Ernest Prabhakar wrote:

I think this number is actually the crux of the issue.   If the size of
a census tract is far smaller than the size of the district, then I
would argue it doesn't matter how much bias there is in how the tracts
are defined.  

Matt responds:

To summarize:  All of the non-bias burden then falls on the method for assembling the districts.  Census tracts are excellent for unbiased, unmanipulatable methods.  I would argue that the most unbiased, unmanipulatable methods are those based purely on abstractions such as geometry as exemplified by district compactness.  The issue then becotmes one of whether or not a gerrymander resistent result is sufficient or a bias free result is more important.  You argue in favor of the bias of respecting "natural communities" which I think is an ill-defined concept.  You also argue in favor of maintaining stability across re-districtings.  Here we agree - people do want predictability and that is lost if districts change substantially every ten years.

Ernie P. wrote:

This question could probably be settled by empirical calculation.  
We'd need a fine-grained grid describing Republican vs. Democrat, then
impose a coarse-grain grid for each of the tracts.   The challenge
would be to see if it was in fact possible to redraw tracts, or build
additional roadways, to create a gerrymandered district.

If someone was willing to precisely define the conditions, I could
probably code something up.

Matt responds:

If database format electronic versions of historical census district maps are freely available in a then it would be possible to run an experiment and see how much the districts change every ten years using compactness optimization hueristics.  This could then be compared with road count minimization for stability of districts, but you would then also need the road information in the map database.  Do you know how to represent map information like that in a data structure or data base for this purpose?  Do you know if information in such format, or convertable to such a format, is freely available?  If not, are you sure you are prepared to enter such information manually?

I believe that compactness optimization and road count minimization optimization could be identical hueristics.  The edges for compactness optimization would be respresented by adjoining perimeter segment length.  If you think you are up to the task of coding such a hueristic I say go for it.  But that isn't an easy task.  I think this task requires optimization modeling training such as graduate degree in Operations Research.  And it will require a substantial investment in time unless you can find some pre-existing models that fit.  It is the sort of project that may  be food for final semester OR graduate students.  And it may require very expensive software to this properly.