Saturday, December 17, 2011


Wondering about redistricting, I asked a great Mathematics Professor. The following is my question, and the terrific answer by:

Dr. Chris Essex.

Let the re-districting decision makers know!!

On 17 Dec 2011, at 08:46, Roni Bell Sylvester wrote:

CHRIS- - - -we were just talking about you.
As you well know, some states are having to "re-district." Of course "emotion and POLITICS" are weighing in. Colorado's crazy, and now also Wyoming. Couldn't straight forward Mathematics easily re-district? I think so.
Subject: Re: mathematics and state's re-districting...
Date: Sat, 17 Dec 2011 16:00:49 -0500
Dear Roni,
Talking about little old me? No wonder my ears have been itching.
Mathematics is just a tool. You can apply different rules to get different results. There is no objective way to decide what the rules should be used. So politicians will always support rules that give their cause maximum advantage over their opponents. Putting them in charge of drawing the lines is the classical case of the fox managing the hen house.
That said, gerrymandering is so infamous that everyone knows ridiculous and tortured examples. I can't see how it can be eliminated completely, but one could lay out some general mathematical rules to eliminate the more goofy cases. Here are some suggestions:
1. Districts are contiguous. I suppose that is already the case but I am a foreigner you know. I hope and expect it is so.
2. Districts should be "convex." This means that a straight line between any two points in the district is entirely in the district. This rules out hour glasses, moon shapes, dumbbells, conveniently wiggly boundaries, rings and annuluses (i.e. no "multiply connected" districts to use topological language). It does include rectangles, polygons, circles, and many more complex shapes. Exceptions to this would be boundaries along state lines, and significant geographical divides like mountains, major rivers or shore lines.
3. The "set diameter" of a district should be less than an pre-agreed set multiple of the state set diameter divided by the number of districts. If you find the distance between all pairs of points in the district or state, the biggest of these is the "set diameter" of the district or state. This rule would eliminate long skinny districts that would otherwise satisfy the other rules. It basically means that the amount the set diameter for a district exceeds the average over all districts is limited by previous agreement. It also excludes having all of the districts looking like venetian blinds over the whole state.
OK these rules are flexible and general enough that they cannot be considered to give any party an advantage while ruling out the most goofy cases that give this process a bad name. I hope this is what you had in mind. These rules could be tuned a bit I am sure, as this is just off the top of my head.
Dr. Christopher Essex,
Professor,and Associate Chair,Department of Applied Mathematics the University of Western Ontario
London, Canada N6A 5B7


Editor said...
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Editor said...


What a wonderful logical approach to representation. Obviously your life path was able to deftly dodge the dulling effect that politics often brings!

I want to take advantage of this exchange to tell you how much I have grown to appreciate your efforts for “ Taken by Storm”. As I interact with various groups over the past few years, I have always recommended it as a primer for the climate issues and now that Donna Laframboise has generated her wonderful expose, the two books seem to make perfectly complimentary book-ends for a perspective on the issue. And while I’m at it, I also have great appreciation for Ron Bell’s efforts to keep the drum beat of sanity going. Surely, with all of you quality folks that are delivering the goods, we can get this world back on track. For the first time in many years, I actually have a sense of change toward the light beginning to occur.


Editor said...

Yeah thanks. Just the facts ma'am. I would add that the venetian blinds scenario is not actually prevented by item 3 alone, but also that enough politicians not doing it would prevent by item 3 the rest from attempting it. Go ahead make my day and post it. Chris Essex