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Haris Aziz

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

104 papers
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Possible papers

104

AAMAS Conference 2026 Conference Paper

Participation Incentives in Online Cooperative Games

  • Haris Aziz
  • Yuhang Guo
  • Zhaohong Sun

This paper studies cooperative games where coalitions are formed online and the value generated by the grand coalition must be irrevocably distributed among the players at each time step. We investigate the fundamental issue of strategic participation incentives and address these concerns by formalizing participation incentive axioms. Our analysis reveals that existing value-sharing mechanisms fail to meet these criteria. Consequently, we propose a family of equal sharing rules that fulfill these desirable participation incentive axioms. Additionally, we refine our mechanisms under superadditive valuations to ensure individual rationality while preserving the previously established axioms.

AAMAS Conference 2026 Conference Paper

Social Welfare Maximization in Approval-Based Committee Voting under Uncertainty

  • Haris Aziz
  • Yuhang Guo
  • venkateswara Rao Kagita
  • Baharak Rastegari
  • Mashbat Suzuki

Approval voting is widely used for making multi-winner voting decisions. The canonical rule (also called Approval Voting) used in the setting aims to maximize social welfare by selecting candidates with the highest number of approvals. We revisit approval-based multi-winner voting in scenarios where the information regarding the voters’ preferences is uncertain. We present several algorithmic results for problems related to social welfare maximization under uncertainty, including computing the social welfare probability distribution of a given outcome, computing the probability that a givenoutcomeissocialwelfaremaximizing, computinganoutcome that is social welfare maximizing with the highest probability, and understanding how robust an outcome is with respect to social welfare maximization.

JAAMAS Journal 2025 Journal Article

Coordinating monetary contributions in participatory budgeting

  • Haris Aziz
  • Sujit Gujar
  • Jeremy Vollen

Abstract We formalize a framework for coordinating funding and selecting projects, the costs of which are shared among agents with quasi-linear utility functions and individual budgets. Our model contains the discrete participatory budgeting model as a special case, while capturing other useful scenarios. We propose several important axioms and objectives and study how well they can be simultaneously satisfied. We show that whereas welfare maximization admits an FPTAS, welfare maximization subject to a natural and very weak participation requirement leads to a strong inapproximability. This result is bypassed if we consider some natural restricted valuations, namely laminar single-minded valuations and symmetric valuations. Our analysis for the former restriction leads to the discovery of a new class of tractable instances for the Set Union Knapsack problem, a classical problem in combinatorial optimization.

IJCAI Conference 2025 Conference Paper

Distance Preservation Games

  • Haris Aziz
  • Hau Chan
  • Patrick Lederer
  • Shivika Narang
  • Toby Walsh

We introduce and analyze distance preservation games (DPGs). In DPGs, agents express ideal distances to other agents and need to choose locations in the unit interval while preserving their ideal distances as closely as possible. We analyze the existence and computation of location profiles that are jump stable (i. e. , no agent can benefit by moving to another location) or welfare optimal for DPGs, respectively. Specifically, we prove that there are DPGs without jump stable location profiles and identify important cases where such outcomes always exist and can be computed efficiently. Similarly, we show that finding welfare optimal location profiles is NP-complete and present approximation algorithms for finding solutions with social welfare close to optimal. Finally, we prove that DPGs have a price of anarchy of at most 2.

AAMAS Conference 2025 Conference Paper

Fair Allocation of Divisible Goods under Non-Linear Valuations

  • Haris Aziz
  • Zixu He
  • Xinhang Lu
  • Kaiyang Zhou

We study the problem of dividing homogeneous divisible goods among agents with non-linear valuations. Specifically, the value that an agent gains from a given good depends only on the amount of the good they receive, and is not necessarily linear with respect to the amount. For instance, under one-breakpoint piecewiseconstant valuations, each agent specifies a threshold for each good such that this agent receives utility zero (resp. , full utility of the good) when getting an amount below (resp. , at least) the threshold. Given non-linear valuations that are additive across the goods, we focus on designing fair allocation algorithms and consider two wellknown fairness properties: the maximin share (MMS) guarantee and envy-freeness (EF). For MMS, we devise an algorithm which always produces a 1 2𝑛−1 -MMS allocation for 𝑛 agents with arbitrary non-decreasing valuations. It is worth noting that this algorithmic result is almost tight as we give an impossibility of guaranteeing more than 1/𝑛 approximation to MMS, even when agents have onebreakpoint piecewise-constant valuations. For 𝑛 ≤ 3 agents, we show the ratio 1/𝑛 is tight. For EF, we show it is NP-hard to check the existence of an EF and Pareto optimal (PO) allocation for 𝑛 agents and at least three goods, even when agents have one-breakpoint piecewise-constant valuations. We complement the hardness result by considering the case with a single divisible good, and devising a polynomial-time algorithm to check whether an EF and PO allocation exists or not for agents with piecewise-linear valuations.

AAMAS Conference 2025 Conference Paper

Group Fairness in Multi-period Mobile Facility Location Problems

  • Haris Aziz
  • Hau Chan
  • Xingchen Sha
  • Toby Walsh
  • Lirong Xia

We study the group-fair multi-period mobile facility location problems, where agents from different groups are located on a real line and arrive in different periods. Our goal is to locate 𝑘 mobile facilities at each period to serve the arriving agents in order to minimize the maximum total group-fair cost and the maximum average group-fair cost objectives that measure the costs or distances of groups of agents to their corresponding facilities across all periods. We first consider the problems from the algorithmic perspective for both group-fair cost objectives. We then consider the problems from the mechanism design perspective, where the agents’ locations and arrival periods are private. For both objectives, we design deterministic strategyproof mechanisms to elicit the agents’ locations and arrival periods truthfully while optimizing the group-fair cost objectives and show that our mechanisms have almost tight bounds on the approximation ratios for certain periods and settings. Finally, we discuss the extensions of our results to the online setting where agent arrival information is only known at each period.

NeurIPS Conference 2025 Conference Paper

Learning-Augmented Facility Location Mechanisms for Envy Ratio

  • Haris Aziz
  • Yuhang Guo
  • Alexander Lam
  • Houyu Zhou

The augmentation of algorithms with predictions of the optimal solution, such as from a machine-learning algorithm, has garnered significant attention in recent years, particularly in facility location problems. Moving beyond the traditional focus on utilitarian and egalitarian objectives, we design learning-augmented facility location mechanisms for the envy ratio objective, a fairness metric defined as the maximum ratio between the utilities of any two agents. For the deterministic setting, we propose a mechanism which utilizes predictions to achieve $\alpha$-consistency and $\frac{\alpha}{\alpha - 1}$-robustness for a selected parameter $\alpha \in [1, 2]$, and prove its optimality. We also resolve open questions raised by Ding et al. [2020], devising a randomized mechanism without predictions to improve upon the best-known approximation ratio from $2$ to $1. 8944$. Building upon these advancements, we construct a novel randomized mechanism which incorporates predictions to achieve improved performance guarantees.

AIJ Journal 2025 Journal Article

Multi-rank smart reserves: A general framework for selection and matching diversity goals

  • Haris Aziz
  • Zhaohong Sun

We study a problem where each school has flexible multi-ranked diversity goals, and each student may belong to multiple overlapping types, and consumes only one of the positions reserved for their types. We propose a novel choice function for a school to select students and show that it is the unique rule that satisfies three fundamental properties: maximal diversity, non-wastefulness, and justified envy-freeness. We provide a fast polynomial-time algorithm for our choice function that is based on the Dulmage Mendelsohn Decomposition Theorem as well as new insights into the combinatorial structure of constrained rank maximal matchings. Even for the case of minimum and maximum quotas for types (that capture two ranks), ours is the first known polynomial-time approach to compute an optimally diverse choice outcome. Finally, we prove that the choice function we design for schools, satisfies substitutability and hence can be directly embedded in the generalized deferred acceptance algorithm to achieve strategyproofness and stability. Our algorithms and results have immediate policy implications and directly apply to a variety of scenarios, such as where hiring positions or scarce medical resources need to be allocated while taking into account diversity concerns or ethical principles.

AAMAS Conference 2025 Conference Paper

Neighborhood Stability in Assignments on Graphs

  • Haris Aziz
  • Grzegorz Lisowski
  • Mashbat Suzuki
  • Jeremy Vollen

We study the problem of assigning agents to the vertices of a graph such that no pair of neighbors can benefit from swapping assignments – a property we term neighborhood stability. We assume that agents’ utilities are based only on their preferences over the assignees of adjacent vertices and that those preferences are binary. Having shown that even this very restricted setting does not guarantee neighborhood stable assignments, we focus on special cases providing such guarantees. We show that when the graph is a cycle or a path, a neighborhood stable assignment always exists for any preference profile. Also, we give a general condition under which neighborhood stable assignments always exist. For each of these results, we give a polynomial-time algorithm to compute a neighborhood stable assignment.

AAMAS Conference 2025 Conference Paper

Weighted Envy-free Allocation with Subsidy

  • Haris Aziz
  • Xin Huang
  • Kei Kimura
  • Indrajit Saha
  • Zhaohong Sun
  • Mashbat Suzuki
  • Makoto Yokoo

We consider the problem of fair allocation of indivisible items with subsidies when agents have weighted entitlements. Specifically, we extend the envy-freeability studied in the unweighted case to the weighted envy-freeability and delve deeper into its properties. We first highlight various important differences from the unweighted case, e. g. , the sufficient conditions that lead to envy-freeability in the unweighted case do not lead to weighted envy-freeability in the weighted case. We then present various results concerning weighted envy-freeability including general characterizations, algorithms for achieving and testing weighted envy-freeability, lower and upper bounds of the amount of subsidies for weighted envy-freeable allocations. Additionally, we design algorithms that ensure weighted envy-freeability while incorporating other fairness properties, such as weighted envy-freeness up to one item transfer.

