Linear and quadratic utility loss functions in voting behavior research

Numerous studies examine voting behavior based on the formal theoretical predictions of the spatial utility model. These studies model individual utility from the election of a preferred party or candidate as decreasing as the alternative deviates from one’s ideal point, but differ as to whether this loss should be modeled linearly or quadratically. After advancing a theoretical argument for linear loss, this paper uses a wealth of data across 20 countries to empirically examine the predictive power of these two loss functions in terms of both voter choice and voter turnout. Results indicate that the linear loss function outperforms the quadratic loss function. The findings have important implications for theoretical scholars seeking to model voter behavior, for observational scholars, who must assign utility values across parties to individuals under study, and for experimental researchers, who must entice individuals with particular utility loss functions.