The stable matching problem sets the economic foundation of several practical applications ranging from school choice and medical residency to ridesharing and refugee placement. It is concerned with finding a matching between two disjoint sets of agents wherein no pair of agents prefer each other to their matched partners. The Deferred Acceptance (DA) algorithm is an elegant procedure that guarantees a stable matching for any input; however, its outcome may be unfair as it always favors one side by returning a matching that is optimal for one side (say men) and pessimal for the other side (say women). A desirable fairness notion is minimizing the sex-equality cost, i.e. the difference between the total rankings of both sides. Computing such stable matchings is a strongly NP-hard problem, which raises the question of what tractable algorithms to adopt in practice. We conduct a series of empirical evaluations on the properties of sex-equal stable matchings when preferences of agents on both sides are correlated. Our empirical results suggest that under correlated preferences, the DA algorithm returns stable matchings with low sex-equality cost, which further confirms its broad use in many practical applications.
Indian Institute of Science（印度科学学院）；IIT, Kanpur（坎普尔印度理工学院）；ISI, Kolkata（加尔各答印度统计研究所）
We study fairness in social choice settings under single-peaked preferences. Construction and characterization of social choice rules in the single-peaked domain has been extensively studied in prior works. In fact, in the single-peaked domain, it is known that unanimous and strategy-proof deterministic rules have to be min-max rules and those that also satisfy anonymity have to be median rules. Further, random social choice rules satisfying these properties have been shown to be convex combinations of respective deterministic rules. We non-trivially add to this body of results by including fa…
NICTA（澳大利亚国家信息与通信技术研究院）；University of New South Wales（新南威尔士大学）
We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of proportionality and envy-freeness for discrete assignments. The computational complexity of checking whether a fair assignment exists is studied for these fairness notions. We also characterize the conditions under which a fair assignment is guaranteed to exist. For a number of fairness concepts, polynom…
Allocating multiple scarce items across a set of individuals is an important practical problem. In the case of divisible goods and additive preferences a convex program can be used to find the solution that maximizes Nash welfare (MNW). The MNW solution is equivalent to finding the equilibrium of a market economy (aka. the competitive equilibrium from equal incomes, CEEI) and thus has good properties such as Pareto optimality, envy-freeness, and incentive compatibility in the large. Unfortunately, this equivalence (and nice properties) breaks down for general preference classes. Motivated by r…
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…
Envy-freeness up to any good (EFX) provides a strong and intuitive guarantee of fairness in the allocation of indivisible goods. But whether such allocations always exist or whether they can be efficiently computed remains an important open question. We study the existence and computation of EFX in conjunction with various other economic properties under lexicographic preferences--a well-studied preference model in artificial intelligence and economics. In sharp contrast to the known results for additive valuations, we not only prove the existence of EFX and Pareto optimal allocations, but in …
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…
Agents vote to choose a fair mixture of public outcomes; each agent likes or dislikes each outcome. We discuss three outstanding voting rules. The Conditional Utilitarian rule, a variant of the random dictator, is Strategyproof and guarantees to any group of like-minded agents an influence proportional to its size. It is easier to compute and more efficient than the familiar Random Priority rule. Its worst case (resp. average) inefficiency is provably (resp. in numerical experiments) low if the number of agents is low. The efficient Egalitarian rule protects similarly individual agents but not…
We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule -- maximum Nash welfare (MNW) -- provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic tie-breaking is group strategyproof in addition to being envy-free up to one good and Pareto optimal. We also prove that fractional MNW -- known to be group strategyproof, envy-free, and Pareto op…
When Graph Traversal Meets Structured Preferences: Unified Framework and Complexity Results
School of Computer and Communication Engineering, Changsha University of Science and Technology（长沙理工大学计算机与通信工程学院）；Department of Economics, Saarland University（萨尔兰大学经济学系）
We study the following multiagent variant of the knapsack problem. We are given a set of items, a set of voters, and a value of the budget; each item is endowed with a cost and each voter assigns to each item a certain value. The goal is to select a subset of items with the total cost not exceeding the budget, in a way that is consistent with the voters' preferences. Since the preferences of the voters over the items can vary significantly, we need a way of aggregating these preferences, in order to select the socially best valid knapsack. We study three approaches to aggregating voters' prefe…
We study the problem of fair and efficient allocation of a set of indivisible chores to agents with additive cost functions. We consider the popular fairness notion of envy-freeness up to one good (EF1) with the efficiency notion of Pareto-optimality (PO). While it is known that an EF1+PO allocation exists and can be computed in pseudo-polynomial time in the case of goods, the same problem is open for chores. Our first result is a strongly polynomial-time algorithm for computing an EF1+PO allocation for bivalued instances, where agents have (at most) two disutility values for the chores. To th…
Rationalizing collective revealed preferences with an application in fair resource allocation
Booth School of Business, University of Chicago（芝加哥大学布斯商学院）；Antai College of Economics and Management, Shanghai Jiao Tong University（上海交通大学安泰经济与管理学院）；School of Data Science, School of Management and Economics, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院、管理学院与经济学院）；Department of Management Science and Engineering, Stanford University（斯坦福大学管理科学与工程系）
The past few years have seen a surge of work on fairness in allocation problems where items must be fairly divided among agents having individual preferences. In comparison, fairness in settings with preferences on both sides, that is, where agents have to be matched to other agents, has received much less attention. Moreover, two-sided matching literature has largely focused on ordinal preferences. This paper initiates the study of fairness in stable many-to-one matchings under cardinal valuations. Motivated by real-world settings, we study leximin optimality over stable many-to-one matchings…
We consider the assignment problem in which agents express ordinal preferences over $m$ objects and the objects are allocated to the agents based on the preferences. In a recent paper, Brams, Kilgour, and Klamler (2014) presented the AL method to compute an envy-free assignment for two agents. The AL method crucially depends on the assumption that agents have strict preferences over objects. We generalize the AL method to the case where agents may express indifferences and prove the axiomatic properties satisfied by the algorithm. As a result of the generalization, we also get a $O(m)$ speedup…
Chore division is the problem of fairly dividing some divisible, undesirable bad, such as a set of chores, among a number of players. Each player has their own valuation of the chores, and must be satisfied they did not receive more than their fair share. In this paper, I consider the problem of strategyproof chore division, in which the algorithm must ensure that each player cannot benefit from mis-representing their position. I present an algorithm that performs proportional and strategyproof chore division for any number of players given piecewise uniform valuation functions.
