[EM] Theoretical Issues In Districting

[Kristofer Munsterhjelm]

Warren Smith wrote:
> A preliminary web page on this topic is now available here
> 
> http://rangevoting.org/TheorDistrict.html
> 
> Your comments would be appreciated to help me improve this page.
> 
> [There is a much longer scientific paper in the works by me & others
> on this, but it unfortunately has been in the works several years
> already :(  I'm too lazy and/or bit off
> more than could chew.]
> 

Writing as I read...

There is a third way of doing this. Taking a page out of Stafford Beer's 
book, it's "better to dissolve problems than to solve them". In other 
words, if you can get a multiwinner system, redistricting becomes more 
or less a non-issue because minorities get represented anyway.

Over here (where we use list PR), electoral districts follow the second 
level administrative division ("fylke") boundaries. This means that some 
districts get fewer reps than others, but that's not a problem. In our 
particular case, to keep politics somewhat decentralized, large 
districts get proportionally more reps than small ones, and large 
parties are also favored by a tweak of Sainte-Laguë, but neither of 
these features are required to make multiwinner work.

For that matter, now that I think about it, there's a fourth way, too, 
although you touch on it. Have an independent commission draw the 
boundaries - something like Elections Canada in, well, Canada, or the 
Boundary Commissions of the UK. This might be rather difficult to do in 
the United States, though.

-

Other than that, some comments:

I don't know of any laws that have mandated and described certain 
formats, but I do think there have been laws that say something like 
"all data of this type must be given in [ISO standard X] format" or "all 
data of this type must be given in a format standardized by 
[organization]". This was part of the reason, AFAIK, that MS went to 
such lengths to get their XML Office format standardized by ISO.

It'd be possible to do a combination of these. Have the state produce a 
standard (according to current algorithm knowledge), then people can 
improve it if they want by submitting their own solutions.

I suppose you could quantify the degree to which the measure could be 
manipulated by considering how great a change in the score altering the 
outer shape of the district will produce. For the measures you call 
"stupid", you can change the shape a lot without altering the score; for 
measures 1 and 2, you can change the shape quite a bit and only change 
the score a little; and for measure 3, you can barely change the shape 
at all. But in turn, the vulnerability depends on how much you can 
gerrymander given a certain "wiggle budget".

Impartial redistricting can still be "unfair". Consider a very 
simplified model where Democrats live in cities and Republicans live 
outside them. Then an algorithm that draws compact districts will crack 
Republicans because the district centers will tend towards the cities.
In a more mathematical, general sense: single member districts 
invariably introduce some rounding error, and different redistricting 
methods produce different patterns to these rounding errors. The 
distribution of voters might then interfere with the patterns of 
rounding errors so that voters of a particular type tend to have 
disproportionately little (or much) power.

Measures 1 and 2 can be modified to take features into account. I 
actually did that in my "what if" redistricting of the entire world into 
190 or so countries. Simply define a "point to neighboring point" 
distance that takes features into account (e.g. crossing rivers or going 
from water to water costs a lot more). Then you generalize this to 
non-neighboring points by making the distance between two points equal 
to the shortest path according to that point-to-neighboring point distance.

Oh, I see you already mentioned multiwinner. Oops :) I'll mention that 
in what Woodall would call fully proportional methods, the fraction F of 
voters doesn't have to coordinate in order to get a fraction F of the 
assembly. That is, methods like STV (but not RRV or SNTV) are 
proportional by solid coalitions, not just by candidates. Methods that 
are proportional by candidate but not coalition can lead to 
sophisticated vote-distribution efforts - at least this was (is?) the 
case with SNTV in Taiwan - see 
http://en.wikipedia.org/wiki/Single_non-transferable_vote#Potential_for_ta
ctical_voting for more information.