An improvement of the Deegan–Packle index in a voting game

This paper proposes a new power index which is an improvement of the Deegan–Packle index (the D–P index) denoting the influence power of each voter in a voting game. In the D–P index it is assumed that all minimal winning coalitions (MWC) are formed with equal probability. We consider that each MWC is formed with a probability in inverse proportion to the number of voters in the MWC. We show an axioms system on which the new index is based and compare some power indices in case of the House of Councillors in Japan.