[EM] A computationally feasible method

[Raph Frank]

On Sun, Aug 31, 2008 at 4:29 PM, Brian Olson <bql at bolson.org> wrote:
>
> On Aug 31, 2008, at 8:25 AM, Raph Frank wrote:
>> Ofc, he doesn't define "geographic centers of the districts", which
>> presumably means the centre of gravity of the district.
>
> I'm pretty sure I want the average point of the land area, but yes, there
> are different ways to count 'center' or 'middle' and there may be some
> debate between them.

The average point of land is equal to the centre of gravity (unless I
misunderstood/misremembered the maths).

>> Maybe it would be better to define the centre of the district as the
>> average position of all the people in the district.
>
> That's an obvious alternative, and it results in different shaped mappings
> when used, and it's not obvious which way is better, but I'm still leaning
> towards average distance per person to land-area-center rather than
> population-center. I think population center could be more likely to wind up
> with a million people right at center, and a few people flung off far away,
> but land-area-center is less likely for that to happen.

I guess the best way is to try both methods :) for a few States and
see which ones look better.

You are probably right that the land centre would be more likely to be
compact and that should help the districts look better.

However, the cases where there are large narrow tails would be where
people in those tails are also far from the centre of the other
district they are being considered for.

Also, distance could be calculated for the path that occurs inside the
district.  This would favour convex districts or at least districts
where all points in the district can 'see' its centre.

> Given my anectodal experience with running solvers so far, it'll be pretty
> hard to get a good impartial score and also secretly bend the mapping
> towards some objective. This is substantially just because it's hard to get
> a good impartial score. I think the type of organization with the biggest
> chance of affecting the outcomes would be one with a big server farm:
> national labs with supercomputer clusters, Google, Yahoo, Amazon, NSA, etc.

Right.  If most of the near optimal solutions are just slight
modifications of the optimal, then it would require massive effort and
in the end only slightly modify the results.

It is not likely that there will be a few local maxima that are all
roughly equal quality.  Eventually, one will take the lead as the
quality of the solution improves and then all contender results would
be just slight modifications of that local maximum.