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

[Juho]

On Nov 19, 2009, at 5:35 PM, Kristofer Munsterhjelm wrote:

> 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.

My thinking is that it might be easier to agree about the targets  
rather than the whole procedure. The targets can be simpler to define.  
Following Raph Franks model it would be thus enough to say that any N  
points and the kn values and then derive the border lines and the  
jointly agreed value of the solution from this data. That would not  
leave much space for strategies and gerrymandering. The proposed  
solutions would be evaluated and the one with best value would be  
declared the winner.

The optimization procedures may not find the global optimum (but only  
one of the local optima), but if there is an algorithm that can find  
the global optimum then that solution will also be found. It is  
possible that some party (that runs some optimization procedures)  
would not publish the best solution it found (since the second best is  
better to this party) but the field would be free for anyone else to  
find that even better result. At some point one must freeze the  
solution and ignore any better solution that someone might find later.  
In most cases I guess it is quite improbable that better solutions  
would be found later. And if they are found then they might not be  
much better (probably true for most sensible criteria). No rules are  
needed for the optimization algorithm (= just let the scientists and  
politicians and private citizens do their best + maybe arrange some  
official calculations too to make sure that at least someone makes a  
serious attempt to find the best solution).

Juho