Gerrymandering and the Limits of Representative Democracy

We assess the capacity of gerrymandering to undermine the will of the people in a representative democracy. Citizens have political positions represented on a spectrum, and electoral maps separate people into districts. We show that unrestrained gerrymandering can severely distort the composition of a legislature, potentially leading half the population to lose all representation of their views. This means that, under majority rule in the congress, gerrymandering enables politicians to enact any legislation of their choice as long as it falls within the interquartile range of the political spectrum. Just as worrisome, gerrymandering can rig any legislation to pass instead of the median policy, which would otherwise prevail in a referendum against any other choice.