Theoretical vs. Empirical Power Indices: Do Preferences Matter?

This paper considers empirically 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, the Shapley-Shubik, and other power indices, invoking the concepts of connected coalitions
and bloc voting. Our ideal point estimates point to significant differences in member states' preferences, which often translate into significant differences of empirical (versus theoretical) power under individual voting. However, the formation of voting blocs appears to offset differences in countries' ideal points as the bloc size grows. Interestingly, this result does not hold up for the Shapley-Shubik index, whose empirical variant differs from the theoretical one both under individual and bloc voting. (authors' abstract)