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date: 18 September 2019

Abstract and Keywords

This chapter investigates ways to quantify how institutional rules, such as different voting weight arrangements in councils or two-tier voting systems, allocate influence on outcomes among the collective decision makers. After basic concepts of the common binary voting framework have been laid out, several indices of voting power are introduced with their key properties and probabilistic interpretations. Techniques for the computation of these indices, limit results for large voting bodies, and the problem of designing rules with desirable power implications are discussed. The chapter also points out possibilities to analyze the distribution of influence in scenarios richer than just binary voting.

Keywords: simple voting game, power index, Shapley-Shubik index, Penrose-Banzhaf index, nucleolus, Penrose limit theorem, square root rule, linear rule, inverse problem, nonbinary voting

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