We introduce the prediction value (PV) as a measure of players' informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player i's prediction value equals the difference between the conditional...

Power index research has been a very active field in the last decades. Will this continue or are all the important questions solved? We argue that there are still many opportunities to conduct useful research with and on power indices. Positive and normative questions keep calling for...

Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse images, i.e., to determine a voting system which induces a power distribution as close as possible...

The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e., to bring about the required majority or to make this...

Chapter 1. Introduction -- Part I. Social Choice -- Chapter 2. Building Bridges over the Great Divide -- Chapter 3. Social Unacceptability for Simple Voting Procedures -- Chapter 4. Probability of Majority Inversion with Three States and Interval Preferences -- Chapter 5. Strategic Voting and...

Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse images, i.e., to determine a voting system which induces a power distribution as close as possible...