Continuous and discrete isoperimetric inequalities and gerrymandering
Abstract
The Polsby-Popper score, in political science literature, analyzes compactness of congressional districts in area is compared to perimeter. By observing some issues with this shape analysis scores, we discretize the Polsby-Popper score via notions of graph theory and discuss the relationship of isoperimetric inequalities and vertex compactness in various lattices of the Euclidean plane. We further introduce a way to compare continuous and discrete scores of congressional districts to detect gerrymandering.
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- OSU Theses [15752]