Size versus fairness in the assignment problem

Bogomolnaia, Anna; Moulin, Hervé

doi:10.1016/j.geb.2014.11.006

Cited by 24 publications

(10 citation statements)

References 29 publications

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“…Bogomolnaia and Moulin [9] designed a randomised weakly truthful and envy-free mechanism, called the Probabilistic Serial mechanism (PS), for HA with complete lists. Very recently the same authors considered the same approximation problem as ours but in the context of envy-free rather than truthful mechanisms, and for strict preference lists and unweighted agents [11]. They showed that PS has an approximation ratio of e e−1 , which is tight for any envy-free mechanism.…”

Section: Discussion Of Technical Contributionsmentioning

confidence: 65%

Size Versus Truthfulness in the House Allocation Problem

et al. 2019

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We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomised mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomised mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of e e−1 . The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. By using a characterisation result of Bade, we show that any randomised mechanism that is a symmetrisation of a truthful, non-bossy and Pareto optimal mechanism has an improved lower bound of e e−1 . Since our new mechanism is a symmetrisation of RSDM for strict preferences, it follows that this lower bound is tight. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomised strategy of the administrator who interviews the applicants.

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Section: Discussion Of Technical Contributionsmentioning

confidence: 65%

Size Versus Truthfulness in the House Allocation Problem

et al. 2019

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“…This is, as far as we know, our closest work in the study of the underlying properties of Pareto optimality. Of course, there have been other successful studies on Pareto optimality for specific domains and problems like characterizing fairness, or studying the relationship between monotonic solutions and Pareto optimality [5,12], but their focus of study has not been on the exploration of bottom-up approaches for reaching Pareto optimality.…”

Section: Related Workmentioning

confidence: 99%

Bottom-up approaches to achieve Pareto optimal agreements in group decision making

et al. 2019

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In this article, we introduce a new paradigm to achieve Pareto optimality in group decisionmaking processes: bottom-up approaches to Pareto optimality. It is based on the idea that, while resolving a conflict in a group, individuals may trust some members more than others; thus, they may be willing to cooperate and share more information with those members. Therefore, one can divide the group into subgroups where more cooperative mechanisms can be formed to reach Pareto optimal outcomes. This is the first work that studies such use of a bottom-up approach to achieve Pareto optimality in conflict resolution in groups. First, we prove that an outcome that is Pareto optimal for subgroups is also Pareto optimal for the group as a whole. Then, we empirically analyze the appropriate conditions and achievable performance when applying bottom-up approaches under a wide variety of scenarios based on real-life datasets. The results show that bottom-up approaches are a viable mechanism to achieve Pareto optimality with applications to group decision-making, negotiation teams, and decision making in open environments.

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“…This is, as far as we know, our closest work in the study of the underlying properties of Pareto optimality. Of course, there have been other successful studies on Pareto optimality for specific domains and problems like characterizing fairness, or studying the relationship between monotonic solutions and Pareto optimality [4,9], but their focus of study has not been on the exploration of bottom-up approaches for reaching Pareto optimality.…”

Section: Related Workmentioning

confidence: 99%

Can We Reach Pareto Optimal Outcomes Using Bottom-Up Approaches?

Sánchez-Anguix

Aydoğan

Baarslag

et al. 2017

Conflict Resolution in Decision Making

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Abstract. Traditionally, researchers in decision making have focused on attempting to reach Pareto Optimality using horizontal approaches, where optimality is calculated taking into account every participant at the same time. Sometimes, this may prove to be a difficult task (e.g., conflict, mistrust, no information sharing, etc.). In this paper, we explore the possibility of achieving Pareto Optimal outcomes in a group by using a bottom-up approach: discovering Pareto optimal outcomes by interacting in subgroups. We analytically show that Pareto optimal outcomes in a subgroup are also Pareto optimal in a supergroup of those agents in the case of strict , transitive, and complete preferences. Then, we empirically analyze the prospective usability and practicality of bottom-up approaches in a variety of decision making domains.

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Size versus fairness in the assignment problem

Cited by 24 publications

References 29 publications

Size Versus Truthfulness in the House Allocation Problem

Size Versus Truthfulness in the House Allocation Problem

Bottom-up approaches to achieve Pareto optimal agreements in group decision making

Can We Reach Pareto Optimal Outcomes Using Bottom-Up Approaches?

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