Int J Game Theory (2006) 34:229–240 DOI 10.1007/s00182-006-0011-z ORIGINAL ARTICLE Xingwei Hu An asymmetric Shapley–Shubik power index Published online: 18 May 2006 © Springer-Verlag 2006 Abstract This paper extends the traditional “pivoting” and “swing” schemes in the Shapley–Shubik (S-S) power index and the Banzhaf index to the case of “block- ing”. Voters are divided into two groups: those who vote for the bill and those against the bill. The uncertainty of the division is described by a probability dis- tribution. We derive the S-S power index, based on a priori ignorance about the random bipartition. Keywords Shapley–Shubik power index · Banzhaf index · Simple game · Voting JEL Classification Number C710 · D710 · D720 AMS Subject Classification 2000 91A12 · 91A40 · 91B12 1 Preliminaries A generic bill coming to a vote within a voting body is supported by some voters or players, but not by others. Voters with a common interest may cooperate against others. For example, in the United Nations Security Council in the Cold War era the USA and the UK were more likely to vote the same way on a bill, though not always, than the USA and the USSR were. For another example, consider the US House of Representatives. As the growth of one district is beneficial to its neigh- boring districts, representatives from two neighboring districts (one representative X. Hu Department of Mathematics, University of California Los Angeles, P.O.Box 6842, Alhambra, CA 91802, USA E-mail: xhu@math.ucla.edu Tel.: +1-310-8693795 Fax: +1-949-8562044