Pareto Optimal Allocation under Compact Uncertain Preferences

Aziz, Haris; Bíró, Péter; Haan, Ronald de; Rastegari, Baharak

doi:10.1609/aaai.v33i01.33011740

Cited by 5 publications

(16 citation statements)

References 20 publications

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“…By Birkhoff's theorem [22], any bistochastic matrix can be represented as a convex combination of at most quadratic number of permutation matrices. 4 Hence, a ranking preference profile can always be represented as a lottery preference profile. This representation is not necessarily unique; that is, a ranking preference profile may have several or possibly even exponentially many lottery preference profile representation.…”

Section: Ranking Modelmentioning

confidence: 99%

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Pareto optimal allocation under uncertain preferences: uncertainty models, algorithms, and complexity

Aziz

Bíró

Haan

et al. 2019

Artificial Intelligence

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The assignment problem is one of the most well-studied settings in multi-agent resource allocation. Agents express preferences over indivisible items and then the items are allocated based on these preferences. Pareto optimality is regarded as a desirable property for the chosen allocation, requiring that no other allocation exists in which no agent is worse off and at least one agent is better of. We consider the assignment problem with the additional feature that agents' preferences involve uncertainty. The setting with uncertainty leads to a number of interesting questions including the following ones. How to compute an assignment with the highest probability of being Pareto optimal? What is the complexity of computing the probability that a given assignment is Pareto optimal? Does there exist an assignment that is Pareto optimal with probability one? We consider these problems under five natural uncertainty models. For all of the models, we present a number of algorithmic and complexity results highlighting the differences and similarities in the complexity of the models. We also present some general characterization and algorithmic results that apply to large classes of uncertainty models.

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Section: Ranking Modelmentioning

confidence: 99%

“…This paper includes results from two conference papers [8,4]. We are grateful to the anonymous IJCAI and AAAI reviewers for their helpful comments.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Pareto optimal allocation under uncertain preferences: uncertainty models, algorithms, and complexity

Aziz

Bíró

Haan

et al. 2019

Artificial Intelligence

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“…possible linearly ordered preferences. The uncertainty models considered in the paper have further been examined in the context of Pareto optimal assignment of items to agents [4][5][6]. In a subsequent paper, Chen et al [7] consider additional problems related to the joint probability model.…”

Section: Uncertainty Modelsmentioning

confidence: 99%

Stable Matching with Uncertain Linear Preferences

et al. 2019

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We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model-for each agent, there is a probability distribution over linear preferences, (2) compact indifference model-for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model-there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists. We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.

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“…The field of resource allocation problems has been widely studied in recent years. A central class of problems in this field is the class of assignment problems [2,13,1,3,43,7,6,32,28]. In the most general, abstract formulation of an assignment problem (to which we will simply refer as the general assignment problem), an instance consists of a set of n agents and a set of m items.…”

Section: Introductionmentioning

confidence: 99%

“…A verification variant of the general assignment problem includes, in addition, some allocation as part of the input, and the question becomes whether this allocation is "optimal". Different notions of optimality have been considered in the literature, but the one that has received the most attention is pareto optimality (see, e.g., [2,7,6]). Intuitively, an assignment p is called pareto optimal if there is no other assignment q that is at least good as p for all agents and also strictly better than p for at least one agent.…”

Section: Introductionmentioning

confidence: 99%

Verification of Multi-Layered Assignment Problems

Steindl¹,

Zehavi²

2021

Preprint

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The class of assignment problems is a fundamental and wellstudied class in the intersection of Social Choice, Computational Economics and Discrete Allocation. In a general assignment problem, a group of agents expresses preferences over a set of items, and the task is to allocate items to agents in an "optimal" way. A verification variant of this problem includes an allocation as part of the input, and the question becomes whether this allocation is "optimal". In this paper, we generalize the verification variant to the setting where each agent is equipped with multiple incomplete preference lists: Each list (called a layer) is a ranking of items in a possibly different way according to a different criterion.In particular, we introduce three multi-layer verification problems, each corresponds to an optimality notion that weakens the notion of global optimality (that is, pareto optimality in multiple layers) in a different way. Informally, the first notion requires that, for each group of agents whose size is exactly some input parameter k, the agents in the group will not be able to trade their assigned items among themselves and benefit in at least α layers; the second notion is similar, but it concerns all groups of size at most k rather than exactly k; the third notion strengthens these notions by requiring that groups of k agents will not be part of possibly larger groups that benefit in at least α layers. We study the three problems from the perspective of parameterized complexity under several natural parameterizations such as the number of layers, the number of agents, the number of items, the number of allocated items, the maximum length of a preference list, and more. We present an almost comprehensive picture of the parameterized complexity of the problems with respect to these parameters.

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Pareto Optimal Allocation under Compact Uncertain Preferences

Cited by 5 publications

References 20 publications

Pareto optimal allocation under uncertain preferences: uncertainty models, algorithms, and complexity

Pareto optimal allocation under uncertain preferences: uncertainty models, algorithms, and complexity

Stable Matching with Uncertain Linear Preferences

Verification of Multi-Layered Assignment Problems

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