51 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Chore Cutting: Envy and Truth
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
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Fair Allocation of goods and chores -- Tutorial and Survey of Recent Results
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
We study the problem of allocating divisible resources among 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 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 -MNW for
homogeneous divisible items, has an incentive ratio between
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
Proportional Fairness and Strategic Behaviour in Facility Location Problems
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
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 for additive and
subadditive cancelable valuations, the unbounded incentive ratio for cancelable
valuations, and the incentive ratios of and for
submodular and XOS valuations, respectively. Moreover, the incentive ratio is
unbounded for a variant that provides the -approximate maximum social
welfare guarantee. For the algorithm of Plaut and Roughgarden, the incentive
ratio is either unbounded or with lexicographic tie-breaking and is
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 ,
and thus is larger than by a constant
Egalitarian judgment aggregation
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
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
We consider fair division of a set of indivisible goods among 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 -out-of- MMS allocations (for the
smallest possible ). A series of works led to the state-of-the-art factor
of [HSSH21]. We show that -out-of- MMS allocations always exist. In the multiplicative approximation,
the goal is to show the existence of -MMS allocations (for the largest
possible ) which guarantees each agent at least times her
MMS value. A series of works in the last decade led to the state-of-the-art
factor of [AG23]. We introduce a
general framework of -MMS that guarantees
fraction of agents times their MMS values and the remaining
fraction of agents times their MMS values. The -MMS captures both ordinal and multiplicative approximations as
its special cases. We show that -MMS
allocations always exist. Furthermore, since we can choose the
fraction of agents arbitrarily in our algorithm, this
implies (using ) the existence of a randomized allocation
that gives each agent at least 3/4 times her MMS value (ex-post) and at least
times her MMS value in expectation
(ex-ante)
- …