相关论文: Computing Power Indices in Weighted Majority Games…
We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that…
Feature attribution methods have become essential for explaining machine learning models. Many popular approaches, such as SHAP and Banzhaf values, are grounded in power indices from cooperative game theory, which measure the contribution…
This paper provides a serious attempt towards constructing a switching-algebraic theory for weighted monotone voting systems, whether they are scalar-weighted or vector-weighted. The paper concentrates on the computation of a prominent…
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…
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…
We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…
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…
The Penrose-Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning…
This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation,…
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…
We explore the switching-algebraic computation of the Banzhaf indices for general and monotone or unrestricted systems. This computation is achieved via (a) two Boolean-quotient formulas that are valid when the voting system is not…
The Banzhaf and Shapley-Shubik power indices were first introduced to measure the power of voters in a weighted voting system. Given a weighted voting system, the fixed point of such a system is found by continually reassigning each voter's…
In this paper, we propose an improved version of the power index related to the Banzhaf power index for weighted voting systems. This index now takes into account the mutual persuasion power matrix(PPM) existing among the voters. This…
Energy games belong to a class of turn-based two-player infinite-duration games}played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in ${\sf NP} \cap {\sf co\mbox{-}NP}$, but are not…
The Banzhaf Power Index (BPI) is a method of measuring the power of voters in determining the outcome of a voting game. Some voting games exhibit a hierarchical structure, including the US electoral college and ensemble learning methods; we…
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…
This work focuses on developing efficient post-hoc explanations for quantum AI algorithms. In classical contexts, the cooperative game theory concept of the Shapley value adapts naturally to post-hoc explanations, where it can be used to…
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…
We introduce a new simple game, which is referred to as the complementary weighted multiple majority game (C-WMMG for short). C-WMMG models a basic cooperation rule, the complementary cooperation rule, and can be taken as a sister model of…
We provide an algorithm for computing the nucleolus for an instance of a weighted voting game in pseudo-polynomial time. This resolves an open question posed by Elkind. et.al. 2007.