Measuring Closeness in Proportional Representation Systems

We provide closed-form solutions for measuring electoral closeness of candidates in proportional representation (PR) systems. In contrast to plurality systems, closeness in PR systems cannot be directly inferred from votes. Our measure captures electoral closeness for both open- and closed-list systems and for both main families of seat allocation mechanisms. This unified measure quantifies the vote surplus (shortfall) for elected (nonelected) candidates. It can serve as an assignment variable in regression discontinuity designs or as a measure of electoral competitiveness. For illustration, we estimate the incumbency advantage for the parliaments in Switzerland, Honduras, and Norway.