5,114 research outputs found
For One and All: Individual and Group Fairness in the Allocation of Indivisible Goods
Fair allocation of indivisible goods is a well-explored problem.
Traditionally, research focused on individual fairness - are individual agents
satisfied with their allotted share? - and group fairness - are groups of
agents treated fairly? In this paper, we explore the coexistence of individual
envy-freeness (i-EF) and its group counterpart, group weighted envy-freeness
(g-WEF), in the allocation of indivisible goods. We propose several
polynomial-time algorithms that provably achieve i-EF and g-WEF simultaneously
in various degrees of approximation under three different conditions on the
agents' (i) when agents have identical additive valuation functions, i-EFX and
i-WEF1 can be achieved simultaneously; (ii) when agents within a group share a
common valuation function, an allocation satisfying both i-EF1 and g-WEF1
exists; and (iii) when agents' valuations for goods within a group differ, we
show that while maintaining i-EF1, we can achieve a 1/3-approximation to
ex-ante g-WEF1. Our results thus provide a first step towards connecting
individual and group fairness in the allocation of indivisible goods, in hopes
of its useful application to domains requiring the reconciliation of diversity
with individual demands.Comment: Appears in the 22nd International Conference on Autonomous Agents and
Multiagent Systems (AAMAS), 202
Almost Group Envy-free Allocation of Indivisible Goods and Chores
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
Democratic Fair Allocation of Indivisible Goods
We study the problem of fairly allocating indivisible goods to groups of
agents. Agents in the same group share the same set of goods even though they
may have different preferences. Previous work has focused on unanimous
fairness, in which all agents in each group must agree that their group's share
is fair. Under this strict requirement, fair allocations exist only for small
groups. We introduce the concept of democratic fairness, which aims to satisfy
a certain fraction of the agents in each group. This concept is better suited
to large groups such as cities or countries. We present protocols for
democratic fair allocation among two or more arbitrarily large groups of agents
with monotonic, additive, or binary valuations. For two groups with arbitrary
monotonic valuations, we give an efficient protocol that guarantees
envy-freeness up to one good for at least of the agents in each group,
and prove that the fraction is optimal. We also present other protocols
that make weaker fairness guarantees to more agents in each group, or to more
groups. Our protocols combine techniques from different fields, including
combinatorial game theory, cake cutting, and voting.Comment: Appears in the 27th International Joint Conference on Artificial
Intelligence and the 23rd European Conference on Artificial Intelligence
(IJCAI-ECAI), 201
Groupwise Maximin Fair Allocation of Indivisible Goods
We study the problem of allocating indivisible goods among n agents in a fair
manner. For this problem, maximin share (MMS) is a well-studied solution
concept which provides a fairness threshold. Specifically, maximin share is
defined as the minimum utility that an agent can guarantee for herself when
asked to partition the set of goods into n bundles such that the remaining
(n-1) agents pick their bundles adversarially. An allocation is deemed to be
fair if every agent gets a bundle whose valuation is at least her maximin
share.
Even though maximin shares provide a natural benchmark for fairness, it has
its own drawbacks and, in particular, it is not sufficient to rule out
unsatisfactory allocations. Motivated by these considerations, in this work we
define a stronger notion of fairness, called groupwise maximin share guarantee
(GMMS). In GMMS, we require that the maximin share guarantee is achieved not
just with respect to the grand bundle, but also among all the subgroups of
agents. Hence, this solution concept strengthens MMS and provides an ex-post
fairness guarantee. We show that in specific settings, GMMS allocations always
exist. We also establish the existence of approximate GMMS allocations under
additive valuations, and develop a polynomial-time algorithm to find such
allocations. Moreover, we establish a scale of fairness wherein we show that
GMMS implies approximate envy freeness.
Finally, we empirically demonstrate the existence of GMMS allocations in a
large set of randomly generated instances. For the same set of instances, we
additionally show that our algorithm achieves an approximation factor better
than the established, worst-case bound.Comment: 19 page
Approximate Maximin Shares for Groups of Agents
We investigate the problem of fairly allocating indivisible goods among
interested agents using the concept of maximin share. Procaccia and Wang showed
that while an allocation that gives every agent at least her maximin share does
not necessarily exist, one that gives every agent at least of her share
always does. In this paper, we consider the more general setting where we
allocate the goods to groups of agents. The agents in each group share the same
set of goods even though they may have conflicting preferences. For two groups,
we characterize the cardinality of the groups for which a constant factor
approximation of the maximin share is possible regardless of the number of
goods. We also show settings where an approximation is possible or impossible
when there are several groups.Comment: To appear in the 10th International Symposium on Algorithmic Game
Theory (SAGT), 201
Asymptotic Existence of Proportionally Fair Allocations
Fair division has long been an important problem in the economics literature.
In this note, we consider the existence of proportionally fair allocations of
indivisible goods, i.e., allocations of indivisible goods in which every agent
gets at least her proportionally fair share according to her own utility
function. We show that when utilities are additive and utilities for individual
goods are drawn independently at random from a distribution, proportionally
fair allocations exist with high probability if the number of goods is a
multiple of the number of agents or if the number of goods grows asymptotically
faster than the number of agents
- …