Mathematical Theorem Finds Gerrymandering in Pennsylvania Congressional District Map

The slider above shows the current districting map for Pennsylvania and the map produced by an algorithm using a series of small random changes. Pennsylvania's congressional district maps are almost certainly the result of gerrymandering according to an analysis based on a new mathematical theorem on bias in Markov chains developed by Carnegie Mellon University and University of Pittsburgh mathematicians. Their findings are published in the Feb. 28 online early edition of the Proceedings of the National Academy of Sciences (PNAS). Markov chains are algorithms that can generate a random object by starting from a fixed object and evolving in a stepwise fashion, making small random changes at each step. Markov chains have numerous applications, and are used to model things like thermodynamic processes, chemical reactions, economic and financial phenomena, protein folding and DNA sequences. To evaluate gerrymandering of congressional districts, a Markov chain can, in principle, be used to compare the characteristics of the current districting map with a typical districting of the same state by generating truly random districtings as points of comparison.