15 research outputs found
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
How to Cut a Cake Fairly: A Generalization to Groups
A fundamental result in cake cutting states that for any number of players
with arbitrary preferences over a cake, there exists a division of the cake
such that every player receives a single contiguous piece and no player is left
envious. We generalize this result by showing that it is possible to partition
the players into groups of any desired sizes and divide the cake among the
groups, so that each group receives a single contiguous piece and no player
finds the piece of another group better than that of the player's own group
Cutting a Cake Fairly for Groups Revisited
Cake cutting is a classic fair division problem, with the cake serving as a
metaphor for a heterogeneous divisible resource. Recently, it was shown that
for any number of players with arbitrary preferences over a cake, it is
possible to partition the players into groups of any desired size and divide
the cake among the groups so that each group receives a single contiguous piece
and every player is envy-free. For two groups, we characterize the group sizes
for which such an assignment can be computed by a finite algorithm, showing
that the task is possible exactly when one of the groups is a singleton. We
also establish an analogous existence result for chore division, and show that
the result does not hold for a mixed cake
Strategyproof Mechanisms For Group-Fair Facility Location Problems
We study the facility location problems where agents are located on a real
line and divided into groups based on criteria such as ethnicity or age. Our
aim is to design mechanisms to locate a facility to approximately minimize the
costs of groups of agents to the facility fairly while eliciting the agents'
locations truthfully. We first explore various well-motivated group fairness
cost objectives for the problems and show that many natural objectives have an
unbounded approximation ratio. We then consider minimizing the maximum total
group cost and minimizing the average group cost objectives. For these
objectives, we show that existing classical mechanisms (e.g., median) and new
group-based mechanisms provide bounded approximation ratios, where the
group-based mechanisms can achieve better ratios. We also provide lower bounds
for both objectives. To measure fairness between groups and within each group,
we study a new notion of intergroup and intragroup fairness (IIF) . We consider
two IIF objectives and provide mechanisms with tight approximation ratios
Online Algorithms for Matchings with Proportional Fairness Constraints and Diversity Constraints
Matching problems with group-fairness constraints and diversity constraints
have numerous applications such as in allocation problems, committee selection,
school choice, etc. Moreover, online matching problems have lots of
applications in ad allocations and other e-commerce problems like product
recommendation in digital marketing.
We study two problems involving assigning {\em items} to {\em platforms},
where items belong to various {\em groups} depending on their attributes; the
set of items are available offline and the platforms arrive online. In the
first problem, we study online matchings with {\em proportional fairness
constraints}. Here, each platform on arrival should either be assigned a set of
items in which the fraction of items from each group is within specified bounds
or be assigned no items; the goal is to assign items to platforms in order to
maximize the number of items assigned to platforms.
In the second problem, we study online matchings with {\em diversity
constraints}, i.e. for each platform, absolute lower bounds are specified for
each group. Each platform on arrival should either be assigned a set of items
that satisfy these bounds or be assigned no items; the goal is to maximize the
set of platforms that get matched. We study approximation algorithms and
hardness results for these problems. The technical core of our proofs is a new
connection between these problems and the problem of matchings in hypergraphs.
Our experimental evaluation shows the performance of our algorithms on
real-world and synthetic datasets exceeds our theoretical guarantees.Comment: 16 pages, Full version of a paper accepted in ECAI 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