51 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Chore Cutting: Envy and Truth

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    We study the fair division of divisible bad resources with strategic agents who can manipulate their private information to get a better allocation. Within certain constraints, we are particularly interested in whether truthful envy-free mechanisms exist over piecewise-constant valuations. We demonstrate that no deterministic truthful envy-free mechanism can exist in the connected-piece scenario, and the same impossibility result occurs for hungry agents. We also show that no deterministic, truthful dictatorship mechanism can satisfy the envy-free criterion, and the same result remains true for non-wasteful constraints rather than dictatorship. We further address several related problems and directions.Comment: arXiv admin note: text overlap with arXiv:2104.07387 by other author

    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

    The Incentive Guarantees Behind Nash Welfare in Divisible Resources Allocation

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    We study the problem of allocating divisible resources among nn agents, hopefully in a fair and efficient manner. With the presence of strategic agents, additional incentive guarantees are also necessary, and the problem of designing fair and efficient mechanisms becomes much less tractable. While the maximum Nash welfare (MNW) mechanism has been proven to be prominent by providing desirable fairness and efficiency guarantees as well as other intuitive properties, no incentive property is known for it. We show a surprising result that, when agents have piecewise constant value density functions, the incentive ratio of the MNW mechanism is 22 for cake cutting, where the incentive ratio of a mechanism is defined as the ratio between the largest possible utility that an agent can gain by manipulation and his utility in honest behavior. Remarkably, this result holds even without the free disposal assumption, which is hard to get rid of in the design of truthful cake cutting mechanisms. We also show that the MNW mechanism is group strategyproof when agents have piecewise uniform value density functions. Moreover, we show that, for cake cutting, the Partial Allocation (PA) mechanism proposed by Cole et al., which is truthful and 1/e1/e-MNW for homogeneous divisible items, has an incentive ratio between [e1/e,e][e^{1 / e}, e] and when randomization is allowed, can be turned to be truthful in expectation. Given two alternatives for a trade-off between incentive ratio and Nash welfare provided by the MNW and PA mechanisms, we establish an interpolation between them for both cake cutting and homogeneous divisible items. Finally, we study the existence of fair mechanisms with a low incentive ratio in the connected pieces setting. We show that any envy-free cake cutting mechanism with the connected pieces constraint has an incentive ratio of at least Ω(n)\Omega(n)

    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

    Egalitarian judgment aggregation

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    Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation—a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.publishedVersio

    Getting More by Knowing Less: Bayesian Incentive Compatible Mechanisms for Fair Division

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    We study fair resource allocation with strategic agents. It is well-known that, across multiple fundamental problems in this domain, truthfulness and fairness are incompatible. For example, when allocating indivisible goods, there is no truthful and deterministic mechanism that guarantees envy-freeness up to one item (EF1), even for two agents with additive valuations. Or, in cake-cutting, no truthful and deterministic mechanism always outputs a proportional allocation, even for two agents with piecewise-constant valuations. Our work stems from the observation that, in the context of fair division, truthfulness is used as a synonym for Dominant Strategy Incentive Compatibility (DSIC), requiring that an agent prefers reporting the truth, no matter what other agents report. In this paper, we instead focus on Bayesian Incentive Compatible (BIC) mechanisms, requiring that agents are better off reporting the truth in expectation over other agents' reports. We prove that, when agents know a bit less about each other, a lot more is possible: using BIC mechanisms we can overcome the aforementioned barriers that DSIC mechanisms face in both the fundamental problems of allocation of indivisible goods and cake-cutting. We prove that this is the case even for an arbitrary number of agents, as long as the agents' priors about each others' types satisfy a neutrality condition. En route to our results on BIC mechanisms, we also strengthen the state of the art in terms of negative results for DSIC mechanisms.Comment: 26 page

    Improving Approximation Guarantees for Maximin Share

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    We consider fair division of a set of indivisible goods among nn agents with additive valuations using the desirable fairness notion of maximin share (MMS). MMS is the most popular share-based notion, in which an agent finds an allocation fair to her if she receives goods worth at least her MMS value. An allocation is called MMS if all agents receive their MMS values. However, since MMS allocations do not always exist, the focus shifted to investigating its ordinal and multiplicative approximations. In the ordinal approximation, the goal is to show the existence of 11-out-of-dd MMS allocations (for the smallest possible d>nd>n). A series of works led to the state-of-the-art factor of d=⌊3n/2⌋d=\lfloor 3n/2 \rfloor [HSSH21]. We show that 11-out-of-⌈4n/3⌉\lceil 4n/3\rceil MMS allocations always exist. In the multiplicative approximation, the goal is to show the existence of α\alpha-MMS allocations (for the largest possible α<1\alpha < 1) which guarantees each agent at least α\alpha times her MMS value. A series of works in the last decade led to the state-of-the-art factor of α=34+33836\alpha = \frac{3}{4} + \frac{3}{3836} [AG23]. We introduce a general framework of (α,β,γ)(\alpha, \beta, \gamma)-MMS that guarantees α\alpha fraction of agents β\beta times their MMS values and the remaining (1−α)(1-\alpha) fraction of agents γ\gamma times their MMS values. The (α,β,γ)(\alpha, \beta, \gamma)-MMS captures both ordinal and multiplicative approximations as its special cases. We show that (2(1−β)/β,β,3/4)(2(1 -\beta)/\beta, \beta, 3/4)-MMS allocations always exist. Furthermore, since we can choose the 2(1−β)/β2(1-\beta)/\beta fraction of agents arbitrarily in our algorithm, this implies (using β=3/2\beta=\sqrt{3}/2) the existence of a randomized allocation that gives each agent at least 3/4 times her MMS value (ex-post) and at least (173−24)/43>0.785(17\sqrt{3} - 24)/4\sqrt{3} > 0.785 times her MMS value in expectation (ex-ante)
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