Related papers: Computing Power Indices in Weighted Majority Games…
Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting…
In this paper new algorithm for calculating power indices is described. The complexity class of the problem is #P-complete and even calculating power index of the biggest player is NP-hard task. Constructed algorithm is a mix of ideas of…
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…
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…
Weighted voting is a classic model of cooperation among agents in decision-making domains. In such games, each player has a weight, and a coalition of players wins the game if its total weight meets or exceeds a given quota. A players power…
Weighted voting games are a family of cooperative games, typically used to model voting situations where a number of agents (players) vote against or for a proposal. In such games, a proposal is accepted if an appropriately weighted sum of…
The Banzhaf index, Shapley-Shubik index and other voting power indices measure the importance of a player in a coalitional game. We consider a simple coalitional game called the spanning connectivity game (SCG) based on an undirected,…
Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of weighted voting games in which agents' weights are induced by a transitive support structure. This class of simple games is notably well suited to study the…
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…
Weighted voting games apply to a wide variety of multi-agent settings. They enable the formalization of power indices which quantify the coalitional power of players. We take a novel approach to the study of the power of big vs.~small…
The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown…
Coalitional voting games appear in different forms in multi-agent systems, social choice and threshold logic. In this paper, the complexity of comparison of influence between players in coalitional voting games is characterized. The…
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…
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…
Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the…
We study the inverse power index problem for weighted voting games: the problem of finding a weighted voting game in which the power of the players is as close as possible to a certain target distribution. Our goal is to find algorithms…
Weighted voting games are a popular class of coalitional games that are widely used to model real-life situations of decision-making. They can be applied, for instance, to analyze legislative processes in parliaments or voting in corporate…
We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard…
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…
We use simplicial complexes to model simple games as well as weighted voting games where certain coalitions are considered impossible. Topological characterizations of various ideas from simple games are provided, as are the expressions for…