312 research outputs found

    Machine Learning-powered Course Allocation

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    We introduce a machine learning-powered course allocation mechanism. Concretely, we extend the state-of-the-art Course Match mechanism with a machine learning-based preference elicitation module. In an iterative, asynchronous manner, this module generates pairwise comparison queries that are tailored to each individual student. Regarding incentives, our machine learning-powered course match (MLCM) mechanism retains the attractive strategyproofness in the large property of Course Match. Regarding welfare, we perform computational experiments using a simulator that was fitted to real-world data. Our results show that, compared to Course Match, MLCM increases average student utility by 4%-9% and minimum student utility by 10%-21%, even with only ten comparison queries. Finally, we highlight the practicability of MLCM and the ease of piloting it for universities currently using Course Match

    The Good, the Bad and the Submodular: Fairly Allocating Mixed Manna Under Order-Neutral Submodular Preferences

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    We study the problem of fairly allocating indivisible goods (positively valued items) and chores (negatively valued items) among agents with decreasing marginal utilities over items. Our focus is on instances where all the agents have simple preferences; specifically, we assume the marginal value of an item can be either −1-1, 00 or some positive integer cc. Under this assumption, we present an efficient algorithm to compute leximin allocations for a broad class of valuation functions we call order-neutral submodular valuations. Order-neutral submodular valuations strictly contain the well-studied class of additive valuations but are a strict subset of the class of submodular valuations. We show that these leximin allocations are Lorenz dominating and approximately proportional. We also show that, under further restriction to additive valuations, these leximin allocations are approximately envy-free and guarantee each agent their maxmin share. We complement this algorithmic result with a lower bound showing that the problem of computing leximin allocations is NP-hard when cc is a rational number

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Fair Allocation of goods and chores -- Tutorial and Survey of Recent Results

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    Fair resource allocation is an important problem in many real-world scenarios, where resources such as goods and chores must be allocated among agents. In this survey, we delve into the intricacies of fair allocation, focusing specifically on the challenges associated with indivisible resources. We define fairness and efficiency within this context and thoroughly survey existential results, algorithms, and approximations that satisfy various fairness criteria, including envyfreeness, proportionality, MMS, and their relaxations. Additionally, we discuss algorithms that achieve fairness and efficiency, such as Pareto Optimality and Utilitarian Welfare. We also study the computational complexity of these algorithms, the likelihood of finding fair allocations, and the price of fairness for each fairness notion. We also cover mixed instances of indivisible and divisible items and investigate different valuation and allocation settings. By summarizing the state-of-the-art research, this survey provides valuable insights into fair resource allocation of indivisible goods and chores, highlighting computational complexities, fairness guarantees, and trade-offs between fairness and efficiency. It serves as a foundation for future advancements in this vital field

    Inherited inequality: a general framework and an application to South Africa

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    Scholars have sought to quantify the extent of inequality which is inherited from past generations in many different ways, including a large body of work on intergenerational mobility and inequality of opportunity. This paper makes three contributions to that broad literature. First, we show that many of the most prominent approaches to measuring mobility or inequality of opportunity fit within a general framework which involves, as a first step, a calculation of the extent to which inherited circumstances can predict current incomes. The importance of prediction has led to recent applications of machine learning tools to solve the model selection challenge in the presence of competing upward and downward biases. Our second contribution is to apply transformation trees to the computation of inequality of opportunity. Because the algorithm is built on a likelihood maximization that involves splitting the sample into groups with the most salient differences between their conditional cumulative distributions, it is particularly well-suited to measuring ex-post inequality of opportunity, following Roemer (1998). Our third contribution is to apply the method to data from South Africa, arguably the world’s most unequal country, and find that almost threequarters of its current inequality is inherited from predetermined circumstances, with race playing the largest role, but parental background also making an important contribution

    Multi-agent Online Scheduling: MMS Allocations for Indivisible Items

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    We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents.Comment: 29 pages, 1 figure (to appear in ICML 2023

