Which compactness measures are used to detect gerrymandering?

• A. Efficiency gap
• B. Population parity index
• C. Polsby-Popper and Reock scores
• D. Gerrymandering risk index

Answer: (C)

Compactness in redistricting is about how regular and tight a district’s shape is. Polsby-Popper and Reock scores are the standard ways to quantify that shape, which is why they’re used to detect gerrymandering.

Polsby-Popper looks at area and boundary length through the formula 4π times area divided by the square of the perimeter. A perfectly circular district would give the maximum value (near 1); as a district becomes more jagged or elongated, the perimeter grows relative to area and the score drops, signaling less compactness. Reock measures how much of the district fits inside the smallest circle that can enclose it, by taking the district’s area and dividing it by that circle’s area. If the district fills the circle well, the score is high; if it leaves a lot of empty space within the enclosing circle, the score is low.

These scores focus on shape, which is exactly what compactness is about. Other options aim at fairness of votes or population distribution rather than the geographic form of the district, so they don’t serve as compactness measures.