Abstract
This article presents a general framework for using continuity-based regression discontinuity designs as an identification strategy in multi-seat electoral contests. First, I extend single winner-close-race designs by developing precise definitions of electoral tightness in elections where multiple winners are possible. These narrowness measures can be used to formulate forcing variables for conducting regression discontinuity designs. Moreover, I show that it is possible to construct different running variables to identify different (local) causal effects. I further specialize my method to proportional election systems, the most prominent family of multi-seat assignment methods, covering its most common variations: the highest average methods and largest remainder algorithms. The proposed approach improves existing methodologies for causal inference on multi-seat systems in four dimensions: it relies on weaker identifying assumptions, estimated quantities have a clear interpretation as causal effects, it does not hinge on discretionary choices, and it is easier to scale into problems with many political entities and seats.
