Related papers: Banzhaf Power in Hierarchical Voting Games
Among two-candidate elections that treat the candidates symmetrically and never result in a tie, which voting rules are fair? A natural requirement is that each voter exerts an equal influence over the outcome, i.e., is equally likely to…
We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote…
This paper deals with a new measure of the influence of each feature on the response variable in classification problems, accounting for potential dependencies among certain feature subsets. Within this framework, we consider a sample of…
Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., "yes" and "no", every voting system can be described by a (monotone) Boolean function…
The International Monetary Fund is one of the largest international organizations using a weighted voting system. The weights of its 188 members are determined by a fixed amount of basic votes plus some extra votes for so-called Special…
We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified…
This paper handles a kind of strategic game called potential games and develops a novel learning algorithm Payoff-based Inhomogeneous Partially Irrational Play (PIPIP). The present algorithm is based on Distributed Inhomogeneous Synchronous…
Voting by sequential elimination is a low-communication voting protocol: voters play in sequence and eliminate one or more of the remaining candidates, until only one remains. While the fairness and efficiency of such protocols have been…
Like many other voting systems, Majority Judgement suffers from the weaknesses of the underlying mathematical model: Elections as problem of choice or ranking. We show how the model can be enhanced to take into account the complete process…
Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the…
Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…
Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game…
We consider the Banzhaf-Coleman and Owen power indices for weighted majority games modified by a coalition configuration. We present calculation algorithms of them that make use of the method of generating functions. We programmed the…
Since the Fourth Industrial Revolution, AI technology has been widely used in many fields, but there are several limitations that need to be overcome, including overfitting/underfitting, class imbalance, and the limitations of…
Important decisions are likely made by groups of agents. Thus group decision making is very common in practice. Very transparent group aggregating rules are given by weighted voting, where each agent is assigned a weight. Here a proposal is…
Within the domain of game theory, power indexes are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal [D. Felsenthal. A Well-Behaved Index of a Priori P-Power for…
Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the…
It is well known that the Penrose-Banzhaf index of a weighted game can differ starkly from corresponding weights. Limit results are quite the opposite, i.e., under certain conditions the power distribution approaches the weight…
Gradual argumentation is a field of symbolic AI which is attracting attention for its ability to support transparent and contestable AI systems. It is considered a useful tool in domains such as decision-making, recommendation, debate…