Probabilistic spatial power indexes

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.