Favoring Eagerness for Remaining Items: Designing Efficient, Fair, and Strategyproof Mechanisms

In the assignment problem, the goal is to assign indivisible items to agents who have ordinal preferences, efficiently and fairly, in a strategyproof manner. In practice, first-choice maximality, i.e., assigning a maximal number of agents their top items, is often identified as an important efficiency criterion and measure of agents' satisfaction. In this paper, we propose a natural and intuitive efficiency property, favoring-eagerness-for-remaining-items (FERI), which requires that each item is allocated to an agent who ranks it highest among remaining items, thereby implying first-choice maximality. Using FERI as a heuristic, we design mechanisms that satisfy ex-post or ex-ante variants of FERI together with combinations of other desirable properties of efficiency (Pareto-efficiency), fairness (strong equal treatment of equals and sd-weak-envy-freeness), and strategyproofness (sd-weak-strategyproofness). We also explore the limits of FERI mechanisms in providing stronger efficiency, fairness, or strategyproofness guarantees through impossibility results

Fair Division through Information Withholding

Envy-freeness up to one good (EF1) is a well-studied fairness notion for indivisible goods that addresses pairwise envy by the removal of at most one good. In the worst case, each pair of agents might require the (hypothetical) removal of a different good, resulting in a weak aggregate guarantee. We study allocations that are nearly envy-free in aggregate, and define a novel fairness notion based on information withholding. Under this notion, an agent can withhold (or hide) some of the goods in its bundle and reveal the remaining goods to the other agents. We observe that in practice, envy-freeness can be achieved by withholding only a small number of goods overall. We show that finding allocations that withhold an optimal number of goods is computationally hard even for highly restricted classes of valuations. In contrast to the worst-case results, our experiments on synthetic and real-world preference data show that existing algorithms for finding EF1 allocations withhold close-to-optimal number of goods.Comment: Full version of AAAI2020 paper. V2 has reviewers' comments incorporated. V3 consists of updates to Section 7.

Hide, Not Seek: Perceived Fairness in Envy-Free Allocations of Indivisible Goods

Fair division provides a rich computational and mathematical framework for the allocation of indivisible goods, which has given rise to numerous fairness concepts and their relaxations. In recent years, much attention has been given to theoretical and computational aspects of various fairness concepts. Nonetheless, the choice of which fairness concept is in practice perceived to be fairer by individuals is not well understood. We consider two conceptually different relaxations of envy-freeness and investigate how individuals perceive the induced allocations as fair. In particular, we examine a well-studied relaxation of envy-freeness up to one good (EF1) which is based on counterfactual thinking that any pairwise envy can be eliminated by the hypothetical removal of a single good from the envied agent's bundle. In contrast, a recently proposed epistemic notion, namely envy-freeness up to $k$ hidden goods (HEF-$k$), provides a relaxation by hiding information about a small subset of $k$ goods. Through various crowdsourcing experiments, we empirically demonstrate that allocations achieved by withholding information are perceived to be fairer compared to two variants of EF1.Comment: 21 pages, 10 figure

Multi-type Resource Allocation with Partial Preferences

We propose multi-type probabilistic serial (MPS) and multi-type random priority (MRP) as extensions of the well known PS and RP mechanisms to the multi-type resource allocation problem (MTRA) with partial preferences. In our setting, there are multiple types of divisible items, and a group of agents who have partial order preferences over bundles consisting of one item of each type. We show that for the unrestricted domain of partial order preferences, no mechanism satisfies both sd-efficiency and sd-envy-freeness. Notwithstanding this impossibility result, our main message is positive: When agents' preferences are represented by acyclic CP-nets, MPS satisfies sd-efficiency, sd-envy-freeness, ordinal fairness, and upper invariance, while MRP satisfies ex-post-efficiency, sd-strategy-proofness, and upper invariance, recovering the properties of PS and RP

Mechanism Design for Multi-Type Housing Markets with Acceptable Bundles

We extend the Top-Trading-Cycles (TTC) mechanism to select strict core allocations for housing markets with multiple types of items, where each agent may be endowed and allocated with multiple items of each type. In doing so, we advance the state of the art in mechanism design for housing markets along two dimensions: First, our setting is more general than multi-type housing markets (Moulin 1995; Sikdar, Adali, and Xia 2017) and the setting of Fujita et al. (2015). Further, we introduce housing markets with acceptable bundles (HMABs) as a more general setting where each agent may have arbitrary sets of acceptable bundles. Second, our extension of TTC is strict core selecting under the weaker restriction on preferences of CMI-trees, which we introduce as a new domain restriction on preferences that generalizes commonly-studied languages in previous works