Gerrymandering is the process of designing legislative districts for the purpose of decreasing the power of the other party’s voters.  There are chiefly two methods in general use.  These methods are known as packing and cracking.

Packing involves designing districts in such a way as to cram as many of the other party’s voters into a small number of regions, thereby reducing the total number of candidates that could represent them.  Cracking entails splitting regions with high numbers of the other party’s voters into separate regions, thereby diluting their votes and rendering them less likely to gain representation.

Gerrymandering has been employed at all levels of government since the earliest days of the republic.  These schemes can be tremendously effective.  In 2011 the redistricting of Wisconsin resulted in Republicans winning 61 percent of the state’s 99 legislative districts despite taking only 48.6 percent of the total popular vote in the state.

The courts have not been particularly sympathetic to cases challenging gerrymandering.  They have generally adopted the view that defining legislative districts is fully within the purview of state powers and that therefore courts shouldn’t intervene.

A method known as the “wasted vote” metric has recently been employed to demonstrate the cumulative effect of gerrymandering.  This metric was employed in a case in 2016 in which the Wisconsin redistricting of 2011 was invalidated by a U.S. District court.

It is certainly helpful to invoke a method for identifying gerrymandering when it occurs, but that is really an after-the-fact method.  By the time the effects of gerrymandering can be measured, votes have already been cast.  It would be far more helpful to develop a method for redistricting that can be employed automatically, without fear that the end result will be an excess of wasted votes.  Such a method of drawing districts should at the very least be:

  1. based on rules– that is, codified in law;
  2. independent of voting patterns;
  3. comprehensive, in that it fully covers all possible cases; and
  4. easy to validate.

A typically gerrymandered district looks like squiggle.  Its boundary meanders about, carefully following the borders of voting regions according to the way their residents vote.  According to principle #2 above, district shapes shouldn’t be based on voting practices.  Therefore district mapping should be purely topological in nature.  To that end, I propose the following principle: that legislative districts should be based on boundaries of equal population density.

Consider a region that has a single major population center, and that population density increases smoothly as one approaches its center.  Regions of equal population as measured from the population center would comprise a set of nested annuli.  Such regions wouldn’t be likely to correspond to any naturally arising neighborhoods, but they would be fully compliant with the principles set forth above.

It might be argued that an annulus is precisely the sort of shape that should not be allowed.  While it might not look like a squiggle, it nonetheless encloses other regions.  And in locations with multiple population centers the resulting equal population shapes would not be simple rings but would instead be more complex nested shapes.

This objection amounts to the concern that the four principles identified above must be supplemented with some additional constraints.  One such constraint might be that the resulting regions must be convex (in the topological sense).  While conditions of this sort might have an emotional appeal, I don’t believe that there are any such conditions that meet all four of the conditions stated above.  It might be possible to “fix up” a set of automatically generated nested annuli to turn them into a collection of disjoint convex sets, but any such method for doing that would be based on human taste and preference.  And that is precisely the sort of decision element that should be eliminated in drawing legislative districts.

Written 2020-11-23

Copyright (c) 2020, David S. Moore

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