Related papers: Monotone Randomized Apportionment
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
Social decision schemes (SDSs) map the preferences of a group of voters over some set of $m$ alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard implies that there…
Typical voting rules do not work well in settings with many candidates. If there are just several hundred candidates, then even a simple task such as choosing a top candidate becomes impractical. Motivated by the hope of developing group…
Over the last few years, researchers have put significant effort into understanding of the notion of proportional representation in committee election. In particular, recently they have proposed the notion of proportionality degree. We…
We study organizational elections in which each group nominates one candidate and receives as payoff its members expected utility under a probabilistic winning rule. We empirically justify a standard monotonicity assumption by simulating…
We consider voting on multiple independent binary issues. In addition, a weighting vector for each voter defines how important they consider each issue. The most natural way to aggregate the votes into a single unified proposal is…
This paper studies the allocation of voting weights in a committee representing groups of different sizes. We introduce a partial ordering of weight allocations based on stochastic comparison of social welfare. We show that when the number…
We study a resource allocation setting where $m$ discrete items are to be divided among $n$ agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common…
We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their…
Since Downs proposed that the act of voting is irrational in 1957, myriad models have been proposed to explain voting and account for observed turnout patterns. We propose a model in which partisans consider both the instrumental and…
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…
Proportional representation (PR) has long been believed the ideal system for the equality of individuals in apportioning the seats of a legislature body to subgroups. We observe that PR implicitly assumes the (standard) number of…
Several multi-winner systems that use approval voting have been developed but they each suffer from various problems. Six of these methods are discussed in this paper. They are Satisfaction Approval Voting, Minimax Approval Voting,…
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…
Unlimited asynchronism is intolerable in real physically distributed computer systems. Such systems, synchronous or not, use clocks and timeouts. Therefore the magnitudes of elapsed absolute time in the system need to satisfy the axiom of…
Even though proportional representation is a fundamental goal in multiwinner voting and a plethora of proportionality notions has been introduced, the normative justifications for choosing one notion over another remain poorly understood.…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
How to elect the representatives in legislative bodies is a question that every modern democracy has to answer. This design task has to consider various elements so as to fulfill the citizens' expectations and contribute to the maintenance…
In an election where $n$ voters rank $m$ candidates, a Condorcet winning set is a committee of $k$ candidates such that for any outside candidate, a majority of voters prefer some committee member. Condorcet's paradox shows that some…