Related papers: On minimum sum representations for weighted voting…

In this article, we study a sum of squares of integers except for a fixed one. For any nonnegative integer $n$, we find the minimum number of squares of integers except for $n$ whose sums represent all positive integers that are represented…

Electing a committee of size k from m alternatives (k < m) is an interesting problem under the multi-winner voting rules. However, very few committee selection rules found in the literature consider the coalitional possibilities among the…

Quantum voting protocols aim to offer ballot secrecy and publicly verifiable tallies using physical guarantees from quantum mechanics, rather than relying solely on computational hardness. This article surveys whether such quantum voting…

The Coalitional Manipulation (CM) problem has been studied extensively in the literature for many voting rules. The CM problem, however, has been studied only in the complete information setting, that is, when the manipulators know the…

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…

Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional…

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…

We investigate how robust approval-based multiwinner voting rules are to small perturbations in the votes. In particular, we consider the extent to which a committee can change after we add/remove/swap one approval, and we consider the…

We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice…

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…

The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games,…

We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we…

Our aim is to give for some classes non-additive measures some limit theorems. For balanced games we obtain a weak and strong law of large numbers for bounded random variables, a sharper conclusion is obtain with exact games. We provide an…

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…

Cooperative games with nonempty core are called balanced, and the set of balanced games is a polyhedron. Given a game with empty core, we look for the closest balanced game, in the sense of the (weighted) Euclidean distance, i.e., the…

Election rules are formal processes that aggregate voters preferences, typically to select a single candidate, called the winner. Most of the election rules studied in the literature require the voters to rank the candidates from the most…

When are all positions of a game numbers? We show that two properties are necessary and sufficient. These properties are consequences of that, in a number, it is not an advantage to be the first player. One of these properties implies the…

We consider a spatial voting model where both candidates and voters are positioned in the $d$-dimensional Euclidean space, and each voter ranks candidates based on their proximity to the voter's ideal point. We focus on the scenario where…

In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are…

In this paper, we experimentally compare major approval-based multiwinner voting rules. To this end, we define a measure of similarity between two equal-sized committees subject to a given election. Using synthetic elections coming from…