Government identifiability and the number of parties: No sweet spots, just a steady linear increase

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 show that a recent measure of bargaining complexity by Cronert and Nyman acts as a ratio-level measure of government identifiability measured in bits – or equivalently, the number of yes/no questions needed to identify the composition of the government. I then show how identifiability is linearly related to the number of seat-winning parties in three different contexts: parliamentary governments, presidential cabinets, and municipal governments. Across all three contexts, an additional seat-winning party increases entropy of government formation by between 0.7 and 0.8 bits. Since identifiability is linearly related to the number of parties, any increase in the number of parties through electoral reform will worsen identifiability by the same amount. Conversely, there are no “sweet spots” where we can achieve high levels of identifiability at low cost in terms of the number of parties.