GELMAN, Andrew; KATZ, Jonathan N.; BAFUMI, Joseph <br/><br/>
Standard Voting Power Indexes Do Not Work :  an empirical analysis 

 - Cambridge  :  Cambridge University Press,  October 2004 
<br/><br/> Voting power indexes such as that of Banzhaf are derived, explicity or implicity, from the assumption that all votes are equally likely (i.e., random voting). That assumption implies that the probability of a vote being decisive in a jurisdiction with n voteres is proportional to 1/n. In this article the authors show how this hypothesis has been empirically tested and rejected using data from various US and European elections. They find that the probability proportional to 1/n. The random voting model (and, more generally, the square-root rule) overestimates the probability of close elections in larger jurisdictions. As a result, classical voting power indexes make voters in large jurisdictions appear more powerful than they really are. The most important political implication of their result is that proportionally weighted voting systems (that is, each jurisdiction gets a number of votes proportional to n) are basically fair. This contradicts the claim in the voting power literature that weights should be aproximately proportional to n