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  1. Simple Majority Achievable Hierarchies.Dwight Bean, Jane Friedman & Cameron Parker - 2008 - Theory and Decision 65 (4):285-302.
    We completely characterize the simple majority weighted voting game achievable hierarchies, and, in doing so, show that a problem about representative government, noted by J. Banzhaf [Rutgers Law Review 58, 317–343 (1965)] cannot be resolved using the simple majority quota. We also demonstrate that all hierarchies achievable by any quota can be achieved if the simple majority quota is simply incremented by one.
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  • Achievable Hierarchies In Voting Games.Jane Friedman, Lynn Mcgrath & Cameron Parker - 2006 - Theory and Decision 61 (4):305-318.
    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 simple voting game. Swap preserving measures include the Banzhaf, the Shapley–Shubik and other commonly used measures of a priori voting power. In this paper, we completely characterize the achievable hierarchies for any such measure on a swap robust (...)
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  • Ordinal equivalence of power notions in voting games.Lawrence Diffo Lambo & Joël Moulen - 2002 - Theory and Decision 53 (4):313-325.
    In this paper, we are concerned with the preorderings (SS) and (BC) induced in the set of players of a simple game by the Shapley–Shubik and the Banzhaf–Coleman's indices, respectively. Our main result is a generalization of Tomiyama's 1987 result on ordinal power equivalence in simple games; more precisely, we obtain a characterization of the simple games for which the (SS) and the (BC) preorderings coincide with the desirability preordering (T), a concept introduced by Isbell (1958), and recently reconsidered by (...)
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  • Simple Games: Desirability Relations, Trading, Pseudoweightings.Alan D. Taylor, William S. Zwicker & William Zwicker - 1999 - Princeton University Press.
    Introductory material receives a fresh treatment, with an emphasis on Boolean subgames and the Rudin-Keisler order as unifying concepts. Advanced material focuses on the surprisingly wide variety of properties related to the weightedness of a game."--BOOK JACKET.
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