Related papers: Random Almost-Popular Matchings
We study stochastic object assignment problems in which objects may have minimum and maximum requirements, such as with classes with upper and lower enrollment bounds. We construct a new random assignment mechanism, the minimums…
We consider the problem of finding a compromise between the opinions of a group of individuals on a number of mutually independent, binary topics. In this paper, we quantify the loss in representativeness that results from requiring the…
Aggregated data in real world recommender applications often feature fat-tailed distributions of the number of times individual items have been rated or favored. We propose a model to simulate such data. The model is mainly based on social…
Let $M$ be an ordered matching of size $n$, that is, a partition of the set $[2n]$ into 2-element subsets. The sock number of $M$ is the maximum size of a sub-matching of $M$ in which all left-ends of the edges precede all the right-ends…
Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…
We find a nontrivial upper bound on the average value of the function M(n) which associates to every positive integer n the minimal Hamming weight of a multiple of n. Some new results about the equation M(n)=M(n') are given.
The matching hypothesis in social psychology claims that people are more likely to form a committed relationship with someone equally attractive. Previous works on stochastic models of human mate choice process indicate that patterns…
We consider the problem $(\mathrm{P})$ of fitting $n$ standard Gaussian random vectors in $\mathbb{R}^d$ to the boundary of a centered ellipsoid, as $n, d \to \infty$. This problem is conjectured to have a sharp feasibility transition: for…
Population protocols are a fundamental model in distributed computing, where many nodes with bounded memory and computational power have random pairwise interactions over time. This model has been studied in a rich body of literature aiming…
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
To address the problem of narrow recommendation ranges caused by an emphasis on prediction accuracy, serendipitous recommendations, which consider both usefulness and unexpectedness, have attracted attention. However, realizing…
Global popularity (GP) bias is the phenomenon that popular items are recommended much more frequently than they should be, which goes against the goal of providing personalized recommendations and harms user experience and recommendation…
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…
The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…
A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…
Aligning large language models (LLMs) with diverse human preferences is critical for ensuring fairness and informed outcomes when deploying these models for decision-making. In this paper, we seek to uncover fundamental statistical limits…
We study the dynamical aspects of the top rank statistics of particles, performing Brownian motions on a half-line, which are ranked by their distance from the origin. For this purpose, we introduce an observable that we call the overlap…
We examine the following voting situation. A committee of $k$ people is to be formed from a pool of n candidates. The voters selecting the committee will submit a list of $j$ candidates that they would prefer to be on the committee. We…
We consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312--316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at…
We consider an assignment problem that has aspects of fair division as well as social choice. In particular, we investigate the problem of assigning a small subset from a set of indivisible items to multiple players so that the chosen…