[EM] Re: redistricting - objectively

[Dr.Ernie Prabhakar]

On Jan 8, 2005, at 10:22 AM, Dr.Ernie Prabhakar wrote:
> However, I think Brian makes an excellent point:  the most important  
> question is what is the *goal* of redistricting.  If we can come up  
> with an objective criteria for measuring the 'goodness' of a map, then  
> it really doesn't matter how it is drawn or by whom. That would  
> effectively decouple the political issues from the technical ones.
> In the debate (generally, not just here) I've heard a range of  
> criteria/concerns that people want to maximize:
>
> 1. Equality Population (P)
> 2. Community Connectedness (C)
> 3. Geographic Compactness (G)
> 4. Consistency with existing Districts (D)

I've been thinking about this some more, and wanted to be a little more  
precise.  Here's my best attempt to define Objective Districting  
Criteria -- please let me know your thoughts.

-- Ernie P.

Objective Districting, Draft 2, 1/9/2005
Ernest Prabhakar <drernie at radicalcentrism.org>


In order to objectively evaluate the goodness of a redistricting  
proposal, we need to evaluate various quantities for each proposed  
district, which are then combined over all districts to generate a  
unique figure of merit ("M"); the proposal with the best M is then  
objectively the best redistricting option based on all the available  
information.

I realize that it may be difficult to reach consensus on these  
criteria, and the appropriate weighting to be used.  However, I believe  
it is still easier -- and far more important -- than trying to reach  
agreement over a process for redistricting.  Armed with objective  
criteria, a redistricting panel of, say, retired judges can focus on  
validating and evaluating submissions (i.e., judging), which is a  
reasonable thing to trust them to do.

I believe there are four valid concerns (criteria) that should be  
jointly minimized during redistricting.

1. Population variance: p
2. Community disconnect: c
3. Geographical dispersion: g
4. Fragmentation of previous districts: f

While these are all valid, I do not believe they are equally important.  
   In fact, I have listed them in order of importance, which would imply  
a weighting like M = 4 * p + 3 * c + 2*g * 1*f.   The numbers are  
slightly arbitrary, but the assertion is that these factors are at  
least qualitatively correct, and politically neutral, which is what we  
are trying to achieve.  Even weighting them all equally (M = p + c + g  
+ f) would still improve representation over time.

Of course, to use any sort of weighting requires that we be able to a)  
calculate p, c, g, and f for each proposed district, and b) normalize  
them so one unit of "badness" is roughly consistent across all four  
criteria.  Fortunately, there are reasonable measures or proxies for  
all of these:

1. Population variance: p[i]

To obtain p[i] for District 'i', we need three numbers:
	P[i] = the population of the proposed district
	P_avg, the average population over all districts
	S, the standard deviation of the current districting map
Then:

	p[i] = (P[i] - P_avg)/S

This, as specified, give us a variable which is 0 if ideal, and +1/-1  
if as bad(good) as the existing districting.

2. Community disconnect: c[i]

The best objective measure of community connectedness is traffic flow,  
as that reflects whom we live, work, learn, and socialize with.   
Disconnects can thus be modeled by the number of lanes of traffic (L)  
intersected by the circumference of the district (including rail,  
etc.): dividing two tightly-coupled neighborhoods is worse than placing  
the boundary in the middle of nowhere.   To normalize, we need to know  
"R" - the number of roads contained in the district.  While neither of  
those numbers is currently part of the standard State database, they  
should be trivial to obtain from any commercial GIS system. Since for a  
random distribution of roads R the number intersecting the boundary  
would grow as the square root, we get:

	c[i] = L / sqrt(R)

3. Geographical dispersion: g[i]

The simplest mathematical measure of dispersion is the moment of  
inertia (I), which is related to how difficult it is to 'spin' an  
object, and is determined by how far the population is from the center  
of mass of the district.   The minimum (0) would of course be if all  
the population lived at the exact center, but a reasonable baseline is  
a uniformly circular disk, which for a given population P[i] and area  
A[i] has a moment of inertia equal to (1/2) * P[i] * sqrt(A[i]/PI).   
This gives a normalization of:

	g[i] = 2 * I[i] * sqrt (PI/Area) / P[i]

4. Fragmentation of previous districts: f

While from a purely aesthetic perspective this is less important than  
the other, intrinsic criteria, continuity of representation is still a  
valid consideration.   A good measure of continuity is the largest  
overlap of the proposed district with any existing district.  This  
gives an overlap O[i] which is 1 if identical to a current district and  
can approach zero if a new district is composed entirely of tiny pieces  
from existing districts.   Thus, our normalized values is:

	f[i] = 1 - O[i]

Again, I'm not claiming that any of these criteria -- or the means of  
calculating them -- are completely perfect and reliable.  However, I  
*am* claiming that they are "good", in that a redistricting scheme that  
does well against these criteria is in generally better than one that  
does poorly.  More importantly, there are only four free parameters  
(the weightings) which can be manipulated politically, and these must  
be set ahead of time, making it impossible to 'rig' the system to favor  
one party over another.

This system is not perfect, but I submit that it is vastly preferable  
to the current system of letting politicians pick their voters (rather  
than vice versa), and more objective even than a panel of judges.  Yes,  
it requires asking voters to trust some slightly abstract mathematics  
(though nothing beyond a bright high-school senior), but that still  
seems more reasonable than trusting politicians.   Plus, if the  
criteria, algorithms, and data are all published freely on the web,  
then any interested citizen group can easily check the results.

To sum it up: I believe this sort of objective criteria would optimize  
redistricting to maximize representation, rather than political  
stagnation.  Isn't that worth the price?

------------------------------------------------------------------------ 
-----------------
Ernest N. Prabhakar, Ph.D. <DrErnie at RadicalCentrism.org>
The mission of www.RadicalCentrism.org is to help individuals,  
communities, and systems become sustainably centered — happy, healthy &  
holy — by being properly rooted in humility, justice & love.
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