How can we measure legislative district compactness by simply seeing it?

Background: Many state constitutions require legislative districts to be "compact" to deter gerrymandering, but the legal definition often defaults to subjective assessment ("you know it when you see it"). Concurrently, academics debate whether compactness has multiple dimensions and if no single measure captures its essence.

Data & Methods: We developed a survey instrument designed to capture people's intuitive understanding of district shape. This approach yielded high inter-rater reliability where standard paired comparisons often fail. Based on these survey responses, we created a statistical model that predicts assessments of compactness by judges and public officials responsible for redistricting.

Key Findings: Our validated measure accurately reflects compactness evaluations using only geometric district features. We demonstrate its predictive power across various jurisdictions.

Why It Matters: This provides an objective tool to operationalize the subjective concept of "compactness," crucial for transparent and fair legislative redistricting processes at both state and federal levels.