AIJ Journal 2024 Journal Article

Almost proportional allocations of indivisible chores: Computation, approximation and efficiency

  • Haris Aziz
  • Bo Li
  • Hervé Moulin
  • Xiaowei Wu
  • Xinran Zhu

Proportionality (PROP) is one of the simplest and most intuitive fairness criteria used for allocating items among agents with additive utilities. However, when the items are indivisible, ensuring PROP becomes unattainable, leading to increased focus on its relaxations. In this paper, we focus on the relaxation of proportionality up to any item (PROPX), where proportionality is satisfied if an arbitrary item is removed from every agent's allocation. We show that PROPX is an appealing fairness notion for the allocation of indivisible chores, which approximately implies some share-based notions, such as maximin share (MMS) and AnyPrice share (APS). We further provide a comprehensive understanding of PROPX allocations, regarding the computation, approximation, and compatibility with efficiency. On top of these, we extend the study to scenarios where agents do not share equal liability towards the chores, and approximate PROPX allocations using partial information about agents' utilities.

JAIR Journal 2024 Journal Article

Efficient and Fair Healthcare Rationing

  • Haris Aziz
  • Florian Brandl

The rationing of healthcare resources has emerged as an important issue, which has been discussed by medical experts, policy-makers, and the general public. We consider a rationing problem where medical units are to be allocated to patients. Each unit is reserved for one of several categories, and each category has a priority ranking over the patients. We present a class of allocation rules that respect the priorities, comply with the eligibility requirements, allocate the largest feasible number of units, and do not penalize agents for rising in the priority ranking of a category. The rules characterize all possible allocations that satisfy the first three properties and are polynomial-time computable.

AAAI Conference 2024 Conference Paper

Envy-Free House Allocation under Uncertain Preferences

  • Haris Aziz
  • Isaiah Iliffe
  • Bo Li
  • Angus Ritossa
  • Ankang Sun
  • Mashbat Suzuki

Envy-freeness is one of the most important fairness concerns when allocating items. We study envy-free house allocation when agents have uncertain preferences over items and consider several well-studied preference uncertainty models. The central problem that we focus on is computing an allocation that has the highest probability of being envy-free. We show that each model leads to a distinct set of algorithmic and complexity results, including detailed results on (in-)approximability. En route, we consider two related problems of checking whether there exists an allocation that is possibly or necessarily envy-free. We give a complete picture of the computational complexity of these two problems for all the uncertainty models we consider.

AAAI Conference 2024 Conference Paper

Fair Lotteries for Participatory Budgeting

  • Haris Aziz
  • Xinhang Lu
  • Mashbat Suzuki
  • Jeremy Vollen
  • Toby Walsh

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend---the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.

AAMAS Conference 2024 Conference Paper

Proportional Fairness in Obnoxious Facility Location

  • Alexander Lam
  • Haris Aziz
  • Bo Li
  • Fahimeh Ramezani
  • Toby Walsh

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, we show that our proportional fairness axioms are incompatible with strategyproofness, and prove asymptotically tight 𝑒𝑝𝑠𝑖𝑙𝑜𝑛-price of anarchy and stability bounds for proportionally fair welfare-optimal mechanisms. In the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare. Finally, we prove existence results for two extensions to our model.

AAAI Conference 2023 Conference Paper

Approval-Based Voting with Mixed Goods

  • Xinhang Lu
  • Jannik Peters
  • Haris Aziz
  • Xiaohui Bei
  • Warut Suksompong

We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called EJR for mixed goods (EJR-M) and a weaker one called EJR up to 1 (EJR-1). We extend three multiwinner voting rules to our setting—GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV)—and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules.

AAMAS Conference 2023 Conference Paper

Best of Both Worlds Fairness under Entitlements

  • Haris Aziz
  • Aditya Ganguly
  • Evi Micha

We consider probabilistic allocation of indivisible items to agents with additive valuations and weighted entitlements. We explore how far ex-ante and ex-post fairness properties can be achieved simultaneously. Our first result is that in contrast to the case of same entitlements, well-established adaptations of ex-ante envy-freeness and ex-post envy-freeness up to one item (EF1) to the case of entitlements are not compatible. We then present a polynomial-time algorithm that achieves weighted ex-ante envy-freeness and ex-post weighted envy-freeness up to 1 transfer. The outcome is ex-ante weighted envy-free for all utilities consistent with the underlying ordinal preferences but it is not Pareto optimal. We then present an alternative polynomial-time algorithm that satisfies Pareto optimality (both ex-ante and ex-post), ex-ante weighted envy-freeness and ex-post weighted proportionality up to one item.

AAMAS Conference 2023 Conference Paper

Fair Allocation of Two Types of Chores

  • Haris Aziz
  • Jeremy Lindsay
  • Angus Ritossa
  • Mashbat Suzuki

We consider the problem of fair allocation of indivisible chores under additive valuations. We assume that the chores are divided into two types and under this scenario, we present several results. Our first result is a new characterization of Pareto optimal allocations in our setting and a polynomial-time algorithm to compute an envy-free up to one item (EF1) and Pareto optimal allocation. We then turn to the question of whether we can achieve a stronger fairness concept called envy-free up any item (EFX). We present a polynomial-time algorithm that returns an EFX allocation. Finally, we show that for our setting, it can be checked in polynomial time whether an envy-free allocation exists or not.

AIJ Journal 2023 Journal Article

Fair division of indivisible goods: Recent progress and open questions

  • Georgios Amanatidis
  • Haris Aziz
  • Georgios Birmpas
  • Aris Filos-Ratsikas
  • Bo Li
  • Hervé Moulin
  • Alexandros A. Voudouris
  • Xiaowei Wu

Allocating resources to individuals in a fair manner has been a topic of interest since ancient times, with most of the early mathematical work on the problem focusing on resources that are infinitely divisible. Over the last decade, there has been a surge of papers studying computational questions regarding the indivisible case, for which exact fairness notions such as envy-freeness and proportionality are hard to satisfy. One main theme in the recent research agenda is to investigate the extent to which their relaxations, like maximin share fairness (MMS) and envy-freeness up to any good (EFX), can be achieved. In this survey, we present a comprehensive review of the recent progress made in the related literature by highlighting different ways to relax fairness notions, common algorithm design techniques, and the most interesting questions for future research.

AAAI Conference 2023 Conference Paper

Fairness Concepts for Indivisible Items with Externalities

  • Haris Aziz
  • Warut Suksompong
  • Zhaohong Sun
  • Toby Walsh

We study a fair allocation problem of indivisible items under additive externalities in which each agent also receives utility from items that are assigned to other agents. This allows us to capture scenarios in which agents benefit from or compete against one another. We extend the well-studied properties of envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) to this setting, and we propose a new fairness concept called general fair share (GFS), which applies to a more general public decision making model. We undertake a detailed study and present algorithms for finding fair allocations.

AAMAS Conference 2023 Conference Paper

Group Fairness in Peer Review

  • Haris Aziz
  • Evi Micha
  • Nisarg Shah

Conferences like AAMAS and NeurIPS have attracted submissions from a large number of communities. This has resulted in a poor reviewing experience for communities, whose submissions are assigned to less qualified reviewers outside of their communities. An often-advocated solution is to break up such large conferences into smaller conferences, but this can lead to the isolation of various communities. We tackle this challenge by introducing a notion of group fairness, called core, which requires every subset of researchers to be treated in such a manner such that they cannot benefit from organizing a smaller conference on their own. We study a simple peer review model, prove that it always admits a reviewing assignment in the core, and design an efficient algorithm to find one such assignment. On the negative side, we show that the core is incompatible with achieving a good worstcase approximation of social welfare, an often-sought desideratum. We complement these results by conducting experiments with real data.

NeurIPS Conference 2023 Conference Paper

Group Fairness in Peer Review

  • Haris Aziz
  • Evi Micha
  • Nisarg Shah

Large conferences such as NeurIPS and AAAI serve as crossroads of various AI fields, since they attract submissions from a vast number of communities. However, in some cases, this has resulted in a poor reviewing experience for some communities, whose submissions get assigned to less qualified reviewers outside of their communities. An often-advocated solution is to break up any such large conference into smaller conferences, but this can lead to isolation of communities and harm interdisciplinary research. We tackle this challenge by introducing a notion of group fairness, called the core, which requires that every possible community (subset of researchers) to be treated in a way that prevents them from unilaterally benefiting by withdrawing from a large conference. We study a simple peer review model, prove that it always admits a reviewing assignment in the core, and design an efficient algorithm to find one such assignment. We use real data from CVPR and ICLR conferences to compare our algorithm to existing reviewing assignment algorithms on a number of metrics.

AAMAS Conference 2023 Conference Paper

Matching Algorithms under Diversity-Based Reservations

  • Haris Aziz
  • Sean Morota Chu
  • Zhaohong Sun

Selection under category or diversity constraints is a ubiquitous and widely-applicable problem that is encountered in immigration, school choice, hiring, and healthcare rationing. These diversity constraints are typically represented by minimum and maximum quotas on various categories or types. We undertake a detailed comparative study of applicant selection algorithms with respect to the diversity goals.

AIJ Journal 2023 Journal Article

Portioning using ordinal preferences: Fairness and efficiency

  • Stéphane Airiau
  • Haris Aziz
  • Ioannis Caragiannis
  • Justin Kruger
  • Jérôme Lang
  • Dominik Peters

A divisible public resource is to be divided among projects. We study rules that decide on a distribution of the budget when voters have ordinal preference rankings over projects. Examples of such portioning problems are participatory budgeting, time shares, and parliament elections. We introduce a family of rules for portioning, inspired by positional scoring rules. Rules in this family are given by a scoring vector (such as plurality or Borda) associating a positive value with each rank in a vote, and an aggregation function such as leximin or the Nash product. Our family contains well-studied rules, but most are new. We discuss computational and normative properties of our rules. We focus on fairness, and introduce the SD-core, a group fairness notion. Our Nash rules are in the SD-core, and the leximin rules satisfy individual fairness properties. Both are Pareto-efficient.

