The Measurement of Voting Power
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The Measurement of Voting Power

Theory and Practice, Problems and Paradoxes

Dan S. Felsenthal and Moshé Machover

This book is the first of its kind: a monograph devoted to a systematic critical examination and exposition of the theory of a priori voting power. This important branch of social-choice theory overlaps with game theory and is concerned with the ability of members in bodies that make yes or no decisions by vote to affect the outcome. The book includes, among other topics, a reasoned distinction between two fundamental types of voting power, the authors' discoveries on the paradoxes of voting power, and a novel analysis of decision rules that admit abstention.
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Chapter 8: Taking Abstention Seriously

Dan S. Felsenthal and Moshé Machover


1 8.1 Why Bother? As we observed in Com. 2.2.4, the mainstream literature on voting power has confined itself almost exclusively to the SVG model, which does not admit abstention as a tertium quid that can affect the outcome of a division differently from both a ‘yes’ and ‘no’ vote.2 Moreover, real-life decision rules that do treat abstention as a distinct option — whose effect is not always the same as ‘yes’ or always the same as ‘no’ — are often mis-reported as though they conform to the binary, SVG model. Thus, decisions in each of the two Houses of the US Congress require the ‘yes’ vote of a simple majority or, in some cases, two-thirds of the members present (provided the members present constitute the needed quorum of a simple majority of the entire membership);3 but some of the best writers on voting power erroneously substitute the total membership for those present.4 Also, in the UNSC a permanent member’s abstention, as distinct from a ‘no’ vote, does not count as a veto;5 but the voting1 2 This chapter is largely based on our [32] and [35]. In the mainstream literature, Fishburn [39, pp. 53–55] is an isolated and brief exception. 3 See [35] for details, including quotation from US Supreme Court opinion in the case of Missouri Pacific Railway Co. v State of Kansas, 248 U.S. 276. For example, [11, p. 192], [16, p. 62], [59, p. 235], [66, p. 212], [95, p....

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