Evaluation of decision power in multi-dimensional rules (Q2070556)

In this paper known indices for social choice are extended to the multidimensional case. Power indices are introduced, which can evaluate the decision power of an individual or of a given dimension; the focus is on the power from the individual perspective. The general framework is given in section 2. In section 3 the well known (private) indices Shapley-Shubik and Banzhaf are extended for the multi-dimensional case. Axioms for multidimensional rules are defined. Both indices are characterized by 4 axioms respectively. Section 4 contains 3 public indices (individuals can have different contributions but share the same amount of power) and the Deegan-Packel index. By defining additional, index-specific axioms these indices can be characterized by 4 axioms, too. Only 2 axioms are relevant for all 6 indices: null individual (if an individual has no influence on the final decision then she has null power) and anonymity.