Characterizations of two power indices for voting games with r alternatives

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote “yes”, “no”, or “abstain”. The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets. Received: 4 April 2000/Accepted: 30 April 2001