design districts to maximize any variable
we wanted. And with a little luck, we might maximize a couple, or even three.
But inevitably, we will encounter some variable that is negatively correlated
with those we already maximize, so even we philosopher kings will be
dissatisfied with the result.
So, you philosopher-kings out there: if you were designing districts out
there, how would you do it. How about all districts at-large? Ranked choice
voting? How about requiring all districts to match the state-wide political
distribution of the whole state and redistricting after every election?
Seriously. How would you do it?
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/
From: Friam
[mailto:[email protected]<mailto:[email protected]>] On Behalf
Of Marcus Daniels
Sent: Saturday, November 03, 2018 11:24 AM
To: The Friday Morning Applied Complexity Coffee Group
<[email protected]<mailto:[email protected]>>
Subject: Re: [FRIAM] gerrymandering algorithm question
Nick writes:
“I don’t mean to say that “fair districts” aren’t possible. I just mean to say
that I, as your philosopher-king, could not design them.”
Wasn’t there a recent effort by the MIT Sloan school to redesign the school bus
routes in Boston? They managed to reduce the cost and time of the routes by a
large amount, but then many complained because it didn’t reflect the underlying
class structure of the community and the preferences of the richer communities.
One can design an optimization to balance any set of goals. It’s just that
some of the goals we don’t talk about. They are wired-in to our reptile brain
as baseline expectations and not reflected in the political conversations of
dinner parties.
Marcus
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