Fair allocations using multicriteria power indices

In an allocation problem to determine a fair distribution of some divisible benefit or cost amongst members of a group, there are often a number of input criteria which may be used to make the allocation. We propose the weighted multicriteria power index, which combines traditional voting power in committees with the concept of criteria weighting, to yield a fair allocation. The multicriteria power index can be refined to allow for a moderation or amplification of the voting power of the members of the group, which in the limit would lead to parity or priority (respectively) of the members' power. Two well-documented power indices (the Shapley-Shubik and Banzhaf-Coleman power indices) are extended to operate under multiple criteria, and are used in an illustrative example.