# [EM] More on Gerrymander prevention

Mon Mar 25 09:33:01 PST 2002

```Josh wrote:

>
>Dense networks of roads should not be separated into separate districts.
>An urban area on two sides of a bridge could easily be divided.

Very slick idea Josh.  The question becomes, how do you come up with a
measure of road connectivity?  I would propose basing it on the same
principles as electrical resistance.  The "resistance" of a road connecting
two points is proportional to its length, and inversely proportional to the
number of lanes.  Find the "resistance" of every road connecting two
adjacent census blocks, and add them in parallel (1/total = 1/first +
1/second + ...).  Invert this total resistance to get the "conductance" or

Build a graph (computer science-type graph, with nodes and edges) out of
the census blocks, with each edge (border) weighted by the connectivity
between those two nodes (census blocks)  Now, we just tell the algorithm to
build equal-population districts that maximize total connectivity.  It's a
well-defined graph theory problem.

>Ignoring real geography in exchange for the human-built road-topology of
>an area isn't actually ignoring geography, since there will be few (and
>
>This also completely plays to the hand of the candidate who actually wants
>to visit his constituents. The road network they would travel would be
>minimal.
>
>Please pardon my lack of effective mathematical terminology for this. I do
>recognize that the problem is the kind with relative minima, and no direct
>course to the solution. However, we could leave the program running for
>years, looking for best examples.

```