Randomly Redistricting More Efficiently

In a forthcoming article, Chen and Rodden estimate the effect of ‘Unintentional gerrymandering’ on number of seats that go to a particular party. To do so they pick a precinct at random, and then add (randomly chosen) adjacent precincts to it till the district is of a certain size (decided by the total number of districts one wants to create). Then they go about creating a new district in the same manner, randomly selecting a precinct bordering the first district. This goes on till all the precincts are assigned to a district. There are some additional details but they are immaterial to the point of the note. A smarter way to do the same thing would be to just create one district over and over again (starting with a randomly chosen precinct). This would reduce the computational burden (memory for storing edges, differencing shapefiles, etc.) while leaving estimates unchanged.