I like natural districts, so one approach would be to let people say
and let history decide. The reason why I find "natural" districts
natural in politics is that when people feel like they are part of
some community it is easier to find consensus and cooperate within
that community. And of course the border lines will then follow
whatever natural dividing lines there are.
One simple approach would be to ask the voters directly about the
(physical/mental) distances. The answers could be of e.g.
Village1>Village2>Village3>... There could be more villages on the
questionnaire than there will be districts. Also the home coordinates
of each voter would be known. With these values you can then draw the
districts so that you serve the voters/inhabitants as well as you can
an let them belong to the districts that they like (because of
driving distance or historical or whatever reason).
One could e.g. first pick n random villages as the district centres
(voters may or may not need to travel there to vote), and then
optimize the border lines so that more and more people are happier
and happier with their district, and occasionally change also the
chosen villages to check if that could lead to better results. Also
some basic rules needed to keep the districts compact. This is thus a
general optimization problem (and sufficiently "computationally
feasible" in line with the theme of this mail stream).
If you have single seat districts you have to force the districts to
be about equal in size. This will work against having natural border
lines, but at at least we can force the results to be as natural as
possible.
There's some risk of someone trying to gerrymander the border lines
by giving guidance on how to vote. But this may not be a practical
strategy.
Juho
On Sep 3, 2008, at 22:46 , Jonathan Lundell wrote:
I haven't been following this thread in great detail, but I do have
a question: what is the distance function actually trying to
measure and minimize? What exactly are we trying to optimize when
we minimize "distance", by whatever measure? I might be close in a
crow's-flight sense to a neighbor on the other side of a river or
freeway with a driving distance of several miles.
OK, we could solve that in principle (though not too quickly) by
using Google Maps driving time, or the like. But what does driving
time have to do with grouping voters (unless we're drawing a
precinct and measuring travel time t the polling place)? Maybe we
mean communication: two people with telephones are closer in this
sense than people without (and people with unlimited long distance
are close in this sense independent of cartesian distance).
I live in several voting districts where geographical lines make
sense--my local fire district is a case in point, as would water
and sewerage (except that I provide my own in those cases, as it
happens). But legislative districts? I can't think what I'm trying
to optimize for which straight-line vs manhattan distance would be
relevant. I've never met my representatives on business; I
communicate with them via email or telephone, and I neither know
nor care where there local offices are.
On Sep 3, 2008, at 12:17 PM, Raph Frank wrote:
On Wed, Sep 3, 2008 at 1:57 PM, Brian Olson <[EMAIL PROTECTED]> wrote:
I checked my code and I'm not doing the expensive square root.
It's not
quite the second though, it's actually:
((dx*dx + dy*dy) * weight)
The weight gets nudged by multiplying by 1.01 or 0.99. Squaring
the weight
or not and how it's nudged is probably just an efficiency issue
and not a
correctness issue, it should still get to the weight it needs,
just maybe
along some suboptimal curve.
I think it is equivalent anyway. Well, you might have to multiple by
1.02 and 0.98 instead to get the same as weight squared.
I think multiplicative weight makes more sense. No chance of
underflow, and
might scale better between districts with different densities.
Well, negative distances are fine too :).
However, it could mean that the point ends up outside its district.
Yes, the block shape file determines adjacency. They handily
label every
line segment with what block is on either side of it, so I can
pretty
quickly filter that to keep a list of all pairings I've seen.
Ahh, cool.
I might have a look at that file again. It just seemed more trouble
than it was worth.
In my software, I just assume that the people are compressed down to
the location point given in the block group table.
Of course I do
also wind up going back and rendering that geometry to an actual
map.
So, the maps on your site draw the boundary as it using the
block-group boundary info?
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