Government Identifiability Increases Linearly in the Number of Parties

• In Event: Governments, Electoral Systems and Voter Perceptions

Abstract

Government identifiability -- the degree to which the party composition of the eventual government can be predicted given the election results -- is a desirable characteristic of a political system. But the measurement of identifiability has remained impressionistic, limiting our ability to speak precisely about trade-offs between identifiability and other characteristics of the political system. I build on the literature on coalition formation, and use as a measure of government identifiability the entropy of predicted probabilities of coalition formation. This gives a ratio-level measure of identifiability, measured in bits: informally, the number of maximally-informative yes/no questions needed to identify which government formed. I then set out a parsimonious model connecting identifiability to the number of seat-winning parties. I find that each additional seat-winning party results in an increase in entropy of three-quarters of a bit. I show this for 1084 governments formed in parliamentary systems. I supplement this analysis with an analysis based on plausible counterfactuals based on elections where parties narrowly passed an electoral threshold, and an analysis based on predicted numbers of seat-winning parties from the seat product model (Shugart and Taagepera, 2017). I then extend my analysis back to model government identifiability as a function of the seat product, or district magnitude times assembly size. I use my findings to delineate trade-offs between majoritarian and proportional visions of democracy, and in particular the nonlinear relationship between identifiability and proportionality: small increases in disproportionality greatly increase identifiability, but show decreasing marginal returns.

Author

• Chris Hanretty, Royal Holloway, University of London