Probabilistic spatial power indexes

In this study, we present a generalization of spatial power indexes able to overcome their main limitations, namely (i) the excessive concentration of power measures; (ii) the too high sensitivity to players’ location in the ideological space. Voters’ propensity to support an issue is modeled via a random utility function with two additive terms: the deterministic term accounts for voters’ preference-driven/predictable behavior; the random one is a catch-all term that accounts for all the idiosyncratic/unpredictable factors. The relative strength of the two terms gives rise to a continuum of cases ranging from the Shapley value, where all aggregation patterns are equally probable, to a standard spatial value, like the Owen–Shapley index, where instead the conditional order is fully deterministic. As an illustrative application, we analyze the distribution of power in the Council of Ministers under three different scenarios: (i) EU15 Pre-Nice; (ii) EU27 Nice Treaty; (iii) EU27 Lisbon Treaty.