Related papers: Weighted Committee Games
We study minimum integer representations of weighted games, i.e., representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if the…
Hierarchical simple games - both disjunctive and conjunctive - are natural generalizations of simple majority games. They take their origin in the theory of secret sharing. Another important generalization of simple majority games with…
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…
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 $W$…
Many real-world voting systems consist of voters that occur in just two different types. Indeed, each voting system with a {\lq\lq}House{\rq\rq} and a {\lq\lq}Senat{\rq\rq} is of that type. Here we present structural characterizations and…
Apportionment is the task of assigning resources to entities with different entitlements in a fair manner, and specifically a manner that is as proportional as possible. The best-known application is the assignment of parliamentary seats to…
We study the problem of coalitional manipulation in elections using the unweighted Borda rule. We provide empirical evidence of the manipulability of Borda elections in the form of two new greedy manipulation algorithms based on intuitions…
We study the problem of coalitional manipulation---where $k$ manipulators try to manipulate an election on $m$ candidates---under general scoring rules, with a focus on the Borda protocol. We do so both in the weighted and unweighted…
This paper is a survey of some of the ways in which the representation theory of the symmetric group has been used in voting theory and game theory. In particular, we use permutation representations that arise from the action of the…
In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify…
A strong placement game $G$ played on a board $B$ is equivalent to a simplicial complex $\Delta_{G,B}$. We look at weight games, a subclass of strong placement games, and introduce upper bounds on the number of positions with $i$ pieces in…
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…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
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…
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,…
While proportionality is frequently named as a desirable property of voting rules, its interpretation in multiwinner voting differs significantly from that in apportionment. We aim to bridge these two distinct notions of proportionality by…
We introduce a game where players selfishly choose a resource and endure a cost depending on the number of players choosing nearby resources. We model the influences among resources by a weighted graph, directed or not. These games are…
Gvozdeva, Hemaspaandra, and Slinko (2011) have introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of (roughly) weighted voting games. Their third class $\mathcal{C}_\alpha$…
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…