Related papers: But some are more equal than others

The problem of dividing resources fairly occurs in many practical situations and is therefore an important topic of study in economics. In this paper, we investigate envy-free divisions in the setting where there are multiple players in…

Fair machine learning is receiving an increasing attention in machine learning fields. Researchers in fair learning have developed correlation or association-based measures such as demographic disparity, mistreatment disparity, calibration,…

The well-known Simpson's Paradox, or Yule-Simpson Effect, in statistics is often illustrated by the following thought experiment: A drug may be found in a trial to increase the survival rate for both men and women, but decrease the rate for…

An inequality, recently proposed by Franson [Phys. Rev. A 54, 3808 (1996)] is analyzed and improved. The inequality connects the change of the expectation value of an observable with the uncertainty of this observable. A strict bound on the…

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued…

The friendship paradox -- the observation that, on average, one's friends have more friends than oneself -- admits two common formulations depending on whether averaging is performed over edges or over nodes. These two definitions, the…

Consider a gambler and a prophet who observe a sequence of independent, non-negative numbers. The gambler sees the numbers one-by-one whereas the prophet sees the entire sequence at once. The goal of both is to decide on fractions of each…

The classical measure of similarity between two polygonal chains in Euclidean space is the Fr\'echet distance, which corresponds to the coordinated motion of two mobile agents along the chains while minimizing their maximum distance. As…

We give a different and simpler proof of a slightly modified (and weaker) variant of a recent theorem of Shelukhin extending Franks' "two-or-infinitely-many" theorem to Hamiltonian diffeomorphisms in higher dimensions and establishing a…

Fair division of indivisible goods is a central challenge in artificial intelligence. For many prominent fairness criteria including envy-freeness (EF) or proportionality (PROP), no allocations satisfying these criteria might exist. Two…

Liberalism-oriented political philosophy reasons that all individuals should be treated equally independently of their protected characteristics. Related work in machine learning has translated the concept of \emph{equal treatment} into…

We give a new theorem describing a relation between the quasi-random property of regular tournaments and their spectra. This provides many solutions to a constructing problem mentioned by Erd\H{o}s and Moon (1965) and Spencer (1985).

A set of divisible resources becomes available over a sequence of rounds and needs to be allocated immediately and irrevocably. Our goal is to distribute these resources to maximize fairness and efficiency. Achieving any non-trivial…

On being told that a piece of work he thought was his discovery had duplicated an earlier mathematician's work, Larry Shepp once replied "Yes, but when {\em I} discovered it, it {\em stayed} discovered". In this spirit we give discussion…

In this paper we prove that the number of partitions into squares with an even number of parts is asymptotically equal to that of partitions into squares with an odd number of parts. We further show that, for $ n $ large enough, the two…

Sex is considered as an evolutionary paradox, since its evolutionary advantage does not necessarily overcome the two fold cost of sharing half of one's offspring's genome with another member of the population. Here we demonstrate that…

This paper is a contribution to the study of parity games and the recent constructions of three quasipolynomial time algorithms for solving them. We revisit a result of Czerwi\'nski, Daviaud, Fijalkow, Jurdzi\'nski, Lazi\'c, and Parys…

We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found…

In 1987, Orrin Frink introduced the concept of almost Pythagorean triples. He defined them as an ordered triple $(x,y,z)$ that satisfies the equation $x^2+y^2=z^2+1$ where $x,y$ and $z$ are positive integers. In his paper, he showed that…

In this article, we study a nonlocal game with two questions and three answers per player, which was first considered by Feige in 1991, and show that there is quantum advantage in this game. We prove that the game is a robust self-test for…