[EM] District continuity preserving re-districting

[Niemzinski at ecybermind.net]

Quoting Ernest Prabhakar <drernie at mac.com>:

> We were just discussing this a couple months ago.   The general 
> consensus seemed to be that there were two useful compactness measures:
> 
> 	a) Weighted perimeter length (# lanes of traffic cut)
> 	b) 'moment of intertia' - extended distribution of population
> 
> In principle, I suspect both of these criteria would over time preserve 
> continuity of communities and districts based on natural geography, 
> without the need for explicit district continuity requirements like 
> your first four points.

a) is  a measure of transportation connectivity, I don't consider it a measure
of compactness and I prefer pure compactness measures over a).  a) runs the
risk of becoming obsolete as more people telecommute.  b) by itself,
like any compactness measure by itself, still allows dramatic district
population transfer changes, thus it still needs a district continuity
constraint if we are serious about trying to limit district discontinuity. 
Points 2 and 3, in addition to protecting district continuity, are also
directed against gerrymandering.  Unnecessary and unconstrained district
splitting and joining opens the door to gerrymandering.

> 
> Using existing census data, one could trivially create open source 
> software that would suggest possible districts.  Anyone could submit 
> potential redistricting, and  and one could have a university collect 
> and publish the results based on objectively verifiable criteria.   I 
> suppose one could even add a third measure of 'minimal population 
> transfers' to reward proposals that minimized discontinuities, if the 
> first two weren't definitive enough.

I don't know how to simultaneously combine two different optimization goals like
# lanes of traffic cut and population moment of intertia, let alone adding a
third such as population transfers.  My assumption is that we can only optimize
on a single goal so all other goals within the optimization model must be
represented as constraints.  Point 4 sets a maximum population transfer
constraint.  As with measure of compactness, I am not opinionated about the
district continuity constraint.  I just presented one as an example.  It is
important, of course, that the constraints be designed to try to ensure that
the optimization model is feasible and has enough slack to allow many possible
solutions.  There would also be a maximum difference in district population
constraint.  Anymore constraints would raise the risk of feasibility problems.

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