Related papers: Majority and Plurality Problems
We prove a tight quantum query lower bound $\Omega(n^{k/(k+1)})$ for the problem of deciding whether there exist $k$ numbers among $n$ that sum up to a prescribed number, provided that the alphabet size is sufficiently large. This is an…
We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which…
The minority model was introduced to study the competition between agents with limited information. It has the remarkable feature that, as the amount of information available increases, the collective gain made by the agents is reduced.…
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and…
We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives everyday, and there is reward to each member of the smaller group. The agents cannot communicate with each other, but try to…
In many practical scenarios, a population is divided into disjoint groups for better administration, e.g., electorates into political districts, employees into departments, students into school districts, and so on. However, grouping people…
We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be…
This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive…
We propose a framework that uses majorization to model diversity and representativeness in school admissions. We generalize the standard notion of majorization to accommodate arbitrary distributional targets, such as a student body that…
The Kneser-Poulsen conjecture says that if a finite collection of balls in a d-dimensional Euclidean space is rearranged so that the distance between each pair of centers does not get smaller, then the volume of the union of these balls…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…
A voter sits on each vertex of an infinite tree of degree $k$, and has to decide between two alternative opinions. At each time step, each voter switches to the opinion of the majority of her neighbors. We analyze this majority process when…
We study colored coverage and clustering problems. Here, we are given a colored point set where the points are covered by (unknown) $k$ clusters, which are monochromatic (i.e., all the points covered by the same cluster, have the same…
Clustering is a well-studied unsupervised learning task that aims to partition data points into a number of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV…
Given a graph $G$, a 2-coloring of the edges of $K_n$ is said to contain a balanced copy of $G$ if we can find a copy of $G$ such that half of its edges is in each color class. If there exists an integer $k$ such that, for $n$ sufficiently…
Justified representation (JR) is a standard notion of representation in multiwinner approval voting. Not only does a JR committee always exist, but previous work has also shown through experiments that the JR condition can typically be…
A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is…
The aim of this paper is to study the asymptotic behavior of strongly reinforced interacting urns with partial memory sharing. The reinforcement mechanism considered is as follows: draw at each step and for each urn a white or black ball…
We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the…