AAMAS Conference 2023 Conference Paper

Possible Fairness for Allocating Indivisible Resources

  • Haris Aziz
  • Bo Li
  • Shiji Xing
  • Yu Zhou

Fair division of indivisible resources has attracted significant attention from multi-agent systems and computational social choice. Two popular solution concepts are envy-freeness up to any item (EFX) and maximin share (MMS) fairness which are defined using agents’ cardinal preferences. On one hand, accurate cardinal values are hard to express in real-life applications, and on the other hand, with cardinal values, MMS and EFX may not be easy to satisfy. In this work, we study a new setting where agents have arbitrary ordinal preferences for the items (possibly with indifferences), and an allocation is called possible EFX (p-EFX) or possible MMS (p- MMS) if there exist cardinal preferences that are consistent with the ordinal ones so that the allocation is EFX or MMS. We first design a polynomial-time algorithm to compute an allocation that is p-EFX and p-MMS under lexicographic preferences. This result also strengthens a result of Hosseini et al. (AAAI 2021) who proved the existence of EFX and MMS allocations under strict lexicographic preferences (i. e. , the items do not have ties). Although it has been well justified that lexicographic preferences are natural and common, there are situations where they do not fit appropriately, especially when the items have similar types. Therefore, on top of p-EFX and p-MMS, we want the allocation to be balanced (i. e. , the numbers of items allocated to the agents differ by at most one). We then design another algorithm that satisfies p-EFX, p-MMS, and balanced simultaneously.

AAMAS Conference 2023 Conference Paper

Probabilistic Rationing with Categorized Priorities: Processing Reserves Fairly and Efficiently

  • Haris Aziz

In recent years, a market design approach for rationing problems with multi-category priorities has been considered for various applications including healthcare, immigration, and school choice. We consider a probabilistic or fractional approach to rationing that is geared towards achieving symmetry axioms such as anonymity and neutrality in conjunction to primary axioms such as eligibility compatibility, respect of priorities, and non-wastefulness. We present new algorithms for the problem that have advantages over the simultaneous reservation rule of Delacrétaz (ACM EC 2021) with respect to fairness, efficiency, and simplicity.

AAMAS Conference 2023 Conference Paper

Proportional Fairness in Obnoxious Facility Location

  • Haris Aziz
  • Alexander Lam
  • Bo Li
  • Fahimeh Ramezani
  • Toby Walsh

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, not only are our proportional fairness axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare within a constant factor of the optimal welfare. On the other hand, in the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare.

AAAI Conference 2022 Conference Paper

Matching Market Design with Constraints

  • Haris Aziz
  • Péter Biró
  • Makoto Yokoo

Two-sided matching is an important research area that has had a major impact on the design of real-world matching markets. One consistent feature in many of the real-world applications is that they impose new feasibility constraints that lead to research challenges. We survey developments in the field of two-sided matching with various constraints, including those based on regions, diversity, multi-dimensional capacities, and matroids.

NeurIPS Conference 2022 Conference Paper

Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location Mechanism

  • Haris Aziz
  • Alexander Lam
  • Mashbat Suzuki
  • Toby Walsh

Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality, which ensures that when there are two groups of agents at different locations, both groups incur the same total cost. We show that although Strong Proportionality is a well-motivated and basic axiom, there is no deterministic strategyproof mechanism satisfying the property. We then identify a randomized mechanism called Random Rank (which uniformly selects a number $k$ between $1$ to $n$ and locates the facility at the $k$'th highest agent location) which satisfies Strong Proportionality in expectation. Our main theorem characterizes Random Rank as the unique mechanism that achieves universal truthfulness, universal anonymity, and Strong Proportionality in expectation among all randomized mechanisms. Finally, we show via the AverageOrRandomRank mechanism that even stronger ex-post fairness guarantees can be achieved by weakening universal truthfulness to strategyproofness in expectation.

TCS Journal 2022 Journal Article

Stable matching with uncertain pairwise preferences

  • Haris Aziz
  • Péter Biró
  • Tamás Fleiner
  • Serge Gaspers
  • Ronald de Haan
  • Nicholas Mattei
  • Baharak Rastegari

We study a two-sided matching problem under preferences, where the agents have independent pairwise comparisons on their possible partners and these preferences may be uncertain. Preferences may be intransitive and agents may even have cycles in their preferences; e. g. an agent a may prefer b to c, c to d, and d to b, all with probability one. If an instance has such a cycle, then there may not exist any matching that is stable with positive probability. We focus on the computational problems of checking the existence of possibly and certainly stable matchings, i. e. , matchings whose probability of being stable is positive or one, respectively. We show that finding possibly stable matchings is NP-hard, even if only one side can have cyclic preferences. On the other hand we show that the problem of finding a certainly stable matching is polynomial-time solvable if only one side can have cyclic preferences and the other side has transitive preferences, but that this problem becomes NP-hard when both sides can have cyclic preferences.

AAAI Conference 2021 Conference Paper

Achieving Envy-freeness and Equitability with Monetary Transfers

  • Haris Aziz

When allocating indivisible resources or tasks, an envy-free allocation or equitable allocation may not exist. We present a sufficient condition and an algorithm to achieve envyfreeness and equitability when monetary transfers are allowed. The approach works for any agent valuation functions as long as they satisfy superadditivity. For the case of additive valuations, we present a characterization of allocations that can simultaneously be made equitable and envy-free via payments. We then present a distributed algorithm to compute an approximately envy-free outcome for any class of valuations.

JAAMAS Journal 2021 Journal Article

Fair allocation of indivisible goods and chores

  • Haris Aziz
  • Ioannis Caragiannis
  • Toby Walsh

Abstract We consider the problem of fairly dividing a set of indivisible items. Much of the fair division literature assumes that the items are “goods” that yield positive utility for the agents. There is also some work in which the items are “chores” that yield negative utility for the agents. In this paper, we consider a more general scenario in which an agent may have positive or negative utility for each item. This framework captures, e. g. , fair task assignment, where agents can experience both positive and negative utility for each task. We demonstrate that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new and efficient algorithms for finding fair allocations in this general setting. We also point out several gaps in the literature regarding the existence of allocations that satisfy certain fairness and efficiency properties and examine the complexity of computing such allocations.

AAMAS Conference 2021 Conference Paper

Multi-Robot Task Allocation-Complexity and Approximation

  • Haris Aziz
  • Hau Chan
  • Ágnes Cseh
  • Bo Li
  • Fahimeh Ramezani
  • Chenhao Wang

Multi-robot task allocation is one of the most fundamental classes of problems in robotics and is crucial for various real-world robotic applications such as search, rescue and area exploration. We consider the Single-Task robots and Multi-Robot tasks Instantaneous Assignment (ST-MR-IA) setting where each task requires at least a certain number of robots and each robot can work on at most one task and incurs an operational cost for each task. Our aim is to consider a natural computational problem of allocating robots to complete the maximum number of tasks subject to budget constraints. We consider budget constraints of three different kinds: (1) total budget, (2) task budget, and (3) robot budget. We provide a detailed complexity analysis including results on approximations as well as polynomial-time algorithms for the general setting and important restricted settings.

AAAI Conference 2021 Conference Paper

Optimal Kidney Exchange with Immunosuppressants

  • Haris Aziz
  • Ágnes Cseh
  • John P. Dickerson
  • Duncan C. McElfresh

Algorithms for exchange of kidneys is one of the key successful applications in market design, artificial intelligence, and operations research. Potent immunosuppressant drugs suppress the body’s ability to reject a transplanted organ up to the point that a transplant across blood- or tissue-type incompatibility becomes possible. In contrast to the standard kidney exchange problem, we consider a setting that also involves the decision about which recipients receive from the limited supply of immunosuppressants that make them compatible with originally incompatible kidneys. We firstly present a general computational framework to model this problem. Our main contribution is a range of efficient algorithms that provide flexibility in terms of meeting meaningful objectives. Motivated by the current reality of kidney exchanges using sophisticated mathematical-programming-based clearing algorithms, we then present a general but scalable approach to optimal clearing with immunosuppression; we validate our approach on realistic data from a large fielded exchange.

AAAI Conference 2021 Conference Paper

Proportionally Representative Participatory Budgeting with Ordinal Preferences

  • Haris Aziz
  • Barton E. Lee

Participatory budgeting (PB) is a democratic paradigm whereby voters decide on a set of projects to fund with a limited budget. We consider PB in a setting where voters report ordinal preferences over projects and have (possibly) asymmetric weights. We propose proportional representation axioms and clarify how they fit into other preference aggregation settings, such as multi-winner voting and approvalbased multi-winner voting. As a result of our study, we also discover a new solution concept for approval-based multiwinner voting, which we call Inclusion PSC (IPSC). IPSC is stronger than proportional justified representation (PJR), incomparable to extended justified representation (EJR), and yet compatible with EJR. The well-studied Proportional Approval Voting (PAV) rule produces a committee that satisfies both EJR and IPSC; however, both these axioms can also be satisfied by an algorithm that runs in polynomial-time.

IJCAI Conference 2021 Conference Paper

School Choice with Flexible Diversity Goals and Specialized Seats

  • Haris Aziz
  • Zhaohong Sun

We present a new and rich model of school choice with flexible diversity goals and specialized seats. The model also applies to other settings such as public housing allocation with diversity objectives. Our method of expressing flexible diversity goals is also applicable to other settings in moral multi-agent decision making where competing policies need to be balanced when allocating scarce resources. For our matching model, we present a polynomial-time algorithm that satisfies desirable properties, including strategyproofness and stability under several natural subdomains of our problem. We complement the results by providing a clear understanding about what results do not extend when considering the general model.

IJCAI Conference 2020 Conference Paper

Almost Group Envy-free Allocation of Indivisible Goods and Chores

  • Haris Aziz
  • Simon Rey

We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger and relaxed versions that are especially suitable for the allocation of indivisible items. Of particular interest is a concept called group envy-freeness up to one item (GEF1). We then present a clear taxonomy of the fairness concepts. We study which fairness concepts guarantee the existence of a fair allocation under which preference domain. For two natural classes of additive utilities, we design polynomial-time algorithms to compute a GEF1 allocation. We also prove that checking whether a given allocation satisfies GEF1 is coNP-complete when there are either only goods, only chores or both.

JAAMAS Journal 2020 Journal Article

Computing and testing Pareto optimal committees

  • Haris Aziz
  • Jérôme Monnot

Abstract Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that each agent specifies a weak order on single alternatives, from which a preference relation over subsets is derived using some preference extension. We consider five prominent extensions (responsive, downward lexicographic, upward lexicographic, best, and worst). For each of them, we consider the corresponding Pareto optimality notion, and we study the complexity of computing and verifying Pareto optimal outcomes. For each of the preference extensions, we give a complete characterization of the complexity of testing Pareto optimality when preferences are dichotomous or linear. We also consider strategic issues: for four of the set extensions, we present a linear-time, Pareto optimal and strategyproof algorithm that even works for weak preferences.

