Related papers: Banzhaf Power in Hierarchical Voting Games
The Shapley-Shubik index was designed to evaluate the power distribution in committee systems drawing binary decisions and is one of the most established power indices. It was generalized to decisions with more than two levels of approval…
This paper examines an area of Game Theory called Voting Power Theory. With the adoption of a measure theoretic framework it argues that the many different indices and tools currently used for measuring voting power can be replaced by just…
We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this…
In many applications of cooperative game theory -- from corporate governance and cartel formation to parliamentary voting -- not all winning coalitions are feasible. Ideological distances, institutional constraints, or pre-electoral…
False-name manipulation refers to the question of whether a player in a weighted voting game can increase her power by splitting into several players and distributing her weight among these false identities. Analogously to this splitting…
For artificially intelligent learning systems to have widespread applicability in real-world settings, it is important that they be able to operate decentrally. Unfortunately, decentralized control is difficult -- computing even an…
In approval-based multiwinner voting, voters express approval preferences over a set of candidates, and the goal is to return a winning committee. This model captures a broad range of subset selection problems under preferences. Prior work…
We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the $k$-th…
A recently proposed graph-theoretic metric, the influence gap, has shown to be a reliable predictor of the effect of social influence in two-party elections, albeit only tested on regular and scale-free graphs. Here, we investigate whether…
This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class…
Quantifying the contribution of database facts to query answers has been studied as means of explanation. The Banzhaf value, originally developed in Game Theory, is a natural measure of fact contribution, yet its efficient computation for…
Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. Specifically, PPI methods provide tighter confidence intervals by combining small amounts of human-labeled data with…
Condorcet's jury theorem states that the correct outcome is reached in direct majority voting systems with sufficiently large electorates as long as each voter's independent probability of voting for that outcome is greater than 0.5. Yet,…
Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…
Valuation problems, such as feature interpretation, data valuation and model valuation for ensembles, become increasingly more important in many machine learning applications. Such problems are commonly solved by well-known game-theoretic…
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…
The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in…
Value-based reinforcement-learning algorithms provide state-of-the-art results in model-free discrete-action settings, and tend to outperform actor-critic algorithms. We argue that actor-critic algorithms are limited by their need for an…
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…
We study the complexity of the following problem: Given two weighted voting games G' and G'' that each contain a player p, in which of these games is p's power index value higher? We study this problem with respect to both the…