Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to attain but is generally viewed as less fair.  This paper presents a general reduction scheme that, given a utilitarian solver, produces a distribution over outcomes that is leximin in expectation. 
Importantly, the scheme is robust in the sense that, given an approximate utilitarian solver, it produces an outcome that is approximately-leximin (in expectation) - with the same approximation factor.  We apply our scheme to several social choice problems: stochastic allocations of indivisible goods, giveaway lotteries, and fair lotteries for participatory budgeting.

Reducing Leximin Fairness to Utilitarian Optimization


We study the problem of fairly allocating a set of $m$ indivisible chores (i.e. items with non-positive value) to $n$ agents. We consider the desirable fairness notion of $1$-out-of-$d$ maximin share (MMS)---the minimum value that an agent can guarantee by partitioning items into $d$ bundles and selecting the least valued bundle---and focus on ordinal approximation of MMS that aims at finding the largest $d$ for which $1$-out-of-$d$ MMS exists. Our main theoretical contribution is showing the existence of $1$-out-of-$\lfloor\frac{3n}{4}\rfloor$ MMS allocations and proving that $1$-out-of-$\lfloor\frac{2n}{3}\rfloor$ MMS allocations of chores can be computed in polynomial time. Furthermore, we show that practical polynomial-time algorithms exist for approximating $1$-out-of-$\lfloor\frac{3n}{4}\rfloor$ MMS bound for chores. This is in contrast to computing allocations that guarantee a fraction of MMS to each agent, where only a polynomial-time approximation scheme (PTAS) with run-time exponential in the approximation accuracy $1/\epsilon$ is known.

Ordinal Maximin Share Approximation for Chores

We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smaller-weight or larger-weight agents should be given a higher priority. We show that each notion in these families can always be satisfied, but any two cannot necessarily be fulfilled simultaneously. We then introduce an intuitive weighted generalization of maximin share fairness and establish the optimal approximation of it that can be guaranteed. Furthermore, we characterize the implication relations between the various weighted fairness notions introduced in this and prior work, and relate them to the lower and upper quota axioms from apportionment.

Weighted Fairness Notions for Indivisible Items Revisited

We present an ascending-price mechanism for a multi-sided market with a variety of participants, such as manufacturers, logistics agents, insurance providers, and assemblers. Each deal in the market may consist of a combination of agents from separate categories, and different such combinations are simultaneously allowed. This flexibility lets multiple intersecting markets be resolved as a single global market. Our mechanism is obviously-truthful, strongly budget-balanced, individually rational, and attains almost the optimal gain-from-trade when the market is sufficiently large.

A Global Multi-Sided Market with Ascending-Price Mechanism

We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for example, constraints arising from social distancing guidelines. While it is sometimes impossible to allocate a proportional share to every agent under the separation requirement, we show that the well-known criterion of maximin share fairness can always be attained. We then establish several computational properties of maximin share fairness---for instance, the maximin share of an agent cannot be computed exactly by any finite algorithm, but can be approximated with an arbitrarily small error. In addition, we consider the division of a pie (i.e., a circular cake) and show that an ordinal relaxation of maximin share fairness can be achieved.

Mind the Gap: Cake Cutting with Separation

We study fair allocation of indivisible goods among additive agents with feasibility constraints. 
In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles.
Such scenarios have been of great interest to the AI community due to their applicability to real-world problems.
Following some impossibility results, we restrict attention to matroid feasibility constraints that capture natural scenarios, such as the allocation of shifts to medical doctors, and the allocation of conference papers to referees.

We focus on the common fairness notion of envy-freeness up to one good (EF1).
Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints, or allow free disposal of items.
An open problem is the existence of EF1 complete allocations among heterogeneous agents, where the heterogeneity is both in the agents' feasibility constraints and in their valuations.
In this work, we make progress on this problem by providing positive and negative results for different matroid and valuation types.
Among other results, we devise poly-time algorithms for finding EF1 allocations in the following settings: (i) n agents with heterogeneous partition matroids and heterogeneous binary valuations, (ii) 2 agents with heterogeneous partition matroids and heterogeneous valuations, and (iii) at most 3 agents with heterogeneous binary valuations and identical base-orderable matroids.

On Fair Division under Heterogeneous Matroid Constraints

Fair Division 1

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SHORT BIO

Presentations

Reducing Leximin Fairness to Utilitarian Optimization

Ordinal Maximin Share Approximation for Chores

Weighted Fairness Notions for Indivisible Items Revisited

A Global Multi-Sided Market with Ascending-Price Mechanism

A Global Multi-Sided Market with Ascending-Price Mechanism

Mind the Gap: Cake Cutting with Separation

On Fair Division under Heterogeneous Matroid Constraints

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