Related papers: Average Weights and Power in Weighted Voting Games
This paper addresses Monte Carlo algorithms for calculating the Shapley-Shubik power index in weighted majority games. First, we analyze a naive Monte Carlo algorithm and discuss the required number of samples. We then propose an efficient…
We compare the notions "Decisiveness" and "Success" for certain weighted voting systems and various underlying voting measures. In particular, we compute the success rate for the Shapley-Shubik meassure and, more generally, for Common…
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…
We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual…
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…
An important aspect of mechanism design in social choice protocols and multiagent systems is to discourage insincere and manipulative behaviour. We examine the computational complexity of false-name manipulation in weighted voting games…
For a wide range of functions $W\colon\mathbb{N}\to\mathbb{N}$, we establish a general result for estimating weighted averages of the form \[ \mathbb{E}^{W}_{n \le N} f(\vartheta(n))= \frac{1}{W(N)}\sum_{n=1}^N (W(n)-W(n-1))f(\vartheta(n)),…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
In this paper, we study the problem of learning the skill distribution of a population of agents from observations of pairwise games in a tournament. These games are played among randomly drawn agents from the population. The agents in our…
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 present a Karchmer-Wigderson game to study the complexity of hazard-free formulas. This new game is both a generalization of the monotone Karchmer-Wigderson game and an analog of the classical Boolean Karchmer-Wigderson game. Therefore,…
Voting algorithms have been widely used as consensus protocols in the realization of fault-tolerant systems. These algorithms are best suited for distributed systems of nodes with low computational power or heterogeneous networks, where…
In recent years, enlargement of the European Union has led to increased interest in the allocation of voting weights to member states with hugely differing population numbers. While the eventually agreed voting scheme lacks any strict…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
In this paper, we develop a logistic regression model to estimate the probability that a particular shot in an NHL game will result in a goal, and use the results to evaluate the performance of NHL skaters, goalies, and teams. We weight…
Forcing finite state mean field games by a relevant form of common noise is a subtle issue, which has been addressed only recently. Among others, one possible way is to subject the simplex valued dynamics of an equilibrium by a so-called…
In this study, we propose a generalization of the classic model of liquid democracy that allows fractional delegation of voting weight, while simultaneously allowing for the existence of equilibrium states. Our approach empowers agents to…
In this paper, a novel approach for the optimal combination of binary classifiers is proposed. The classifier combination problem is approached from a Game Theory perspective. The proposed framework of adapted weighted majority rules (WMR)…
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…
Voters from m disjoint constituencies (regions, federal states, etc.) are represented in an assembly which contains one delegate from each constituency and applies a weighted voting rule. All agents are assumed to have single-peaked…