Measuring Electoral Persistence in Multiparty Systems: A Multivariate Fractional Regression Approach

Since most of the world’s democracies feature multiparty systems, the analysis of aggregate electoral data involving three or more parties is of particular interest to political scientists. To handle this type of situation, the present paper adopts a quasi-maximum likelihood approach in the estimation of regression models of multiparty vote shares, which accommodates any number of parties and different functional forms, while relying only on correct specification of conditional means of shares. Rather than introducing a new estimator, this framework is used to quantify and assess the extent of covariate-independent vote persistence in multiparty elections, evincing how the well-known Dogit specification can be used to operationalize and estimate this persistence within a compositional setting. In particular, the distinction between the share of votes that systematically responds to political, economic, and sociodemographic stimuli and the share that remains stable across local contexts can be formulated as an estimation and testing problem using aggregate data. The strategy set forth in the paper is illustrated with cross-sectional data on aggregate vote shares from a Portuguese legislative election.