Declination as a Metric to Detect Partisan Gerrymandering

We explore the Declination δ , a new metric intended to detect partisan gerrymandering. We show that when vote share is fixed, δ  = 0 allows for a wide array of possible seat shares, even when turnout in each district is equal. In particular, if δ  = 0, the majority party has higher seat share when its average vote share in districts that it wins is closer to the statewide vote share. This range of possible seat shares with δ  = 0 results in a range of responsiveness, again depending on the average vote share in districts won by the majority party. We also prove what kind of vote-share seat-share pairs can result in δ  = 0 when the maximum district turnout to minimum district turnout is bounded, and turnout is unrestricted.

Within our analyses, we show that Declination cannot detect all forms of packing and cracking, and we compare the Declination to the Efficiency Gap. We show that these two metrics can behave quite differently, and give explicit examples of that occurring, including examples from recent election data.