Many voting bodies are constituted on a principle of accountability whereby a member’s influence is intended to be a reflection of a measure of size such as financial contribution or population. Examples include the joint stock company, the US Electoral College, the IMF executive and the EU council of ministers.
Power indices are a tool for addressing the (often ignored) problem inherent in this: that the constitution defines the voting rules and not the effective voting powers they imply. Indices due to Penrose-Banzhaf and Shapley-Shubik are often used. That they ignore preferences is often cited as a limitation with regard to positivistic analysis of existing constitutions but an advantage when they are used to address the normative problem of designing voting rules. Power indices can reveal hidden properties of voting rules that are not obvious at a superficial level. The issue of how to construct behavioral power indices that do take account of preferences remains an important research dimension. Power indices can also help us understand multi-tiered governance structures such as federal constitutions or corporate networks, an area where there is need for further research.
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