AAAI Conference 2020 Conference Paper

Developments in Multi-Agent Fair Allocation

  • Haris Aziz

Fairness is becoming an increasingly important concern when designing markets, allocation procedures, and computer systems. I survey some recent developments in the field of multiagent fair allocation.

AAAI Conference 2020 Conference Paper

Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives

  • Haris Aziz
  • Hau Chan
  • Barton Lee
  • Bo Li
  • Toby Walsh

We consider the facility location problem in the onedimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the corresponding optimization problem, where the goal is to locate facilities to minimize either the total cost to all agents or the maximum cost of any agent is NP-hard. However, we show that the problem is fixed-parameter tractable, and the optimal solution can be computed in polynomial time whenever the number of facilities is bounded, or when all facilities have identical capacities. We then consider the problem from a mechanism design perspective where the agents are strategic and need not reveal their true locations. We show that several natural mechanisms studied in the uncapacitated setting either lose strategyproofness or a bound on the solution quality for the total or maximum cost objective. We then propose new mechanisms that are strategyproof and achieve approximation guarantees that almost match the lower bounds.

JAIR Journal 2020 Journal Article

Fair Allocation with Diminishing Differences

  • Erel Segal-Halevi
  • Avinatan Hassidim
  • Haris Aziz

Ranking alternatives is a natural way for humans to explain their preferences. It is used in many settings, such as school choice, course allocations and residency matches. Without having any information on the underlying cardinal utilities, arguing about the fairness of allocations requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation whenever it exists. Using simulations, we compare the various fairness criteria in terms of their probability of existence, and their probability of being fair by the underlying cardinal valuations. We find that necessary-DD-proportionality fares well in both measures. We also consider envy-freeness and Pareto optimality under diminishing-differences, as well as chore allocation under the analogous condition --- increasing-differences.

IJCAI Conference 2020 Conference Paper

Mechanism Design for School Choice with Soft Diversity Constraints

  • Haris Aziz
  • Serge Gaspers
  • Zhaohong Sun

We study the controlled school choice problem where students may belong to overlapping types and schools have soft target quotas for each type. We formalize fairness concepts for the setting that extend fairness concepts considered for restricted settings without overlapping types. Our central contribution is presenting a new class of algorithms that takes into account the representations of combinations of student types. The algorithms return matchings that are non-wasteful and satisfy fairness for same types. We further prove that the algorithms are strategyproof for the students and yield a fair outcome with respect to the induced quotas for type combinations. We experimentally compare our algorithms with two existing approaches in terms of achieving diversity goals and satisfying fairness.

TCS Journal 2019 Journal Article

Efficient reallocation under additive and responsive preferences

  • Haris Aziz
  • Péter Biró
  • Jérôme Lang
  • Julien Lesca
  • Jérôme Monnot

Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. While finding an arbitrary Pareto optimal allocation is generally easy, checking whether a particular allocation is Pareto optimal can be much more difficult. This problem is equivalent to checking that the allocated objects cannot be reallocated in such a way that at least one agent prefers her new allocation to her old one, and no agent prefers her old allocation to her new one. We consider the problem for two related types of preference relations over sets of objects. In the first part of the paper we focus on the setting in which agents express additive cardinal utilities over objects. We present computational hardness results as well as polynomial-time algorithms for testing Pareto optimality under different restrictions such as two utility values or lexicographic utilities. In the second part of the paper we assume that agents express only their (ordinal) preferences over individual objects, and that their underlying preferences are additively separable. In this setting, we present characterizations and polynomial-time algorithms for possible and necessary Pareto optimality.

IJCAI Conference 2019 Conference Paper

Fair Allocation of Indivisible Goods and Chores

  • Haris Aziz
  • Ioannis Caragiannis
  • Ayumi Igarashi
  • Toby Walsh

We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are ``goods'' i. e. , they yield positive utility for the agents. There is also some work where the items are ``chores'' that yield negative utility for the agents. In this paper, we consider a more general scenario where an agent may have negative or positive utility for each item. This framework captures, e. g. , fair task assignment, where agents can have both positive and negative utilities for each task. We show that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new and efficient algorithms for finding fair allocations in this general setting. We also point out several gaps in the literature regarding the existence of allocations satisfying certain fairness and efficiency properties and further study the complexity of computing such allocations.

IJCAI Conference 2019 Conference Paper

Fair Online Allocation of Perishable Goods and its Application to Electric Vehicle Charging

  • Enrico H. Gerding
  • Alvaro Perez-Diaz
  • Haris Aziz
  • Serge Gaspers
  • Antonia Marcu
  • Nicholas Mattei
  • Toby Walsh

We consider mechanisms for the online allocation of perishable resources such as energy or computational power. A main application is electric vehicle charging where agents arrive and leave over time. Unlike previous work, we consider mechanisms without money, and a range of objectives including fairness and efficiency. In doing so, we extend the concept of envy-freeness to online settings. Furthermore, we explore the trade-offs between different objectives and analyse their theoretical properties both in online and offline settings. We then introduce novel online scheduling algorithms and compare them in terms of both their theoretical properties and empirical performance.

AAMAS Conference 2019 Conference Paper

From Matching with Diversity Constraints to Matching with Regional Quotas

  • Haris Aziz
  • Serge Gaspers
  • Zhaohong Sun
  • Toby Walsh

In the past few years, several new matching models have been proposed and studied that take into account complex distributional constraints. Relevant lines of work include (1) school choice with diversity constraints where students have (possibly overlapping) types and (2) hospital-doctor matching where various regional quotas are imposed. In this paper, we present a polynomial-time reduction to transform an instance of (1) to an instance of (2) and we show how the feasibility and stability of corresponding matchings are preserved under the reduction. Our reduction provides a formal connection between two important strands of work on matching with distributional constraints. We then apply the reduction in two ways. Firstly, we show that it is NP-complete to check whether a feasible and stable outcome for (1) exists. Due to our reduction, these NP-completeness results carry over to setting (2). In view of this, we help unify some of the results that have been presented in the literature. Secondly, if we have positive results for (2), then we have corresponding results for (1). One key conclusion of our results is that further developments on axiomatic and algorithmic aspects of hospital-doctor matching with regional quotas will result in corresponding results for school choice with diversity constraints.

AAMAS Conference 2019 Conference Paper

Maxmin Share Fair Allocation of Indivisible Chores to Asymmetric Agents

  • Haris Aziz
  • Hau Chan
  • Bo Li

We initiate the study of indivisible chore allocation for agents with asymmetric shares. The fairness concepts we focus on are natural generalizations of maxmin share: WMMS fairness and OWMMS fairness. We first highlight the fact that commonly-used algorithms that work well for allocation of goods to asymmetric agents, and even for chores to symmetric agents do not provide good approximations for allocation of chores to asymmetric agents under WMMS. As a consequence, we present a novel polynomial-time constantapproximation algorithm, via linear program, for OWMMS. For two special cases: binary valuation case and 2-agent case, we provide exact or better constant-approximation algorithms.

AAAI Conference 2019 Conference Paper

Pareto Optimal Allocation under Compact Uncertain Preferences

  • Haris Aziz
  • Peter Biro
  • Ronald de Haan
  • Baharak Rastegari

The assignment problem is one of the most well-studied settings in multi-agent resource allocation. Aziz, de Haan, and Rastegari (2017) considered this problem with the additional feature that agents’ preferences involve uncertainty. In particular, they considered two uncertainty models neither of which is necessarily compact. In this paper, we focus on three uncertain preferences models whose size is polynomial in the number of agents and items. We consider several interesting computational questions with regard to Pareto optimal assignments. We also present some general characterization and algorithmic results that apply to large classes of uncertainty models.

AIJ Journal 2019 Journal Article

Pareto optimal allocation under uncertain preferences: uncertainty models, algorithms, and complexity

  • Haris Aziz
  • Péter Biró
  • Ronald de Haan
  • Baharak Rastegari

The assignment problem is one of the most well-studied settings in multi-agent resource allocation. Agents express preferences over indivisible items and then the items are allocated based on these preferences. Pareto optimality is regarded as a desirable property for the chosen allocation, requiring that no other allocation exists in which no agent is worse off and at least one agent is better of. We consider the assignment problem with the additional feature that agents' preferences involve uncertainty. The setting with uncertainty leads to a number of interesting questions including the following ones. How to compute an assignment with the highest probability of being Pareto optimal? What is the complexity of computing the probability that a given assignment is Pareto optimal? Does there exist an assignment that is Pareto optimal with probability one? We consider these problems under five natural uncertainty models. For all of the models, we present a number of algorithmic and complexity results highlighting the differences and similarities in the complexity of the models. We also present some general characterization and algorithmic results that apply to large classes of uncertainty models.

IJCAI Conference 2019 Conference Paper

Portioning Using Ordinal Preferences: Fairness and Efficiency

  • Stéphane Airiau
  • Haris Aziz
  • Ioannis Caragiannis
  • Justin Kruger
  • Jérôme Lang
  • Dominik Peters

A public divisible resource is to be divided among projects. We study rules that decide on a distribution of the budget when voters have ordinal preference rankings over projects. Examples of such portioning problems are participatory budgeting, time shares, and parliament elections. We introduce a family of rules for portioning, inspired by positional scoring rules. Rules in this family are given by a scoring vector (such as plurality or Borda) associating a positive value with each rank in a vote, and an aggregation function such as leximin or the Nash product. Our family contains well-studied rules, but most are new. We discuss computational and normative properties of our rules. We focus on fairness, and introduce the SD-core, a group fairness notion. Our Nash rules are in the SD-core, and the leximin rules satisfy individual fairness properties. Both are Pareto-efficient.

IJCAI Conference 2019 Conference Paper

Strategyproof and Approximately Maxmin Fair Share Allocation of Chores

  • Haris Aziz
  • Bo Li
  • Xiaowei Wu

We initiate the work on fair and strategyproof allocation of indivisible chores. The fairness concept we consider in this paper is maxmin share (MMS) fairness. We consider three previously studied models of information elicited from the agents: the ordinal model, the cardinal model, and the public ranking model in which the ordinal preferences are publicly known. We present both positive and negative results on the level of MMS approximation that can be guaranteed if we require the algorithm to be strategyproof. Our results uncover some interesting contrasts between the approximation ratios achieved for chores versus goods.

