Voting power in municipal annexation elections

In many American states, municipal annexation and consolidation require concurrent majority votes of all affected jurisdictions. The effectiveness and fairness of this voting procedure have been criticized on the grounds that a small minority of voters can frustrate the preferences of the overall majority. This paper investigates the extent to which the relative ability of voters in large and small jurisdictions to influence voting outcomes in procedures requiring concurrent majorities is influenced by jurisdictional size. The Banzhaf index, which counts the number of case4s in which a given voter could reverse the overall group decision by changing positions on an issue, is applied to this problem of concurrent voting majorities. Mathematical analysis indicates that the ratio of power between voters in small and large jurisdictions approximately equals the inverse of the square root of the ratio of their population size.