Related papers: Existence of Fair Resolute Voting Rules

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…

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…

We study the complexity of the following problem: Given two weighted voting games G' and G'' that each contain a player p, in which of these games is p's power index value higher? We study this problem with respect to both the…

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…

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…

A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper…

Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting…

In real-world elections where voters cast preference ballots, voters often provide only a partial ranking of the candidates. Despite this empirical reality, prior social choice literature frequently analyzes fairness criteria under the…

We compare the notions "Decisiveness" and "Success" for certain weighted voting systems and various underlying voting measures. In particular, we compute the success rate for the Shapley-Shubik meassure and, more generally, for Common…

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…

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…

Classical voting rules assume that ballots are complete preference orders over candidates. However, when the number of candidates is large enough, it is too costly to ask the voters to rank all candidates. We suggest to fix a rank k, to ask…

The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in…

Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of the different agents for that function. This generalizes…

Consider elections where the set of candidates is partitioned into parties, and each party must nominate exactly one candidate. The Possible President problem asks whether some candidate of a given party can become the winner of the…

Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the…

To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…

The Shapley-Shubik index was designed to evaluate the power distribution in committee systems drawing binary decisions and is one of the most established power indices. It was generalized to decisions with more than two levels of approval…

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…

Fairness in multiwinner elections is studied in varying contexts. For instance, diversity of candidates and representation of voters are both separately termed as being fair. A common denominator to ensure fairness across all such contexts…