Related papers: On minimum sum representations for weighted voting…
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…
This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions…
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…
A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out…
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…
This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker (1992) showed that a simple game is…
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…
Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the cumulative weight while reaching a target. Used in a reactive synthesis perspective, this…
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 $\mathcal{C}_\alpha$…
In a weighted majority voting game, the players' weights are determined based on the constitutional planner's intentions. The weights are challenging to change in numerous cases, as they represent some desired disparity. However, the voting…
Kurz and Napel (2015) proved that the voting system of the EU council (based on the 2014 population data) cannot be represented as the intersection of six weighted games, i.e., its dimension is at least 7. This set a new record for…
Systems of indirect voting based on the principle of qualified majority can be analysed using the methods of game theory. In particular, this applies to the voting system in the Council of the European Union, which was recently a subject of…
Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., "yes" and "no", every voting system can be described by a (monotone) Boolean function…
In this paper, we propose a pseudo polynomial size LP formulation for finding a payoff vector in the least core of a weighted voting game. The numbers of variables and constraints in our formulation are both bounded by $\mbox{O}(n W_+)$,…
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…
The voting process is formalized as a multistage voting model with successive alternative elimination. A finite number of agents vote for one of the alternatives each round subject to their preferences. If the number of votes given to the…
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…
Determining how close a winner of an election is to becoming a loser, or distinguishing between different possible winners of an election, are major problems in computational social choice. We tackle these problems for so-called weighted…
Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the…
Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…