Theoretical versus empirical power indices: do preferences matter?

This paper investigates whether preference-based (empirical) power indices
differ significantly from their preference-free (theoretical) counterparts. Drawing
on the to date most comprehensive sample of EU Council votes (1993-
2011), we use item-response models to estimate the EU27 member states'
preferences (ideal points) in a one-dimensional policy space. Their posterior
distributions are then used for the calculation of empirical versions of the
Banzhaf and the Shapley-Shubik index, invoking the concepts of connected
coalitions and bloc voting. Our ideal point estimates indicate significant
differences between member states' preferences, which often translate into
significant differences between empirical and theoretical power under individual
voting. However, the formation of voting blocs appears to offset
differences in countries' ideal points as the bloc size grows. This result does
not hold up for the Shapley-Shubik index, whose empirical variants differ
from the theoretical one, both under individual and bloc voting. (authors' abstract)