Redistricting, the Constitutional Equivalent of Fermat’s Last Theorem

The French mathematician, Pierre de Fermat, in 1632 wrote about a problem whose roots went back to ancient Greece. Everyone knew that a squared number could be broken down into two squared components.  Fermat’s Theorem was that it was not possible to do that with any number raised to a power greater than 2.  Fermat’s Theorem withstood being solved until 1994 when a Princeton professor, Andrew Wiles, provided the proof.

What has that to do with redistricting?  The Supreme Court has accepted several gerrymandering cases which creates a problem as complex and difficult as Fermat’s Last Theorem. Article 1, sections 2 and 4 gives state legislatures authority over elections and simply establishes that there will be one representative for every 30,000 people in the states.  

In a review of redistricting by the Congressional Research Service stated that “The goal of redistricting is to draw boundaries around geographic areas such that each district results in “fair” representation.”  However, since districts are drawn by political bodies– state legislatures–it is virtually impossible to eliminate politics in seeking fairness.  The Supreme Court recognized this previously when it ruled that if partisan gerrymandering is extreme, it is unconstitutional.  In 2006, the Court referred to “partisan symmetry” meaning that parties have an equal opportunity to win elections which conflicts with the less than extreme gerrymandering standard.

Partisan symmetry seems to be a simple and straightforward concept.  It is anything but.  How much partisan bias is too much?  Candidates are not necessarily of equal quality and voter intensity is not necessarily equal.  There are no objective metrics for deciding when the line is crossed between acceptably partisan and extreme gerrymandering.  In ruling on the cases before it, the Court could rule narrowly in a way that is case specific or it could rule in a way that gives legislatures constraining criteria for drawing congressional districts.  No matter how it rules, gerrymandering will continue. Legislatures are made up of politicians; not angels.  And political parties that control redistricting will continue to seek to maintain its political control.

Suggestions for redistricting may make the process less partisan but will likely fall short of achieving fairness.  Three approaches have been suggested, none of which are without some degree of political bias.

One popular idea is to use independent commissions instead of legislatures to redraw the districts. However, this solution has the flaw that most humans act in their own self-interests which includes political interests.  

Some have suggested that computer models be used. Although models can be developed in ways that incorporate political biases, models can be tested to determine the “efficiency”—the extent to which votes are wasted—of projected outcomes.  

A Cornell University paper proposed a technique modeled after the “I cut, you choose,” method of sharing. Applied to redistricting, each party would take turns proposing divisions and freezing districts. The controlling party would divide the state into the appropriate number of districts, satisfying all legal requirements. The second party freezes one of those districts and then divides the unfrozen parts into new districts. The first party then freezes one of the new districts, redraws the remaining ones and returns it to the other party. This iterative process continues until all districts have been frozen.

Since the Constitution assigns the redistricting responsibility to state legislatures, they do not have to accept either commission or model results.  The “Cut and Choose” approach probably offers the best approach to achieving relative fairness.

Like Fermat’s Last Theorem achieving redistricting fairness is going to take a lot of time and hard work.


Founder and president of Solutions Consulting which focuses on public policy issues, strategic planning, and strategic communications.

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