Related papers: Average Weights and Power in Weighted Voting Games
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…
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…
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 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…
A natural partial ordering exists on the set of all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper…
Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights,…
Decisions in a shareholder meeting or a legislative committee are often modeled as a weighted game. Influence of a member is then measured by a power index. A large variety of different indices has been introduced in the literature. This…
In this paper, we propose fast pseudo-polynomial-time algorithms for computing power indices in weighted majority games. We show that we can compute the Banzhaf index for all players in $O(n+q\log (q))$ time, where $n$ is the number of…
We examine two aspects of the mathematical basis for two-tier voting systems, such as that of the Council of the European Union. These aspects concern the use of square-root weights and the choice of quota. Square-root weights originate in…
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…
Consider an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is $p>1/2$. Condorcet's Jury Theorem which he derived from the weak law of large…
In this paper, we introduce a notion of mergeable weighted majority games with the aim of providing the first characterization of the Colomer-Mart\'inez power index (Colomer and Mart\'inez in J Theor Polit 7(1):41-63, 1995). Furthermore, we…
Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of…
Members of a shareholder meeting or legislative committee have greater or smaller voting power than meets the eye if the nucleolus of the induced majority game differs from the voting weight distribution. We establish a new sufficient…
In certain bodies, like the Council of the EU, the member states have a voting weight which depends on the population of the re- spective state. In this article we ask the question which voting weight guarantees a `fair' representation of…
A new game-theoretic approach for combining multiple classifiers is proposed. A short introduction in Game Theory and coalitions illustrate the way any collective decision scheme can be viewed as a competitive game of coalitions that are…
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…
A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$…
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…