Probabilistic Spatial Power Indexes: The Impact of Issue Saliences and Distance Selection

We present a twofold generalization of probabilistic spatial voting indexes. In first instance, we introduce issue saliences in the classical application. The voting power is based on a coalition’s estimated consensus position, defined as the gravity center of the parties’ ideal positions. The issue saliences are implemented in the calculation of the gravity center as well as the Euclidean-like distance function, thus incorporating the parties’ policy priorities. The influence of the choice of distance function on voting power is the second focus of our analysis. We compare the results based on the consistent distance application for three functions: squared Euclidean, Euclidean and rectangular. All three functions can be considered either weighted or unweighted by issue saliences. This gives six possible combinations to calculate the voting power. Rather than using the gravity center, this method estimates the consensus as the point that minimizes the weighted sum of distances between itself and the parties’ bliss points. Empirical applications for Belgium illustrate the influence that allowing issue saliences to vary across parties and dimensions and using different distance functions can have on the voting power.