JAAMAS Journal 2019 Journal Article

Strategyproof multi-item exchange under single-minded dichotomous preferences

  • Haris Aziz

Abstract We consider multi-item exchange markets in which agents want to receive one of their target bundles of resources. The model encompasses well-studied markets for kidney exchange, lung exchange, and multi-organ exchange. We identify a general and sufficient condition called weak consistency for the exchange mechanisms to be strategyproof even if we impose any kind of distributional, diversity, or exchange cycle constraints. Within the class of weakly consistent and strategyproof mechanisms, we highlight two important ones that satisfy constrained Pareto optimality and strong individual rationality. Several results in the literature follow from our insights. We also derive impossibility results when constrained Pareto optimality is defined with respect to more permissive individual rationality requirements.

AIJ Journal 2019 Journal Article

Strategyproof peer selection using randomization, partitioning, and apportionment

  • Haris Aziz
  • Omer Lev
  • Nicholas Mattei
  • Jeffrey S. Rosenschein
  • Toby Walsh

Peer reviews, evaluations, and selections are a fundamental aspect of modern science. Funding bodies the world over employ experts to review and select the best proposals from those submitted for funding. The problem of peer selection, however, is much more general: a professional society may want to give a subset of its members awards based on the opinions of all members; an instructor for a Massive Open Online Course (MOOC) or an online course may want to crowdsource grading; or a marketing company may select ideas from group brainstorming sessions based on peer evaluation. We make three fundamental contributions to the study of peer selection, a specific type of group decision-making problem, studied in computer science, economics, and political science. First, we propose a novel mechanism that is strategyproof, i. e. , agents cannot benefit by reporting insincere valuations. Second, we demonstrate the effectiveness of our mechanism by a comprehensive simulation-based comparison with a suite of mechanisms found in the literature. Finally, our mechanism employs a randomized rounding technique that is of independent interest, as it solves the apportionment problem that arises in various settings where discrete resources such as parliamentary representation slots need to be divided proportionally.

IJCAI Conference 2019 Conference Paper

Weighted Maxmin Fair Share Allocation of Indivisible Chores

  • Haris Aziz
  • Hau Chan
  • Bo Li

We initiate the study of indivisible chore allocation for agents with asymmetric shares. The fairness concept we focus on is the weighted natural generalization of maxmin share: WMMS fairness and OWMMS fairness. We first highlight the fact that commonly-used algorithms that work well for allocation of goods to asymmetric agents, and even for chores to symmetric agents do not provide good approximations for allocation of chores to asymmetric agents under WMMS. As a consequence, we present a novel polynomial-time constant-approximation algorithm, via linear program, for OWMMS. For two special cases: the binary valuation case and the 2-agent case, we provide exact or better constant-approximation algorithms.

AAMAS Conference 2018 Conference Paper

Defender Stackelberg Game with Inverse Geodesic Length as Utility Metric

  • Haris Aziz
  • Serge Gaspers
  • Edward J. Lee
  • Kamran Najeebullah

The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices in the network. A Stackelberg game is a strategic game in which one player commits to a strategy while taking into account that other players will respond accordingly. We propose a natural defender-attacker Stackelberg game on a network in which the defender wants to maximize the IGL level of the network and commits to protecting parts of the network while having knowledge of the strength of an attacker that wants to weaken the network. We present several algorithmic and complexity results concerning the problem of finding the optimal commitment for the defender. Some of our computational hardness results also answer open problems posed in prior work on IGL.

IJCAI Conference 2018 Conference Paper

Egalitarian Committee Scoring Rules

  • Haris Aziz
  • Piotr Faliszewski
  • Bernard Grofman
  • Arkadii Slinko
  • Nimrod Talmon

We introduce and study the class of egalitarian variants of committee scoring rules, where instead of summing up the scores that voters assign to committees---as is done in the utilitarian variants---the score of a committee is taken to be the lowest score assigned to it by any voter. We focus on five rules, which are egalitarian analogues of SNTV, the k-Borda rule, the Chamberlin--Courant rule, the Bloc rule, and the Pessimist rule. We establish their computational complexity, provide their initial axiomatic study, and perform experiments to represent the action of these rules graphically.

AIJ Journal 2018 Journal Article

Fixing balanced knockout and double elimination tournaments

  • Haris Aziz
  • Serge Gaspers
  • Simon Mackenzie
  • Nicholas Mattei
  • Paul Stursberg
  • Toby Walsh

Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decision-making. We consider the computational problem of finding the optimal draw for a particular player in such a tournament. The problem has generated considerable research within AI in recent years. We prove that checking whether there exists a draw in which a player wins is NP-complete, thereby settling an outstanding open problem. Our main result has a number of interesting implications on related counting and approximation problems. We present a memoization-based algorithm for the problem that is faster than previous approaches. Moreover, we highlight two natural cases that can be solved in polynomial time. All of our results also hold for the more general problem of counting the number of draws in which a given player is the winner. Finally, we show that our main NP-completeness result extends to a variant of balanced knockout tournaments called double-elimination tournaments.

AAAI Conference 2018 Conference Paper

Knowledge, Fairness, and Social Constraints

  • Haris Aziz
  • Sylvain Bouveret
  • Ioannis Caragiannis
  • Ira Giagkousi
  • Jérôme Lang

In the context of fair allocation of indivisible items, fairness concepts often compare the satisfaction of an agent to the satisfaction she would have from items that are not allocated to her: in particular, envy-freeness requires that no agent prefers the share of someone else to her own share. We argue that these notions could also be defined relative to the knowledge that an agent has on how the items that she does not receive are distributed among other agents. We define a family of epistemic notions of envy-freeness, parameterized by a social graph, where an agent observes the share of her neighbours but not of her non-neighbours. We also define an intermediate notion between envy-freeness and proportionality, also parameterized by a social graph. These weaker notions of envy-freeness are useful when seeking a fair allocation, since envy-freeness is often too strong. We position these notions with respect to known ones, thus revealing new rich hierarchies of fairness concepts. Finally, we present a very general framework that covers all the existing and many new fairness concepts.

AAAI Conference 2018 Conference Paper

On the Complexity of Extended and Proportional Justified Representation

  • Haris Aziz
  • Edith Elkind
  • Shenwei Huang
  • Martin Lackner
  • Luis Sanchez-Fernandez
  • Piotr Skowron

We consider the problem of selecting a fixed-size committee based on approval ballots. It is desirable to have a committee in which all voters are fairly represented. Aziz et al. (2015a; 2017) proposed an axiom called extended justified representation (EJR), which aims to capture this intuition; subsequently, Sánchez-Fernández et al. (2017) proposed a weaker variant of this axiom called proportional justified representation (PJR). It was shown that it is coNP-complete to check whether a given committee provides EJR, and it was conjectured that it is hard to find a committee that provides EJR. In contrast, there are polynomial-time computable voting rules that output committees providing PJR, but the complexity of checking whether a given committee provides PJR was an open problem. In this paper, we answer open questions from prior work by showing that EJR and PJR have the same worst-case complexity: we provide two polynomial-time algorithms that output committees providing EJR, yet we show that it is coNP-complete to decide whether a given committee provides PJR. We complement the latter result by fixedparameter tractability results.

AAMAS Conference 2018 Conference Paper

Proportionally Representative Participatory Budgeting: Axioms and Algorithms

  • Haris Aziz
  • Barton E. Lee
  • Nimrod Talmon

Participatory budgeting is one of the exciting developments in deliberative grassroots democracy. We concentrate on approval elections and propose proportional representation axioms in participatory budgeting, by generalizing relevant axioms for approvalbased multi-winner elections. We observe a rich landscape with respect to the computational complexity of identifying proportional budgets and computing such, and present budgeting methods that satisfy these axioms by identifying budgets that are representative to the demands of vast segments of the voters.

AAAI Conference 2018 Conference Paper

Rank Maximal Equal Contribution: A Probabilistic Social Choice Function

  • Haris Aziz
  • Pang Luo
  • Christine Rizkallah

When aggregating preferences of agents via voting, two desirable goals are to incentivize agents to participate in the voting process and then identify outcomes that are Pareto efficient. We consider participation as formalized by Brandl, Brandt, and Hofbauer (2015) based on the stochastic dominance (SD) relation. We formulate a new rule called RMEC (Rank Maximal Equal Contribution) that is polynomial-time computable, ex post efficient and satisfies the strongest notion of participation. It also satisfies many other desirable fairness properties. The rule suggests a general approach to achieving very strong participation, ex post efficiency and fairness.

AAMAS Conference 2018 Conference Paper

Stability and Pareto Optimality in Refugee Allocation Matchings

  • Haris Aziz
  • Jiayin Chen
  • Serge Gaspers
  • Zhaohong Sun

We focus on the refugee matching problem—a general “two-sided matching under preferences” model with multi-dimensional feasibility constraints. We propose a taxonomy of stability concepts for the problem; identify relations between them; and show that even for two natural weakenings of the standard stability concept, non-existence and NP-hardness results persist. We then identify several natural weaker stability concepts for which we present a polynomial-time and strategy-proof algorithm that returns a stable matching. We also examine the complexity of computing and testing Pareto optimal matchings.

AAAI Conference 2017 Conference Paper

Algorithms for Max-Min Share Fair Allocation of Indivisible Chores

  • Haris Aziz
  • Gerhard Rauchecker
  • Guido Schryen
  • Toby Walsh

We consider Max-min Share (MmS) fair allocations of indivisible chores (items with negative utilities). We show that allocation of chores and classical allocation of goods (items with positive utilities) have some fundamental connections but also differences which prevent a straightforward application of algorithms for goods in the chores setting and viceversa. We prove that an MmS allocation does not need to exist for chores and computing an MmS allocation - if it exists - is strongly NP-hard. In view of these non-existence and complexity results, we present a polynomial-time 2approximation algorithm for MmS fairness for chores. We then introduce a new fairness concept called optimal MmS that represents the best possible allocation in terms of MmS that is guaranteed to exist. We use connections to parallel machine scheduling to give (1) a polynomial-time approximation scheme for computing an optimal MmS allocation when the number of agents is fixed and (2) an effective and efficient heuristic with an ex-post worst-case analysis.

