How Turnout Depends on the Number of Parties: A Logical Model

We illustrate the power of “logical models” (Taagepera, 2007 Taagepera, Rein (2007) Predicting Party Sizes: The Logic of Simple Electoral Systems (NewYork: Oxford University Press).[Crossref] , [Google Scholar]) by offering a three-parameter model of the relationship between the effective number of parties and electoral turnout that makes use of the constraints on what parameter values are internally coherent given boundary conditions to specify functional form, and seeks not optimal curve fitting but rather a direct model testing. In our model, one parameter reflects an effect that generally acts to increase turnout as the effective number of parties increases, another an effect that generally acts to decrease turnout as the effective number of parties increases, while a third parameter allows for baseline variation in turnout across countries (or within countries across elections). We fit this model to district-level data from 237 elections held in 17 countries, representing a wide range of electoral system types generating multi-party contests, with over 20,000 district-election observations. The basic intuition, that turnout rises to a peak as the effective number of parties increases and then falls slowly, fits our data pretty well.