Previous work by Diffo Lambo and Moulen [Theory and Decision 53, 313–325 (2002)] and Felsenthal and Machover [The Measurement of Voting Power, Edward Elgar Publishing Limited (1998)], shows that all swap preserving measures of voting power are ordinally equivalent on any swap robust...

This article completes a characterization of achievable and unachievable hierarchies in weighted voting systems where the quota is a proportion of the total weight, proving the main conjecture of Bean et al. (Soc Choice Welf 34: 397–410, <CitationRef CitationID="CR3">2010</CitationRef>). Copyright Springer-Verlag 2012