In this paper, we study fairness in committee selection problems. We consider a general notion of fairness via stability: A committee is stable if no coalition of voters can deviate and choose a committee of proportional size, so that all these voters strictly prefer the new committee to the existing one. Our main contribution is to extend this definition to stability of a distribution (or lottery) over committees. We consider two canonical voter preference models: the Approval Set setting where each voter approves a set of candidates and prefers committees with larger intersection with this s…
Competitive equilibrium (CE) is a fundamental concept in market economics. Its efficiency and fairness properties make it particularly appealing as a rule for fair allocation of resources among agents with possibly different entitlements. However, when the resources are indivisible, a CE might not exist even when there is one resource and two agents with equal incomes. Recently, Babaioff and Nisan and Talgam-Cohen (2017) have suggested to consider the entire space of possible incomes, and check whether there exists a competitive equilibrium for almost all income-vectors --- all income-space ex…
There are growing concerns that algorithms, which increasingly make or influence important decisions pertaining to individuals, might produce outcomes that discriminate against protected groups. We study such fairness concerns in the context of a two-sided market, where there are two sets of agents, and each agent has preferences over the other set. The goal is producing a matching between the sets. This setting has been the focus of a rich body of work. The seminal work of Gale and Shapley formulated a stability desideratum, and showed that a stable matching always exists and can be found eff…
Using a lab experiment, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. We find that envy-free procedures, in particular Selfridge-Conway, are fairer and also are perceived as fairer than their proportional counterparts, despite the fact that agents very often manipulate them. Our results support the practical use of the celebrated Selfridge-Conway procedure, and more generally, of envy-free cake-cutting mechanisms. We also find that subjects learn their opponents' preferences after repeated in…
Single minded agents have strict preferences, in which a bundle is acceptable only if it meets a certain demand. Such preferences arise naturally in scenarios such as allocating computational resources among users, where the goal is to fairly serve as many requests as possible. In this paper we study the fair division problem for such agents, which is harder to handle due to discontinuity and complementarities of the preferences. Our solution concept---the competitive allocation from equal incomes (CAEI)---is inspired from market equilibria and implements fair outcomes through a pricing mechan…
Many allocation problems in multiagent systems rely on agents specifying cardinal preferences. However, allocation mechanisms can be sensitive to small perturbations in cardinal preferences, thus causing agents who make ``small" or ``innocuous" mistakes while reporting their preferences to experience a large change in their utility for the final outcome. To address this, we introduce a notion of algorithmic stability and study it in the context of fair and efficient allocations of indivisible goods among two agents. We show that it is impossible to achieve exact stability along with even a wea…
Course assignment is a wide-spread problem in education and beyond. Often students have preferences for bundles of course seats or course schedules over the week, which need to be considered. The problem is a challenging distributed scheduling task requiring decision support. First-Come First-Served (FCFS) is simple and the most widely used assignment rule in practice, but it leads to inefficient outcomes and envy in the allocation. Recent theoretical results suggest alternatives with attractive economic and computational properties. Bundled Probabilistic Serial (BPS) is a randomized mechanism…
We design online algorithms for the fair allocation of public goods to a set of $N$ agents over a sequence of $T$ rounds and focus on improving their performance using predictions. In the basic model, a public good arrives in each round, the algorithm learns every agent's value for the good, and must irrevocably decide the amount of investment in the good without exceeding a total budget of $B$ across all rounds. The algorithm can utilize (potentially inaccurate) predictions of each agent's total value for all the goods to arrive. We measure the performance of the algorithm using a proportiona…
We initiate the study of multi-layered cake cutting with the goal of fairly allocating multiple divisible resources (layers of a cake) among a set of agents. The key requirement is that each agent can only utilize a single resource at each time interval. Several real-life applications exhibit such restrictions on overlapping pieces; for example, assigning time intervals over multiple facilities and resources or assigning shifts to medical professionals. We investigate the existence and computation of envy-free and proportional allocations. We show that envy-free allocations that are both feasi…
Fair Division Meets Scheduling: Approximately Envy-Free Interval Scheduling
Max Planck Institute for Informatics（马克斯·普朗克计算机科学研究所）；Saarland Informatics Campus（萨尔兰信息学园区）；University of Bremen（不来梅大学）；Indian Institute of Technology Delhi（德里印度理工学院）
Athens University of Economics and Business（雅典经济与商业大学）；Archimedes/Athena RC（阿尔基米德/雅典研究中心）；HSBC Holdings Plc.（汇丰控股有限公司）；Input Output Global (IOG)（输入输出全球（IOG））