AAMAS Conference 2017 Conference Paper

Coalitional Exchange Stable Matchings in Marriage and Roommate Markets

  • Haris Aziz
  • Adrian Goldwaser

We consider the stable roommates problem with respect to the stability based on exchange of agents. We present three natural variants of coalitional exchange stability and identify the relations between them. We also present a number of impossibility results. In particular, we show that even a (standard) exchange stable matching may not exist for dichotomous preferences. We prove that exchange stability has a fundamental incompatibility with weak Pareto optimality. We also prove that an exchange stable matching mechanism cannot be strategyproof.

AAAI Conference 2017 Conference Paper

Complexity of Manipulating Sequential Allocation

  • Haris Aziz
  • Sylvain Bouveret
  • JŽr™me Lang
  • Simon Mackenzie

Sequential allocation is a simple allocation mechanism in which agents are given pre-specified turns in which they take one item among those that are still available. It has long been known that sequential allocation is not strategyproof. This raises the question of the complexity of computing a preference report that yields a higher utility than the truthful preference. We show that the problem is NP-complete for one manipulating agent with additive utilities and several nonmanipulating agents. In doing so, we correct a wrong claim made in a previous paper. We then give two additional results. First, we present a polynomial-time algorithm for optimal manipulation when the manipulator has additive binary utilities. Second, we consider a stronger notion of manipulation whereby the untruthful outcome yields more utility than the truthful outcome for all utilities consistent with the ordinal preferences; for this notion, we show that a manipulation, if any, can be computed in polynomial time.

IJCAI Conference 2017 Conference Paper

Fair Allocation based on Diminishing Differences

  • Erel Segal-Halevi
  • Haris Aziz
  • Avinatan Hassidim

Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice (NY, Boston), Course allocations, and the Israeli medical lottery. In some cases (such as the latter two), several ``items'' are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where a X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities.

IJCAI Conference 2017 Conference Paper

Pareto Optimal Allocation under Uncertain Preferences

  • Haris Aziz
  • Ronald de Haan
  • Baharak Rastegari

The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider this problem with the additional feature that agents' preferences involve uncertainty. The setting with uncertainty leads to a number of interesting questions including the following ones. How to compute an assignment with the highest probability of being Pareto optimal? What is the complexity of computing the probability that a given assignment is Pareto optimal? Does there exist an assignment that is Pareto optimal with probability one? We consider these problems under two natural uncertainty models: (1) the lottery model in which each agent has an independent probability distribution over linear orders and (2) the joint probability model that involves a joint probability distribution over preference profiles. For both of these models, we present a number of algorithmic and complexity results highlighting the difference and similarities in the complexity of the two models.

AAMAS Conference 2017 Conference Paper

Pareto Optimal Allocation under Uncertain Preferences

  • Haris Aziz
  • Ronald de Haan
  • Baharak Rastegari

The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider this problem with the additional feature that agents’ preferences involve uncertainty. The setting with uncertainty leads to a number of interesting questions including the following ones. How to compute an assignment with the highest probability of being Pareto optimal? What is the complexity of computing the probability that a given assignment is Pareto optimal? Does there exist an assignment that is Pareto optimal with probability one? We consider these problems under two natural uncertainty models: (1) the lottery model in which each agent has an independent probability distribution over linear orders and (2) the joint probability model that involves a joint probability distribution over preference profiles. For both of these models, we present a number of algorithmic and complexity results highlighting the differences and similarities in the complexity of the two models.

AAMAS Conference 2017 Conference Paper

Stable Matching with Uncertain Pairwise Preferences

  • Haris Aziz
  • Pé ter Biró
  • Tamá s Fleiner
  • Serge Gaspers
  • Ronald de Haan
  • Nicholas Mattei
  • Baharak Rastegari

We study a two-sided matching problem where the agents have independent pairwise preferences on their possible partners and these preferences may be uncertain. In this case, the certainly preferred part of an agent’s preferences may admit a cycle and there may not even exist a matching that is stable with non-zero probability. We focus on the computational problems of checking the existence of possibly and certainly stable matchings, i. e. , matchings whose probability of being stable is positive or one, respectively. We show that finding a possibly stable matching is NP-hard, even if only one side can have cyclic preferences. On the other hand we show that the problem of finding a certainly stable matching is polynomial-time solvable if only one side can have cyclic preferences and the other side has transitive preferences, but that this problem becomes NP-hard when both sides can have cyclic preferences. The latter complexity result also implies the hardness of finding a kernel in a special class of directed graphs. CCS Concepts •Theory of computation! Design and analysis of algorithms; •Computing methodologies! Multi-agent systems; •Applied computing! Economics;

IJCAI Conference 2017 Conference Paper

The Condorcet Principle for Multiwinner Elections: From Shortlisting to Proportionality

  • Haris Aziz
  • Edith Elkind
  • Piotr Faliszewski
  • Martin Lackner
  • Piotr Skowron

We study two notions of stability in multiwinner elections that are based on the Condorcet criterion. The first notion was introduced by Gehrlein and is majoritarian in spirit. The second one, local stability, is introduced in this paper, and focuses on voter representation. The goal of this paper is to explore these two notions, their implications on restricted domains, and the computational complexity of rules that are consistent with them.

IJCAI Conference 2017 Conference Paper

Weakening Covert Networks by Minimizing Inverse Geodesic Length

  • Haris Aziz
  • Serge Gaspers
  • Kamran Najeebullah

We consider the problem of deleting nodes in a covert network to minimize its performance. The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices. In the MinIGL problem the input is a graph $G$, a budget $k$, and a target IGL $T$, and the question is whether there exists a subset of vertices $X$ with $|X|=k$, such that the IGL of $G-X$ is at most $T$. In network analysis, the IGL is often used to evaluate how well heuristics perform in strengthening or weakening a network. In this paper, we undertake a study of the classical and parameterized complexity of the MinIGL problem. The problem is NP-complete even if $T=0$ and remains both NP-complete and $W[1]$-hard for parameter $k$ on bipartite and on split graphs. On the positive side, we design several multivariate algorithms for the problem. Our main result is an algorithm for MinIGL parameterized by the twin cover number.

JAIR Journal 2016 Journal Article

A Study of Proxies for Shapley Allocations of Transport Costs

  • Haris Aziz
  • Casey Cahan
  • Charles Gretton
  • Philip Kilby
  • Nicholas Mattei
  • Toby Walsh

We survey existing rules of thumb, propose novel methods, and comprehensively evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Cost to serve analysis has applications both strategically and operationally in transportation settings. The problem is formally modeled as the traveling salesperson game (TSG), a cooperative transferable utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The total cost to serve all locations in the TSP is the length of an optimal tour. An allocation divides the total cost among individual locations, thus providing the cost to serve each of them. As one of the most important normative division schemes in cooperative games, the Shapley value gives a principled and fair allocation for a broad variety of games including the TSG. We consider a number of direct and sampling-based procedures for calculating the Shapley value, and prove that approximating the Shapley value of the TSG within a constant factor is NP-hard. Treating the Shapley value as an ideal baseline allocation, we survey six proxies for it that are each relatively easy to compute. Some of these proxies are rules of thumb and some are procedures international delivery companies use(d) as cost allocation methods. We perform an experimental evaluation using synthetic Euclidean games as well as games derived from real-world tours calculated for scenarios involving fast-moving goods; where deliveries are made on a road network every day. We explore several computationally tractable allocation techniques that are good proxies for the Shapley value in problem instances of a size and complexity that is commercially relevant.

IS Journal 2016 Journal Article

AI's 10 to Watch

  • Haris Aziz
  • Elias Bareinboim
  • Yejin Choi
  • Daniel Hsu
  • Shivaram Kalyanakrishnan
  • Reshef Meir
  • Suchi Saria
  • Gerardo I. Simari

IEEE Intelligent Systems once again selected 10 young AI scientists as " AI's 10 to Watch. " This acknowledgment and celebration not only recognizes these young scientists and makes a positive impact in their academic career but also promotes the community and cutting-edge AI research among next-generation AI researchers, the industry, and the general public alike. The contributions are "Collective Decision Making in Multi-Agent Systems, " by Haris Aziz, "From Causal Inference and Data Fusion to an Automated Scientist, " by Elias Bareinboim, "Language, Vision, and Social AI, " by Yejin Choi, "Algorithms for Machine Learning, " by Daniel Hsu, "Learning Agents, " by Shivaram Kalyanakrishnan, "Strategy and Bounded Rationality, " by Reshef Meir, "; A Reasoning Engine for Tailoring Healthcare to the Individual, " by Suchi Saria, "Pushing the Limits of Knowledge Representation and Reasoning, " by Gerardo I. Simari, "Better Group Decision Making, " by Lirong Xia, and "Distributed Constraint Optimization, " by William Yeoh.

KR Conference 2016 Conference Paper

Boolean Hedonic Games

  • Haris Aziz
  • Paul Harrenstein
  • Jérôme Lang
  • Michael Wooldridge

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player’s preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player’s preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.

IJCAI Conference 2016 Conference Paper

Computational Social Choice: Some Current and New Directions

  • Haris Aziz

Computational social choice is an exciting interdisciplinary field at the intersection of computer science and social choice theory. In this article, I discuss some current and new directions in the field. This is an accompanying paper of my IJCAI 2016 Early Career Spotlight invited talk.

IJCAI Conference 2016 Conference Paper

Computing Pareto Optimal Committees

  • Haris Aziz
  • ocirc; me Lang
  • J
  • eacute; r
  • ocirc; me Monnot

Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that each agent specifies a weak order on single alternatives, from which a preference relation over subsets is derived using some preference extension. We consider four prominent extensions (responsive, leximax, best, and worst). For each of them, we consider the corresponding Pareto optimality notion, and we study the complexity of computing and verifying Pareto optimal outcomes. We also consider strategic issues: for three of the set extensions, we present linear-time, Pareto optimal and strategyproof algorithms that work even for weak preferences.

