10,203 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
Equivalence of Resource/Opportunity Egalitarianism and Welfare Egalitarianism in Quasilinear Domains
We study the allocation of indivisible goods when monetary transfers are possible and preferences are quasilinear. We show that the only allocation mechanism (upto Pareto-indifference) that satisfies the axioms supporting resource and opportunity egalitarianism is the one that equalizes the welfares. We present alternative characterizations, and budget properties of this mechanism and discuss how it would ensure fair compensation in government requisitions and condemnations.egalitarianism, egalitarian-equivalence, no-envy, distributive justice, allocation of indivisible goods and money, fair auctions, the Groves mechanisms, strategy-proofness, population monotonicity, cost monotonicity, government requisitions, eminent domain
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
Distributed Fair Allocation of Indivisible Goods
International audienceDistributed mechanisms for allocating indivisible goods are mechanisms lacking central control, in which agents can locally agree on deals to exchange some of the goods in their possession. We study convergence properties for such distributed mechanisms when used as fair division procedures. Specifically, we identify sets of assumptions under which any sequence of deals meeting certain conditions will converge to a proportionally fair allocation and to an envy-free allocation, respectively. We also introduce an extension of the basic framework where agents are vertices of a graph representing a social network that constrains which agents can interact with which other agents, and we prove a similar convergence result for envy-freeness in this context. Finally, when not all assumptions guaranteeing envy-freeness are satisfied, we may want to minimise the degree of envy exhibited by an outcome. To this end, we introduce a generic framework for measuring the degree of envy in a society and establish the computational complexity of checking whether a given scenario allows for a deal that is beneficial to every agent involved and that will reduce overall envy
On Approximate Envy-Freeness for Indivisible Chores and Mixed Resources
We study the fair allocation of undesirable indivisible items, or chores. While the case of desirable indivisible items (or goods) is extensively studied, with many results known for different notions of fairness, less is known about the fair division of chores. We study envy-free allocation of chores and make three contributions. First, we show that determining the existence of an envy-free allocation is NP-complete even in the simple case when agents have binary additive valuations. Second, we provide a polynomial-time algorithm for computing an allocation that satisfies envy-freeness up to one chore (EF1), correcting a claim in the existing literature. A modification of our algorithm can be used to compute an EF1 allocation for doubly monotone instances (where each agent can partition the set of items into objective goods and objective chores). Our third result applies to a mixed resources model consisting of indivisible items and a divisible, undesirable heterogeneous resource (i.e., a bad cake). We show that there always exists an allocation that satisfies envy-freeness for mixed resources (EFM) in this setting, complementing a recent result of Bei et al. [Bei et al., 2021] for indivisible goods and divisible cake
Fair allocation of indivisible goods among two agents
One must allocate a finite set of indivisible goods among two agents without monetary compensation. We impose Pareto-efficiency, anonymity, a weak notion of no-envy, a welfare lower bound based on each agent’s ranking of the sets of goods, and a monotonicity property relative to changes in agents’ preferences. We prove that there is a rule satisfying these axioms. If there are three goods, it is the only rule, with one of its subcorrespondences, satisfying each fairness axiom and not discriminating between goods. Further, we confirm the clear gap between these economies and those with more than two agents.indivisible goods, no monetary compensation, no-envy, lower bound, preference-monotonicity
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