About half of the states currently impose some form of standard on their districting plans. Yet there is no commonly accepted definition of how is to be measured. This paper surveys some of the principal measures gleaned from the literature in political science, geography, law, and mathematics. Although some of these measures are better than others, all are defective in some crucial respect; that is, they fail to give satisfactory results on certain types of geographical configurations. The conclusion is that compactness is not a sufficiently precise concept to be used as a legal standard for districting plans.
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