[EM] Another auto districting proposal (Crystal districting?)

[Kristofer Munsterhjelm]

Juho wrote:
> Well, this approach is also complex in the sense that the general 
> optimization algorithms may be as complex as you want, but the 
> optimization algorithms are totally independent of the politics and the 
> basic rules that determine what the final outcome should be (the 
> criterion) can be quite simple and intuitive.
> 
> (Additional criteria like favouring border lines that follow the borders 
> of states or rivers etc. can be easily included in the agreed criterion. 
> Maybe even higher cost of splitting cities etc.)

Splitline works because it's recursive. Any sort of divison algorithm 
where you can smoothly control the relative sizes of the two districts 
will work, also. Just subdivide into two, then freeze one and subdivide 
the other. After you're done, unfreeze the first (and so on). It may not 
produce the best result if the borders can move on the unfrozen areas, 
but should work.

As for general optimization, if you're dealing with an election method, 
then the optimization's approximation to the optimum (you can't ensure 
it'll reach the true optimum if there are multiple local optima and no 
additional structure) becomes a different rule itself. For instance, 
Borda is a 5-approximation to the optimal Kemeny ordering, but Borda is 
a completely different method from Kemeny.

If you're dealing with redistricting, the competition solution that you 
mentioned could work, but it might well be that, for redistricting, 
capturing the exact tradeoff between looking like "communities of 
interest" and being completely neutral is a task best left to an 
independent commission. Of course, one can also dissolve the problem 
rather than solve it, and employ some PR method which would greatly 
diminish the incentive to do any gerrymandering in the first place.