Measuring Voting Power in Convex Policy Spaces

Abstract

Classical power index analysis considers the individual’s ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either “yes” or “no”. Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like, e.g., tax rates or spending that otherwise would not be covered in binary models.

Keywords

• power
• single peaked preferences
• convex policy space
• group decision making
• Shapley-Shubik index
• Banzhaf index
• nucleolus
• simple games
• multiple levels of approval