1985 Volume 12 Issue 18 Pages 53-66
A “formal coalition” in a voting body is defined as a subgroup of members in which their vote is completely dependent, voting as a bloc. The formation of such a formal coalition sometimes yields the unexpected effects on the power of members in the voting body. They are the non-increase of power of coalitional members and the increase of power of non-coalitional members. This paper shows that the unexpected effects above will occur with respect to the Banzhaf power index and explores that the formal coalition of what members will yield what effects on the Banzhaf power of members. Throughout the paper, it is assumed that there is only one two-member formal coalition in the voting body and that there are no other formal coalitions in it. Using the well-known concepts of veto and dummy, we then obtained the necessary and sufficient condition that the unexpected effects on coalitional member's power will occur. In addition, introducing the three new concepts about non-coalitional members, we obtained several sufficient conditions that the unexpected effects on non-coalitional member's power will occur. Finally, by use of the obtained results we analysed the effects of all possible two-party formal coalitions on the power distribution in the House of Representatives of Japan.