
The notion of envy-freeness is a natural and intuitive fairness requirement in resource allocation. With indivisible goods, such fair allocations are unfortunately not guaranteed to exist. Classical works have avoided this issue by introducing an additional divisible resource, i.e., money, to subsidize envious agents. In this paper, we aim to design a truthful allocation mechanism of indivisible goods to achieve both fairness and efficiency criteria with a limited amount of subsidy. Following the work of Halpern and Shah, our central question is as follows: to what extent do we need to rely on the power of money to accomplish these objectives? We show that, when agents have matroidal valuations, there is a truthful allocation mechanism that achieves envy-freeness and utilitarian optimality by subsidizing each agent with at most 1, the maximum marginal contribution of each item for each agent. The design of the mechanism rests crucially on the underlying matroidal M-convexity of the Lorenz dominating allocations. For superadditive valuations, we show that there is a truthful mechanism that achieves envy-freeness and utilitarian optimality, with each agent receiving a subsidy of at most m; furthermore, we show that the amount m is necessary even when agents have additive valuations.

Fair and Truthful Mechanism with Limited Subsidy

In multiwinner approval voting, the goal is to select k-member committees based on voters' approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large cohesive group of voters remains unrepresented. However, the JR axiom may conflict with other desiderata, such as coverage (maximizing the number of voters who approve at least one committee member) or social welfare (maximizing the number of approvals obtained by committee members). In this work, we investigate the impact of imposing the JR axiom (as well as the more demanding EJR axiom) on social welfare and coverage. Our approach is threefold: we derive worst-case bounds on the loss of welfare/coverage that is caused by imposing JR, study the computational complexity of finding 'good' committees that provide JR (obtaining a hardness result, an approximation algorithm, and an exact algorithm for one-dimensional preferences), and examine this setting empirically on several synthetic datasets.

The Price of Justified Representation

We study the allocation of indivisible goods that form an undirected graph and quantify the loss of fairness when we impose a constraint that each agent must receive a connected subgraph. Our focus is on the well-studied fairness notion of maximin share fairness. We introduce the price of connectivity to capture the largest gap between the graph-specific and the unconstrained maximin share, and derive bounds on this quantity which are tight for large classes of graphs in the case of two agents and for paths and stars in the general case. For instance, with two agents we show that for biconnected graphs it is possible to obtain at least 3/4 of the maximin share with connected allocations, while for the remaining graphs the guarantee is at most 1/2. Our work demonstrates several applications of graph-theoretic tools and concepts to fair division problems.

The Price of Connectivity in Fair Division

Oral Session 2B1-1

technical paper

AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

The AAMAS conference series was initiated in 2002 in Bologna, Italy as a joint event comprising the 6th International Conference on Autonomous Agents (AA), the 5th International Conference on Multiagent Systems (ICMAS), and the 9th International Workshop on Agent Theories, Architectures, and Languages (ATAL).

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AAMAS 2022

AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

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The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Ayumi Igarashi

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SHORT BIO

Presentations

Fair and Truthful Mechanism with Limited Subsidy

The Price of Justified Representation

The Price of Connectivity in Fair Division

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