House of Representatives or House of Lords? How to Abolish the Gerrymander: An Algorithmic Approach to Redistricting

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House of Representatives or House of Lords?

How to Abolish the Gerrymander:

An Algorithmic Approach to Redistricting

By David A. Burton

There is an inherent conflict of interest with having politicians draw political districts. They will inevitably draw them with a particular outcome in mind, to predetermine election results and protect their own interests. Even when the resulting districts don't look like Elbridge Gerry's Massachusetts salamander, the process disenfranchises voters to protect the interests of politicians.

A politician in an artificially safe district is not accountable to the voters. He is not, in any meaningful sense, their representative. He needn't be much concerned with their needs or their opinions.

We might as well grant lifetime appointments and dispense with the pretense of republican government: Don't call it the U.S. House of Representatives anymore, call it the U.S. House of Lords.

There is a better way. It is possible to create a truly fair redistricting process, which is immune to gerrymandering, and which draws the most regular, compact districts that are physically possible. It will be a three step process:

Step 1: Identify a set of neutral, non-partisan principles for drawing districts.

That's not difficult. There is general agreement about what makes a good plan: the more counties or towns it splits, the worse it is; the more irregular or elongated the districts are, the worse it is. Plus, we must limit the maximum allowable population variance between districts, and we should probably forbid split precincts and multiple-member districts.

Step 2: Quantify those principles, by devising a mathematical formula to “score” proposed redistricting plans.

For example, to test for elongated districts, take the distance between the two most distant points in each district, and sum all the distances; the lower the sum, the better the plan. (See the sidebar for full details of one possible formula.)

Step 3: Find the redistricting plan with the best possible score.

It would not be difficult to write a computer program to find the best plan, using an algorithmic technique called “heuristic search.” An independent commission could be given the task of supervising the process.

Another way to find the best plan is to simply permit any citizen to devise a plan and submit it to the NC Board of Elections, and require that the BOE score the plans according to the formula, and select the plan with the best score.

This approach to redistricting is straightforward, foolproof, and totally immune to gerrymandering. It will take the politics out of redistricting, and end the disreputable practice of politicians drawing safe districts for themselves and their allies. It will create regular, compact districts with an absolute minimum of split counties and cities, and it will enable us, for the first time, to prove to the courts that the districts were drawn without racial or partisan bias. If we write this process into the State Constitution, then North Carolina citizens will never again be disenfranchised by gerrymanders.

© 1998, 2000 by David A. Burton. Earlier versions of this article appeared in Carolina Journal and several newspapers, in 1998.

Vita: David A. Burton is the founder and President of Burton Systems Software, POB 4157, Cary, NC 27519. He has a BS in Systems Science from Michigan State University, and an MA in Computer Sciences from the University of Texas at Austin. Contact him by telephone at 919-481-0098, or by email at

Details: A Formula to Quantify the Quality of Redistricting Plans

Or: How to Answer the Question, “Which Plan is Best?”


1) Minimize elongation of districts.

2) Minimize irregularity of districts.

3) Minimize number of split counties and municipalities.


The formula will consist of three scores (one per goal), added together. The lower the total score, the better the plan.

Formulas to score a plan’s conformance to each goal:

1) A measurement of elongation:

For each proposed district, find the distance “as the crow flies” between the two most distant points in the district. Square each of these distances, and sum the squared distances. (Elongated districts result in a higher sum.)

2) A measurement of irregularity:

Sum the “rubber-band areas” of all districts. For each proposed district, draw the minimum-sized convex polygon which surrounds it, excluding territory outside the State of North Carolina. Call this the “rubber-band area” for that district. (Visualize the shape enclosed by a rubber band stretched tightly around a map of the district, except exclude territory that is outside the State of North Carolina.) Sum the land area inside the resulting polygons. (Irregular districts result in the same land area being counted two or more times, hence a higher sum.) [1]

3) A measurement of how badly the plan splits counties and municipalities:

For each county or municipality that the plan splits, take the number of districts that it is split into (or, if a county or municipality is too large to fit into a single district, take the number of “excess” splits), and cube that number. Sum the cubed numbers for all split counties and municipalities, and multiply the sum by 1/20 of the average land area in a district. (I.e., multiply by 220 square miles for U.S. Congressional districts, by 53 square miles for NC Senate districts, or by 22 square miles for NC House districts).

Finally, sum the three scores. The lower the total score, the better the plan.

Alternative / Additional goals

Other goals could also be factored into the formula. For example, you could seek to define districts which have reasonably uniform population densities throughout the district, so that you would end up with some districts that are mostly rural, and other districts that are mostly urban. This could be done by first computing the population density for each precinct, and then for each district computing the standard deviation of the precinct population densities. Then add to the total score “penalty points” for high standard deviation values.

[1] The concept of “rubber-band area” is from: 92 Michigan Law Review 483, (C) 1993 by Richard H. Pildes and Richard G. Niemi.


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