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 4: Weighted Voting in the US

Dan S. Felsenthal and Moshé Machover


4.1 One Person, One Vote Weighted voting is widely used with the intention of implementing the principle of OPOV in a two-tier decision-making system: the representatives (or delegates) in a council are assigned weights that reflect the respective sizes of their constituencies. Commonly, weights are roughly proportional to constituency sizes. However, the theory developed in § 3.4 shows that, if the indirect voting powers of the citizens are to be equalized, the voting powers of the representatives must be addressed; and as we pointed out in § 1.1, the latter voting powers may not be proportional to the representatives’ weights. Moreover, according to PSQRR (Thm. 3.4.3) the voting powers of the representatives should be proportional to the square roots of the respective constituency sizes. The question as to whether a representative’s voting power ought to be considered — and if so how exactly it should be measured — became a legally contested issue in the US in the early 1960s and some cases were still before the courts in the early 1990s. In this chapter we shall outline the history of some of the more prominent cases and the courts’ judgments.1 The US Congress is a bicameral system consisting, at present, of 435 members of the House of Representatives and 100 Senators.2 1 Many decision-making bodies throughout the world use weighted voting; however, we know of no country except the US where this practice has been subject to litigation and court rulings. For a long (and rather old) list of international organizations using...

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