A Boundary-Based Measure for Gerrymandering

This paper presents a new measure for quantifying legislative gerrymandering based intuitive observation that in a non-gerrymandered district a randomly placed observer should be able to walk in a straight line and only cross the boundary of the district once, when the district is exited. We make this notion precise in terms of the expected value of such crossings. The result is the Boundary Intersection Number, or BIN. Properties of the BIN score are proven and its computational properties discussed