Related papers: The Boltzmann fair division for distributive justi…

Two simple and attractive mechanisms for the fair division of indivisible goods in an online setting are LIKE and BALANCED LIKE. We study some fundamental computational problems concerning the outcomes of these mechanisms. In particular, we…

Inheritances, divorces or liquidations of companies require common assets to be divided among the entitled parties. Legal methods usually consider the market value of goods, while fair division theory takes into account the parties'…

Concern about income inequality has become prominent in public discourse around the world. However, studies in behavioral economics and psychology have consistently shown that people prefer not equal but fair income distributions. Thus,…

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…

Models of human behavior for prediction and collaboration tend to fall into two categories: ones that learn from large amounts of data via imitation learning, and ones that assume human behavior to be noisily-optimal for some reward…

In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is as follows: at each stage, a designated agent picks one object among those that remain.…

The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…

Algorithmic decision making systems are ubiquitous across a wide variety of online as well as offline services. These systems rely on complex learning methods and vast amounts of data to optimize the service functionality, satisfaction of…

In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework…

The fair division of indivisible goods is not only a subject of theoretical research, but also an important problem in practice, with solutions being offered on several online platforms. Little is known, however, about the characteristics…

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…

The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…

We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on…

How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both…

Machine learning algorithms for prediction are increasingly being used in critical decisions affecting human lives. Various fairness formalizations, with no firm consensus yet, are employed to prevent such algorithms from systematically…

Existing efforts to formulate computational definitions of fairness have largely focused on distributional notions of equality, where equality is defined by the resources or decisions given to individuals in the system. Yet existing…

We consider the kinetic theory of dilute gases in the Boltzmann--Grad limit. We propose a new perspective based on a large deviation estimate for the probability of the empirical distribution dynamics. Assuming Boltzmann molecular chaos…

Fueled by massive data, important decision making is being automated with the help of algorithms, therefore, fairness in algorithms has become an especially important research topic. In this work, we design new streaming and distributed…

Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…