Related papers: Computing the Power Distribution in the IMF
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…
A committee's decisions on more than two alternatives much depend on the adopted voting method, and so does the distribution of power among the committee members. We investigate how different aggregation methods such as plurality runoff,…
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…
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…
In this paper, we propose an improved version of the power index related to the Banzhaf power index for weighted voting systems. This index now takes into account the mutual persuasion power matrix(PPM) existing among the voters. This…
We exhibit the hidden beauty of weighted voting and voting power by applying a generalization of the Penrose-Banzhaf index to social choice rules. Three players who have multiple votes in a committee decide between three options by…
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…
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…
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,…
This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation,…
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…
The Banzhaf and Shapley-Shubik power indices were first introduced to measure the power of voters in a weighted voting system. Given a weighted voting system, the fixed point of such a system is found by continually reassigning each voter's…
We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote…
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…
Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such…
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…
The Banzhaf Power Index (BPI) is a method of measuring the power of voters in determining the outcome of a voting game. Some voting games exhibit a hierarchical structure, including the US electoral college and ensemble learning methods; we…
We explore the switching-algebraic computation of the Banzhaf indices for general and monotone or unrestricted systems. This computation is achieved via (a) two Boolean-quotient formulas that are valid when the voting system is not…
Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse images, i.e., to determine a voting system…