The Coleman-Shapley-index: Being decisive within the coalition of the interested

The Coleman Power of the Collectivity to Act (CPCA) is a popular statistic that reflects the ability of a committee to pass a proposal. Applying the Shapley value to this measure, we derive a new power index that indicates each voter's contribution to the CPCA. This index is characterized by four axioms: anonymity, the null voter property, transfer property, and a property that stipulates that sum of the voters' power equals the CPCA. Similar to the Shapley-Shubik index (SSI) and the Penrose-Banzhaf index (PBI), our new index emerges as the expectation of being a pivotal voter. Here, the coalitional formation model underlying the CPCA and the PBI is combined with the ordering approach underlying the SSI. In contrast to the SSI, the voters are not ordered according to their agreement with a potential bill but according to their vested interest in it. Among the most interested voters, the power is then measured in a similar way as with the PBI. Although we advocate the CSI against the PBI to capture a voter's influence on whether a proposal passes, the CSI gives new meaning to the PBI. The CSI is the decomposer of the PBI, splitting it into a voter's power as such and as her impact on the power of the other voters by threatening to block any proposal. We apply the index to the EU Council and the UN Security Council.