The Shapley-Shubik Index, the Donation Paradox and Ternary Games
In this paper, we show that although the Shapley-Shubik index is immune to the donation paradox in weighted binary games, extension of the index to ternary games along the direction suggested in Felsenthal and Machover (1996, 1997) will cause it to be vulnerable to the paradox and this is the case as long as the number of players in the game exceeds three. This undermines the attractiveness of the Shapley-Shubik index as a measure of a priori voting power.
Social Choice and Welfare
Chua, Vincent and Huang, HC.
The Shapley-Shubik Index, the Donation Paradox and Ternary Games. (2003). Social Choice and Welfare. 20, (3), 387. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/206