Whose patch is this? B. Leighty / Photri Images / Alamy Stock Photo

The method to fairly split a cake between two people is tried, tested, and mathematically proven. One person gets to cut the cake and the other gets to choose which slice they get. To get the biggest piece of cake, the cutter must split it fairly resulting in no hard feeling between the two eaters.

In American politics, however, cutting states into electoral districts doesn’t have a similarly fair method. The political party in charge often decides where the electoral lines are drawn and does so in such a way to gain an advantage – a process called gerrymandering.

But now, Ariel Procaccia, Wesley Pegden, and Dingli Yu at Carnegie Mellon University have come up with a way to extend the cake cutting technique to electoral redistricting to make the system a lot fairer.


“What we think is exciting about this is that it leverages the competition of the two parties. They can both act in their own self-interest and still result in an outcome that is mathematically fair,” says Procaccia.

With the new approach, one political party gets to draw an electoral map that divides the state into the agreed number of districts. The second political party then chooses one district to freeze so that no more changes can be made to it by either side. They then get to redraw the rest of the map.

Once the new map is complete, the first political party freezes one of the new districts so that no further changes can be made to it, and is allowed to redraw the rest of the map again. This process goes back and forth until every district within the state is frozen. In Pennsylvania, for example, this would require 17 cycles as there are 18 districts.

“Because you have this basic symmetry, the first party doesn’t have a big advantage over the other, so it’s a big improvement from just letting one party choose the district,” says Pegden.

To make the process applicable to the real world “there would need to be a mechanism to account for the Voting Rights Act,” which protects voting rights for racial minorities, says Joshua Douglas at the University of Kentucky. Procaccia and Pedgen say this could be checked after the fact in the same way that new districts are now.

Journal reference: arXiv, DOI: arxiv.org/abs/1710.08781

Read more: Electoral dysfunction: Why democracy is always unfair