    Recall, Robustness, and Lexicographic Evaluation

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    Researchers use recall to evaluate rankings across a variety of retrieval, recommendation, and machine learning tasks. While there is a colloquial interpretation of recall in set-based evaluation, the research community is far from a principled understanding of recall metrics for rankings. The lack of principled understanding of or motivation for recall has resulted in criticism amongst the retrieval community that recall is useful as a measure at all. In this light, we reflect on the measurement of recall in rankings from a formal perspective. Our analysis is composed of three tenets: recall, robustness, and lexicographic evaluation. First, we formally define `recall-orientation' as sensitivity to movement of the bottom-ranked relevant item. Second, we analyze our concept of recall orientation from the perspective of robustness with respect to possible searchers and content providers. Finally, we extend this conceptual and theoretical treatment of recall by developing a practical preference-based evaluation method based on lexicographic comparison. Through extensive empirical analysis across 17 TREC tracks, we establish that our new evaluation method, lexirecall, is correlated with existing recall metrics and exhibits substantially higher discriminative power and stability in the presence of missing labels. Our conceptual, theoretical, and empirical analysis substantially deepens our understanding of recall and motivates its adoption through connections to robustness and fairness.Comment: Under revie

    Proportional Fairness and Strategic Behaviour in Facility Location Problems

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    The one-dimensional facility location problem readily generalizes to many real world problems, including social choice, project funding, and the geographic placement of facilities intended to serve a set of agents. In these problems, each agent has a preferred point along a line or interval, which could denote their ideal preference, preferred project funding, or location. Thus each agent wishes the facility to be as close to their preferred point as possible. We are tasked with designing a mechanism which takes in these preferred points as input, and outputs an ideal location to build the facility along the line or interval domain. In addition to minimizing the distance between the facility and the agents, we may seek a facility placement which is fair for the agents. In particular, this thesis focusses on the notion of proportional fairness, in which endogenous groups of agents with similar or identical preferences have a distance guarantee from the facility that is proportional to the size of the group. We also seek mechanisms that are strategyproof, in that no agent can improve their distance from the facility by lying about their location. We consider both deterministic and randomized mechanisms, in both the classic and obnoxious facility location settings. The obnoxious setting differs from the classic setting in that agents wish to be far from the facility rather than close to it. For these settings, we formalize a hierarchy of proportional fairness axioms, and where possible, characterize strategyproof mechanisms which satisfy these axioms. In the obnoxious setting where this is not possible, we consider the welfare-optimal mechanisms which satisfy these axioms, and quantify the extent at which the system efficiency is compromised by misreporting agents. We also investigate, in the classic setting, the nature of misreporting agents under a family of proportionally fair mechanisms which are not necessarily strategyproof. These results are supplemented with tight approximation ratio and price of fairness bounds which provide further insight into the compromise between proportional fairness and efficiency in the facility location problem. Finally, we prove basic existence results concerning possible extensions to our settings

    Incentive Ratios for Fairly Allocating Indivisible Goods: Simple Mechanisms Prevail

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    We study the problem of fairly allocating indivisible goods among strategic agents. Amanatidis et al. show that truthfulness is incompatible with any meaningful fairness notions. Thus we adopt the notion of incentive ratio, which is defined as the ratio between the largest possible utility that an agent can gain by manipulation and his utility in honest behavior under a given mechanism. We select four of the most fundamental mechanisms in the literature on discrete fair division, which are Round-Robin, a cut-and-choose mechanism of Plaut and Roughgarden, Maximum-Nash-Welfare and Envy-Graph Procedure, and obtain extensive results regarding the incentive ratios of them and their variants. For Round-Robin, we establish the incentive ratio of 22 for additive and subadditive cancelable valuations, the unbounded incentive ratio for cancelable valuations, and the incentive ratios of nn and ⌈m/n⌉\lceil m / n \rceil for submodular and XOS valuations, respectively. Moreover, the incentive ratio is unbounded for a variant that provides the 1/n1/n-approximate maximum social welfare guarantee. For the algorithm of Plaut and Roughgarden, the incentive ratio is either unbounded or 33 with lexicographic tie-breaking and is 22 with welfare maximizing tie-breaking. This separation exhibits the essential role of tie-breaking rules in the design of mechanisms with low incentive ratios. For Maximum-Nash-Welfare, the incentive ratio is unbounded. Furthermore, the unboundedness can be bypassed by restricting agents to have a strictly positive value for each good. For Envy-Graph Procedure, both of the two possible ways of implementation lead to an unbounded incentive ratio. Finally, we complement our results with a proof that the incentive ratio of every mechanism satisfying envy-freeness up to one good is at least 1.0741.074, and thus is larger than 11 by a constant
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