Can't you just draw the N districts that you want, then break out N new districts from those by extracting a "ring" from each. Then you have N districts each fully surrounded by another district. The only way to merge pairs of adjacent districts is to restore the original layout.
Seems like a pretty trivial way to break the algorithm. But I probably misunderstood something.
Yes, that would work. The paper has a note about excluding districts like this:
> "Valid districts are contiguous and have equal population. Strict constraints on compactness, geographic splits, or other restrictions are not necessary, but such limitations could be included. However, valid districts may not include “donuts,” where one district entirely encircles another."
No, I think you are absolutely onto something -- as you describe it, it is trivial to transform from N -> 2N districts in a manner which makes it impossible to combine them back 2N -> N in any other way than the original map.
Maybe I'm missing something too. That seems like a pretty big deficiency.
Seems like a pretty trivial way to break the algorithm. But I probably misunderstood something.