IJCAI Conference 2016 Conference Paper

Control of Fair Division

  • Haris Aziz
  • Ildik
  • oacute; Schlotter
  • Toby Walsh

We initiate the study of control actions in fair division problems where a benevolent or malicious central organizer changes the structure of the fair division problem for self-interest or to benefit one, some or all agents. One motivation for such control is to improve fairness by minimally changing the problem. As a case study, we consider the problem of adding or deleting a small number of items to improve fairness. For two agents, we present polynomial-time algorithms for adding or deleting the minimum number of items to achieve ordinal envy-freeness. For three agents, we show that both problems, as well as the more basic problem of checking whether an envy-free allocation exists, are NP-complete. This closes a problem open for over five years. Our framework leads to a number of interesting directions in the area of fair division.

AAMAS Conference 2016 Conference Paper

Egalitarianism of Random Assignment Mechanisms (Extended Abstract)

  • Haris Aziz
  • Aris Filos-Ratsikas
  • Jiashu Chen
  • Simon Mackenzie
  • Nicholas Mattei

We consider the egalitarian welfare of random assignment mechanisms when agents have unrestricted cardinal utilities over the objects. We define and give bounds on how well different random assignment mechanisms approximate the optimal egalitarian value (OEV) and investigate the effect that different well-known properties like ordinality, envyfreeness, and truthfulness have on the achievable egalitarian value. Finally, we conduct detailed experiments analyzing the tradeoffs between efficiency with envy-freeness or truthfulness using two prominent random assignment mechanisms — random serial dictatorship and the probabilistic serial mechanism — for different classes of utility functions and distributions.

IJCAI Conference 2016 Conference Paper

Interdependent Scheduling Games

  • Andres Abeliuk
  • Haris Aziz
  • Gerardo Berbeglia
  • Serge Gaspers
  • Petr Kalina
  • Nicholas Mattei
  • Dominik Peters
  • Paul Stursberg

We propose a model of interdependent scheduling games in which each player controls a set of services that they schedule independently. A player is free to schedule his own services at any time; however, each of these services only begins to accrue reward for the player when all predecessor services, which may or may not be controlled by the same player, have been activated. This model, where players have interdependent services, is motivated by the problems faced in planning and coordinating large-scale infrastructures, e. g. , restoring electricity and gas to residents after a natural disaster or providing medical care in a crisis when different agencies are responsible for the delivery of staff, equipment, and medicine. We undertake a game-theoretic analysis of this setting and in particular consider the issues of welfare maximization, computing best responses, Nash dynamics, and existence and computation of Nash equilibria.

AAMAS Conference 2016 Conference Paper

Optimal Reallocation Under Additive and Ordinal Preferences

  • Haris Aziz
  • Péter Biró
  • Jérôme Lang
  • Julien Lesca
  • Jérôme Monnot

Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. In the first part of the paper we focus on the setting in which agents express additive cardinal utilities over objects. We present computational hardness results as well as polynomial-time algorithms for testing Pareto optimality under different restrictions such as two utility values or lexicographic utilities. In the second part of the paper we assume that agents express only their (ordinal) preferences over single objects, and that their preferences are additively separable. In this setting, we present characterizations and polynomial-time algorithms for possible and necessary Pareto optimality. General Terms Economics, Theory and Algorithms

AAAI Conference 2016 Conference Paper

Strategyproof Peer Selection: Mechanisms, Analyses, and Experiments

  • Haris Aziz
  • Omer Lev
  • Nicholas Mattei
  • Jeffrey Rosenschein
  • Toby Walsh

We study an important crowdsourcing setting where agents evaluate one another and, based on these evaluations, a subset of agents are selected. This setting is ubiquitous when peer review is used for distributing awards in a team, allocating funding to scientists, and selecting publications for conferences. The fundamental challenge when applying crowdsourcing in these settings is that agents may misreport their reviews of others to increase their chances of being selected. We propose a new strategyproof (impartial) mechanism called Dollar Partition that satisfies desirable axiomatic properties. We then show, using a detailed experiment with parameter values derived from target real world domains, that our mechanism performs better on average, and in the worst case, than other strategyproof mechanisms in the literature.

IJCAI Conference 2015 Conference Paper

Equilibria Under the Probabilistic Serial Rule

  • Haris Aziz
  • Serge Gaspers
  • Simon Mackenzie
  • Nicholas Mattei
  • Nina Narodytska
  • Toby Walsh

The probabilistic serial (PS) rule is a prominent randomized rule for assigning indivisible goods to agents. Although it is well known for its good fairness and welfare properties, it is not strategyproof. In view of this, we address several fundamental questions regarding equilibria under PS. Firstly, we show that Nash deviations under the PS rule can cycle. Despite the possibilities of cycles, we prove that a pure Nash equilibrium is guaranteed to exist under the PS rule. We then show that verifying whether a given profile is a pure Nash equilibrium is coNP-complete, and computing a pure Nash equilibrium is NP-hard. For two agents, we present a linear-time algorithm to compute a pure Nash equilibrium which yields the same assignment as the truthful profile. Finally, we conduct experiments to evaluate the quality of the equilibria that exist under the PS rule, finding that the vast majority of pure Nash equilibria yield social welfare that is at least that of the truthful profile.

AIJ Journal 2015 Journal Article

Fair assignment of indivisible objects under ordinal preferences

  • Haris Aziz
  • Serge Gaspers
  • Simon Mackenzie
  • Toby Walsh

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, polynomial-time algorithms are presented to check whether a fair assignment exists. Our algorithmic results also extend to the case of unequal entitlements of agents. Our NP-hardness result, which holds for several variants of envy-freeness, answers an open question posed by Bouveret, Endriss, and Lang (ECAI 2010). We also propose fairness concepts that always suggest a non-empty set of assignments with meaningful fairness properties. Among these concepts, optimal proportionality and optimal weak proportionality appear to be desirable fairness concepts.

AAAI Conference 2015 Conference Paper

Justified Representation in Approval-Based Committee Voting

  • Haris Aziz
  • Markus Brill
  • Vincent Conitzer
  • Edith Elkind
  • Rupert Freeman
  • Toby Walsh

We consider approval-based committee voting, i. e. , the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. We then check if this axiom is fulfilled by well-known approval-based voting rules. We show that the answer is negative for most of the rules we consider, with notable exceptions of PAV (Proportional Approval Voting), an extreme version of RAV (Reweighted Approval Voting), and, for a restricted preference domain, MAV (Minimax Approval Voting). We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR), and show that PAV satisfies EJR, while other rules do not. We also consider several other questions related to JR and EJR, including the relationship between JR/EJR and unanimity, and the complexity of the associated algorithmic problems.

IJCAI Conference 2015 Conference Paper

Online Fair Division: Analysing a Food Bank Problem

  • Martin Damyanov Aleksandrov
  • Haris Aziz
  • Serge Gaspers
  • Toby Walsh

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 axiomatic properties of these mechanisms such as strategy-proofness and envy freeness. Finally, we perform a competitive analysis and compute the price of anarchy.

IJCAI Conference 2015 Conference Paper

Possible and Necessary Allocations via Sequential Mechanisms

  • Haris Aziz
  • Toby Walsh
  • Lirong Xia

A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or all mechanisms for several commonly used classes of sequential allocation mechanisms. In particular, we consider whether a given agent receives a given item, a set of items, or a subset of items for natural classes of sequential allocation mechanisms: balanced, recursively balanced, balanced alternation, and strict alternation. We present characterizations of the allocations that result respectively from the classes, which extend the well-known characterization by Brams and King [2005] for policies without restrictions. In addition, we examine the computational complexity of possible and necessary allocation problems for these classes.

JAIR Journal 2015 Journal Article

Possible and Necessary Winners of Partial Tournaments

  • Haris Aziz
  • Markus Brill
  • Felix Fischer
  • Paul Harrenstein
  • Jerome Lang
  • Hans Georg Seedig

We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them, possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

IJCAI Conference 2015 Conference Paper

The Adjusted Winner Procedure: Characterizations and Equilibria

  • Haris Aziz
  • Simina Br
  • acirc; nzei
  • Aris Filos-Ratsikas
  • S
  • oslash; ren Kristoffer Stiil Frederiksen

The Adjusted Winner procedure is an important mechanism proposed by Brams and Taylor for fairly allocating goods between two agents. It has been used in practice for divorce settlements and analyzing political disputes. Assuming truthful declaration of the valuations, it computes an allocation that is envy-free, equitable and Pareto optimal. We show that Adjusted Winner admits several elegant characterizations, which further shed light on the outcomes reached with strategic agents. We find that the procedure may not admit pure Nash equilibria in either the discrete or continuous variants, but is guaranteed to have -Nash equilibria for each > 0. Moreover, under informed tiebreaking, exact pure Nash equilibria always exist, are Pareto optimal, and their social welfare is at least 3/4 of the optimal.

IJCAI Conference 2015 Conference Paper

Welfare Maximization in Fractional Hedonic Games

  • Haris Aziz
  • Serge Gaspers
  • Joachim Gudmundsson
  • Julian Mestre
  • Hanjo Taubig

We consider the computational complexity of computing welfare maximizing partitions for fractional hedonic games—a natural class of coalition formation games that can be succinctly represented by a graph. For such games, welfare maximizing partitions constitute desirable ways to cluster the vertices of the graph. We present both intractability results and approximation algorithms for computing welfare maximizing partitions.

AAAI Conference 2014 Conference Paper

A Generalization of Probabilistic Serial to Randomized Social Choice

  • Haris Aziz
  • Paul Stursberg

The probabilistic serial rule is one of the most wellestablished and desirable rules for the random assignment problem. We present the egalitarian simultaneous reservation social decision scheme — an extension of probabilistic serial to the more general setting of randomized social choice. We consider various desirable fairness, efficiency, and strategic properties of social decision schemes and show that egalitarian simultaneous reservation compares favorably against existing rules. Finally, we define a more general class of social decision schemes called simultaneous reservation, that contains egalitarian simultaneous reservation as well as the serial dictatorship rules. We show that outcomes of simultaneous reservation characterize efficiency with respect to a natural refinement of stochastic dominance.

