[EM] More on Gerrymander prevention

Adam Tarr atarr at purdue.edu
Mon Mar 25 09:33:01 PST 2002

Josh wrote:

>I think the map should be non-geographic, and, instead, road-based.
>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 
"road connectivity" of two adjacent census blocks.

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 
>windy) mountain roads.
>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
>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.

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