The United Nations is under pressure to make the Security Council more
representative of the membership. The formal literature on voting pow
er has discovered much that can clarify this debate, and the present a
nalysis gives a version of the Shapley-Shubik index of voting power th
at considers likely alliances based on voting in the General Assembly
since the breakup of the Soviet Union. Veto members occupying outlying
positions, like China, have especially high voting power, whereas sta
tes without vetoes hold almost none. However, power in itself is not t
he goal; if another permanent member is already reliably voting as one
wishes, obtaining a veto of one's own is unnecessary. Other benefits
from membership are prestige and access to information. The current de
bate seems at an impasse, but if these alternative goals are recognize
d, other feasible solutions might be found.