I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide items fairly and efficiently. This has involved bringing to bear tools such as those used in knowledge representation, computational complexity, approximation methods, game theory, online analysis and communication complexity
Institute for Logic, Language and Computation（逻辑、语言与计算研究所）；University of Amsterdam（阿姆斯特丹大学）
Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we need to define what is to be understood by a "fair" allocation of goods to individuals. We present an overview of the most important fairness criteria (as well as the closely related criteria for economic efficiency) developed in the literature, together with a short discussion of their axiomatic foundations. Second, we give an introduction to cake-cutting p…
We consider a multi-agent model for fair division of mixed manna (i.e. items for which agents can have positive, zero or negative utilities), in which agents have additive utilities for bundles of items. For this model, we give several general impossibility results and special possibility results for three common fairness concepts (i.e. EF1, EFX, EFX3) and one popular efficiency concept (i.e. PO). We also study how these interact with common welfare objectives such as the Nash, disutility Nash and egalitarian welfares. For example, we show that maximizing the Nash welfare with mixed manna (or …
We study an online model of fair division designed to capture features of a real world charity problem. We consider two simple mechanisms for this model in which agents simply declare what items they like. We analyse several axiomatic properties of these mechanisms like strategy-proofness and envy-freeness. Finally, we perform a competitive analysis and compute the price of anarchy.
Technical University Berlin（柏林工业大学）；UNSW Sydney（悉尼新南威尔士大学）
We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and normative properties that apply to this online setting. The online nature of such fair division problems provides both opportunities and challenges such as the possibility to develop new online mechanisms as well as the difficulty of dealing with an uncertain future.
Facebook AI Research（脸书人工智能研究院）；Facebook Core Data Science（脸书核心数据科学部）
We consider the problem of dividing items between individuals in a way that is fair both in the sense of distributional fairness and in the sense of not having disparate impact across protected classes. An important existing mechanism for distributionally fair division is competitive equilibrium from equal incomes (CEEI). Unfortunately, CEEI will not, in general, respect disparate impact constraints. We consider two types of disparate impact measures: requiring that allocations be similar across protected classes and requiring that average utility levels be similar across protected classes. We…
We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good for some agents and bad for other agents (i.e. mixed), good for everyone (i.e. goods) or bad for everyone (i.e. bads). For this model, we study axiomatic concepts of allocations such as jealousy-freeness up to one item, envy-freeness up to one item and Pareto-optimality. We obtain many new possibility and impossibility results in regard to combinations of th…
University of Virginia（弗吉尼亚大学）；University of Toronto（多伦多大学）
We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identi…
We consider the problem of fairly allocating indivisible goods, among agents, under cardinality constraints and additive valuations. In this setting, we are given a partition of the entire set of goods---i.e., the goods are categorized---and a limit is specified on the number of goods that can be allocated from each category to any agent. The objective here is to find a fair allocation in which the subset of goods assigned to any agent satisfies the given cardinality constraints. This problem naturally captures a number of resource-allocation applications, and is a generalization of the well-s…
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 the following: at each stage, a designated agent picks one object among those that remain. This paper, restricted to the case where the agents have numerical additive preferences over objects, revisits to some extent the seminal paper by Brams and King [9] which was specific to ordinal and linear order preferences over items. We point out similarities and differences with this latter context. In particular, we show that any Pareto-optimal alloca…
Sorbonne Université（索邦大学）；Univ. Grenoble-Alpes（格勒诺布尔-阿尔卑斯大学）；ONERA Toulouse（法国航空航天实验室图卢兹中心）；ENS Paris Saclay（巴黎-萨克雷高等师范学校）
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. Another intuitive way to obtain an allocation is to give objects to agents in the first place, and to let agents exchange them as long as such "deals" are beneficial. This paper investigates these notions, when agents have additive preferences over objects, and unveils surprising connections between them, and with other efficiency and fairness notions. In par…
The paper considers fair allocation of indivisible nondisposable items that generate disutility (chores). We assume that these items are placed in the vertices of a graph and each agent's share has to form a connected subgraph of this graph. Although a similar model has been investigated before for goods, we show that the goods and chores settings are inherently different. In particular, it is impossible to derive the solution of the chores instance from the solution of its naturally associated fair division instance. We consider three common fair division solution concepts, namely proportiona…
Approximate Proportionality in Online Fair Division
Harvard University, USA（哈佛大学）；University of Oxford, UK（牛津大学）；Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research (A*STAR), Singapore（前沿人工智能研究中心（CFAR））；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore（高性能计算研究所（IHPC））；Princeton University, New Jersey, USA（普林斯顿大学）；Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR), Singapore（信息与通信研究所以（I2R））
University of Oxford（牛津大学）；Alan Turing Institute（阿兰·图灵研究所）；City University of Hong Kong（香港城市大学）；University of Edinburgh（爱丁堡大学）；Agency for Science, Technology and Research（科技研究局）
Rankings have become the primary interface in two-sided online markets. Many have noted that the rankings not only affect the satisfaction of the users (e.g., customers, listeners, employers, travelers), but that the position in the ranking allocates exposure -- and thus economic opportunity -- to the ranked items (e.g., articles, products, songs, job seekers, restaurants, hotels). This has raised questions of fairness to the items, and most existing works have addressed fairness by explicitly linking item exposure to item relevance. However, we argue that any particular choice of such a link …
Keep Everyone Happy: Online Fair Division of Numerous Items with Few Copies
Singapore-MIT Alliance for Research and Technology（新加坡-麻省理工联合研究技术联盟）；Faculty of ISEE, Kyushu University（九州大学信息科学与工程学院）；Department of Computer Science, National University of Singapore（新加坡国立大学计算机科学系）
