Political and economic institutions are typically governed by committees that face the challenge to reconcile the preferences of their members. How should decision rules be designed to generate fair and sustainable agreements, for example if committee members represent groups of different sizes?...

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 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...

Weighted committee games generalize n-player simple voting games to m ≥ 3 alternatives. The committee's aggregation rule treats votes anonymously but parties, shareholders, members of supranational organizations, etc. differ in their numbers of votes. Infinitely many vote distributions induce...