3,939 research outputs found
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
Fairly Allocating Contiguous Blocks of Indivisible Items
In this paper, we study the classic problem of fairly allocating indivisible
items with the extra feature that the items lie on a line. Our goal is to find
a fair allocation that is contiguous, meaning that the bundle of each agent
forms a contiguous block on the line. While allocations satisfying the
classical fairness notions of proportionality, envy-freeness, and equitability
are not guaranteed to exist even without the contiguity requirement, we show
the existence of contiguous allocations satisfying approximate versions of
these notions that do not degrade as the number of agents or items increases.
We also study the efficiency loss of contiguous allocations due to fairness
constraints.Comment: Appears in the 10th International Symposium on Algorithmic Game
Theory (SAGT), 201
When Do Envy-Free Allocations Exist?
We consider a fair division setting in which indivisible items are to be
allocated among agents, where the agents have additive utilities and the
agents' utilities for individual items are independently sampled from a
distribution. Previous work has shown that an envy-free allocation is likely to
exist when but not when , and left open the
question of determining where the phase transition from non-existence to
existence occurs. We show that, surprisingly, there is in fact no universal
point of transition---instead, the transition is governed by the divisibility
relation between and . On the one hand, if is divisible by , an
envy-free allocation exists with high probability as long as . On the
other hand, if is not "almost" divisible by , an envy-free allocation is
unlikely to exist even when .Comment: Appears in the 33rd AAAI Conference on Artificial Intelligence
(AAAI), 201
Ordering Pareto-Optima Through Majority Voting
A commodity is shared between some individuals; some selection procedure is used to choose allocations. In order to reflect that laws and rules rather than allocations are implemented and that they involve an element of randomness because of incomplete information, selection procedures are taken to be probability measures over the set of allocations. Illustrations and interpretations of the selection procedures are given.Pareto-optimal allocations; infra-majority voting
Advancing Subgroup Fairness via Sleeping Experts
We study methods for improving fairness to subgroups in settings with overlapping populations and sequential predictions. Classical notions of fairness focus on the balance of some property across different populations. However, in many applications the goal of the different groups is not to be predicted equally but rather to be predicted well. We demonstrate that the task of satisfying this guarantee for multiple overlapping groups is not straightforward and show that for the simple objective of unweighted average of false negative and false positive rate, satisfying this for overlapping populations can be statistically impossible even when we are provided predictors that perform well separately on each subgroup. On the positive side, we show that when individuals are equally important to the different groups they belong to, this goal is achievable; to do so, we draw a connection to the sleeping experts literature in online learning. Motivated by the one-sided feedback in natural settings of interest, we extend our results to such a feedback model. We also provide a game-theoretic interpretation of our results, examining the incentives of participants to join the system and to provide the system full information about predictors they may possess. We end with several interesting open problems concerning the strength of guarantees that can be achieved in a computationally efficient manner
Computing an Approximately Optimal Agreeable Set of Items
We study the problem of finding a small subset of items that is
\emph{agreeable} to all agents, meaning that all agents value the subset at
least as much as its complement. Previous work has shown worst-case bounds,
over all instances with a given number of agents and items, on the number of
items that may need to be included in such a subset. Our goal in this paper is
to efficiently compute an agreeable subset whose size approximates the size of
the smallest agreeable subset for a given instance. We consider three
well-known models for representing the preferences of the agents: ordinal
preferences on single items, the value oracle model, and additive utilities. In
each of these models, we establish virtually tight bounds on the approximation
ratio that can be obtained by algorithms running in polynomial time.Comment: A preliminary version appeared in Proceedings of the 26th
International Joint Conference on Artificial Intelligence (IJCAI), 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
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
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