Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called power indices measuring the influence of a voter. We treat...

Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as...

We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on...

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...

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...

A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights and the quota are restricted to be...

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...

Which voting weights ought to be allocated to single delegates of differently sized groups from a democratic fairness perspective? We operationalize the ‘one person, one vote’ principle by demanding every individual’s influence on collective decisions to be equal a priori. The analysis...

We study minimum integer representations of weighted games, i.e. representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if the exist at all, are linked with some solution concepts in...

For one of the most prominent solution concepts for cooperative TU games, we show that in the weighted case the nucleolus tends to the weights as the number of players increases under very mild conditions. We give a sufficient characterization for the case of coincidence between weights and...