  Algorithmic and statistical approaches to congressional redistricting are
becoming increasingly valuable tools in courts and redistricting commissions
for quantifying gerrymandering in the United States. While there is existing
literature covering how various Markov chain Monte Carlo distributions differ
in terms of projected electoral outcomes and geometric quantifiers of
compactness, there is still work to be done on measuring similarities between
different congressional redistricting plans. This paper briefly introduces an
intuitive and interpretive measure of similarity, and a corresponding
assignment matrix, that corresponds to the percentage of a state's area or
population that stays in the same congressional district between two plans. We
then show how to calculate this measure in polynomial time and briefly
demonstrate some potential use-cases.