AAAI Conference 2014 Conference Paper

Fixing a Balanced Knockout Tournament

  • Haris Aziz
  • Serge Gaspers
  • Simon Mackenzie
  • Nicholas Mattei
  • Paul Stursberg
  • Toby Walsh

Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decision-making. We consider the computational problem of finding the optimal draw for a particular player in such a tournament. The problem has generated considerable research within AI in recent years. We prove that checking whether there exists a draw in which a player wins is NP-complete, thereby settling an outstanding open problem. Our main result has a number of interesting implications on related counting and approximation problems. We present a memoization-based algorithm for the problem that is faster than previous approaches. Moreover, we highlight two natural cases that can be solved in polynomial time. All of our results also hold for the more general problem of counting the number of draws in which a given player is the winner.

AAAI Conference 2014 Conference Paper

On the Incompatibility of Efficiency and Strategyproofness in Randomized Social Choice

  • Haris Aziz
  • Florian Brandl
  • Felix Brandt

Efficiency—no agent can be made better off without making another one worse off—and strategyproofness—no agent can obtain a more preferred outcome by misrepresenting his preferences—are two cornerstones of economics and ubiquitous in important areas such as voting, auctions, or matching markets. Within the context of random assignment, Bogomolnaia and Moulin have shown that two particular notions of efficiency and strategyproofness based on stochastic dominance are incompatible. However, there are various other possibilities of lifting preferences over alternatives to preferences over lotteries apart from stochastic dominance. In this paper, we give an overview of common preference extensions, propose two new ones, and show that the abovementioned incompatibility can be extended to various other notions of strategyproofness and efficiency in randomized social choice.

AIJ Journal 2013 Journal Article

Computing desirable partitions in additively separable hedonic games

  • Haris Aziz
  • Felix Brandt
  • Hans Georg Seedig

An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. Additively separable hedonic games are a fundamental class of coalition formation games in which each player has a value for any other player and the value of a coalition to a particular player is simply the sum of the values he assigns to the members of his coalition. In this paper, we consider a number of solution concepts from cooperative game theory, welfare theory, and social choice theory as criteria for desirable partitions in hedonic games. We then conduct a detailed computational analysis of computing, checking the existence of, and verifying stable, fair, optimal, and popular partitions for additively separable hedonic games.

IJCAI Conference 2013 Conference Paper

Maximal Recursive Rule: A New Social Decision Scheme

  • Haris Aziz

In social choice settings with strict preferences, random dictatorship rules were characterized by Gibbard [1977] as the only randomized social choice functions that satisfy strategyproofness and ex post efficiency. In the more general domain with indifferences, RSD (random serial dictatorship) rules are the well-known and perhaps only known generalization of random dictatorship. We present a new generalization of random dictatorship for indifferences called Maximal Recursive (MR) rule as an alternative to RSD. We show that MR is polynomial-time computable, weakly strategyproof with respect to stochastic dominance, and, in some respects, outperforms RSD on efficiency.

AAAI Conference 2013 Conference Paper

Ties Matter: Complexity of Manipulation when Tie-Breaking with a Random Vote

  • Haris Aziz
  • Serge Gaspers
  • Nicholas Mattei
  • Nina Narodytska
  • Toby Walsh

We study the impact on strategic voting of tie-breaking by means of considering the order of tied candidates within a random vote. We compare this to another non-deterministic tie-breaking rule where we simply choose candidate uniformly at random. In general, we demonstrate that there is no connection between the computational complexity of computing a manipulating vote with the two different types of tie-breaking. However, we prove that for some scoring rules, the computational complexity of computing a manipulation can increase from polynomial to NP-hard. We also discuss the relationship with the computational complexity of computing a manipulating vote when we ask for a candidate to be the unique winner, or to be among the set of co-winners.

AAMAS Conference 2012 Conference Paper

Existence of Stability in Hedonic Coalition Formation Games

  • Haris Aziz
  • Florian Brandl

In this paper, we examine \emph{hedonic coalition formation games} in which each player's preferences over partitions of players depend only on the members of his coalition. We present three main results in which restrictions on the preferences of the players guarantee the existence of stable partitions for various notions of stability. The preference restrictions pertain to \emph{top responsiveness} and \emph{bottom responsiveness} which model optimistic and pessimistic behavior of players respectively. The existence results apply to natural subclasses of \emph{additively separable hedonic games} and \emph{hedonic games with $B$-preferences}. It is also shown that our existence results cannot be strengthened to the case of stronger known stability concepts.

AAAI Conference 2012 Conference Paper

Housing Markets with Indifferences: A Tale of Two Mechanisms

  • Haris Aziz
  • Bart de Keijzer

The (Shapley-Scarf) housing market is a well-studied and fundamental model of an exchange economy. Each agent owns a single house and the goal is to reallocate the houses to the agents in a mutually beneficial and stable manner. Recently, Alcalde-Unzu and Molis (2011) and Jaramillo and Manjunath (2011) independently examined housing markets in which agents can express indifferences among houses. They proposed two important families of mechanisms, known as TTAS and TCR respectively. We formulate a family of mechanisms which not only includes TTAS and TCR but also satisfies many desirable properties of both families. As a corollary, we show that TCR is strict core selecting (if the strict core is non-empty). Finally, we settle an open question regarding the computational complexity of the TTAS mechanism. Our study also raises a number of interesting research questions.

AAMAS Conference 2012 Conference Paper

Individual-based Stability in Hedonic Games depending on the Best or Worst Players

  • Haris Aziz
  • Paul Harrenstein
  • Evangelia Pyrga

We consider classes of hedonic games in which each player’s preferences over coalition structures are induced by the best player (B- and B-hedonic games) or the worst player (Wand W-hedonic games) in his coalition. For these classes, which allow for concise representation, we analyze the computational complexity of deciding the existence of and computing individually stable, Nash stable, and individually rational and contractually individually stable coalition partitions. We identify a key source of intractability in compact coalition formation games in which preferences over players are extended to preferences over coalitions.

AAMAS Conference 2012 Conference Paper

Possible and Necessary Winners of Partial Tournaments

  • Haris Aziz
  • Markus Brill
  • Felix Fischer
  • Paul Harrenstein
  • J
  • eacute; r
  • ocirc; me Lang
  • Hans Georg Seedig

We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

AAMAS Conference 2011 Conference Paper

Complexity of Coalition Structure Generation

  • Haris Aziz
  • Bart de Keijzer

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm to solve the problem for all monotonic coalitional games provided that player types are known and the number of player types is bounded by a constant. As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number of skills. We also consider well-studied and well-motivated coalitional games defined compactly on combinatorial domains. For these games, we characterize the complexity of computing an optimal coalition structure by presenting polynomial-time algorithms, approximation algorithms, or NP-hardness and inapproximability lower bounds.

IJCAI Conference 2011 Conference Paper

Optimal Partitions in Additively Separable Hedonic Games

  • Haris Aziz
  • Felix Brandt
  • Hans Georg Seedig

We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given partition is Pareto optimal is coNP-complete, even when preferences are symmetric and strict. Moreover, computing a partition with maximum egalitarian or utilitarian social welfare or one which is both Pareto optimal and individually rational is NP-hard. We also prove that checking whether there exists a partition which is both Pareto optimal and envy-free is Σ 2p-complete. Even though an envy-free partition and a Nash stable partition are both guaranteed to exist for symmetric preferences, checking whether there exists a partition which is both envy-free and Nash stable is NP-complete.

AAMAS Conference 2011 Conference Paper

Stable Partitions in Additively Separable Hedonic Games

  • Haris Aziz
  • Felix Brandt
  • Hans Georg Seedig

An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. In this paper, we solve various open problems concerning the computational complexity of stable partitions in additively separable hedonic games. First, we propose a polynomial-time algorithm to compute a contractually individually stable partition. This contrasts with previous results such as the NP-hardness of computing individually stable or Nash stable partitions. Secondly, we prove that checking whether the core or the strict core exists is NP-hard in the strong sense even if the preferences of the players are symmetric. Finally, it is shown that verifying whether a partition consisting of the grand coalition is contractual strict core stable or Pareto optimal is coNP-complete.

AAMAS Conference 2010 Conference Paper

Monotone cooperative games and their threshold versions

  • Haris Aziz
  • Felix Brandt
  • Paul Harrenstein

Cooperative games provide an appropriate framework forfair and stable resource allocation in multiagent systems. This paper focusses on monotone cooperative games, a classwhich comprises a variety of games that have enjoyed specialattention within AI, in particular, skill games, connectivity games, flow games, voting games, and matching games. Given a threshold, each monotone cooperative game naturally corresponds to a simple game. The core of a thresholdversion may be empty, even if that is not the case in themonotonic game itself. For each of the subclasses of monotonic games mentioned above, we conduct a computationalanalysis of problems concerning some relaxations of the coresuch as the least-core and the cost of stability. It is shownthat threshold versions of monotonic games are generallyat least as hard to handle computationally. We also introduce the length of a simple game as the size of the smallestwinning coalition and study its computational complexityin various classes of simple games and its relationship withcomputing core-based solutions. A number of computationalhardness results are contrasted with polynomial time algorithms to compute the length of threshold matching gamesand the cost of stability of matching games, spanning connectivity games, and simple coalitional skill games with aconstant number of skills.

AAMAS Conference 2009 Conference Paper

False Name Manipulations in Weighted Voting Games: Splitting, Merging and Annexation

  • Haris Aziz
  • Mike Paterson

An important aspect of mechanism design in social choice protocols and multiagent systems is to discourage insincere and manipulative behaviour. We examine the computational complexity of false-name manipulation in weighted voting games which are an important class of coalitional voting games. Weighted voting games have received increased interest in the multiagent community due to their compact representation and ability to model coalitional formation scenarios. Bachrach and Elkind in their AAMAS 2008 paper examined divide and conquer false-name manipulation in weighted voting games from the point of view of Shapley-Shubik index. We analyse the corresponding case of the Banzhaf index and check how much the Banzhaf index of a player increases or decreases if it splits up into sub-players. A pseudo-polynomial algorithm to find the optimal split is also provided. Bachrach and Elkind also mentioned manipulation via merging as an open problem. In the paper, we examine the cases where a player annexes other players or merges with them to increase their Banzhaf index or Shapley-Shubik index payoff. We characterize the computational complexity of such manipulations and provide limits to the manipulation. The annexation non-monotonicity paradox is also discovered in the case of the Banzhaf index. The results give insight into coalition formation and manipulation.

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