A New Shape Measure for Evaluating Electoral District Patterns

The year 1812 is famous for the birth of that favorite political monster, the gerrymander. Many facets of this creature's subsequent behavior have been studied although most scholars have overlooked its most powerful trait-the ability to hypnotize both friend and foe alike. Politicians, political commentators, and political scientists have become fascinated by the shapes of electoral districts. Politicians have proposed and sometimes enacted legislation to ensure contiguity and compactness;' political commentators have been using their imaginations to conjure up more political monsters ;2 and political scientists have recently been trying to measure some elusive shape ideas.3 In this short note I want to shake off the hypnotic influence of the gerrymander to consider briefly how the concept of shape has been approached in other disciplines, notably geography, so that we may return to the electoral districting problem with what seems to be a new shape measure that is particularly suited to this problem. Shape is in many ways a rather peculiar empirical concept. In its most general form it can only be a classificatory concept.4 Thus areal shapes are often compared to the shapes of familiar objects-Italy is like a boot, etc. This nominal level of measurement is equivalent to that of the political commentators referred to above. But if we compare areal shapes to geo-