Tradeoffs Between Information and Ordinal Approximation for Bipartite Matching

Anshelevich, Elliot; Zhu, Wennan

doi:10.1007/978-3-319-66700-3_21

Cited by 12 publications

(19 citation statements)

References 18 publications

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“…When candidates are independently drawn from the population of voters, the distortion can be better than 2 [7] and the class of scoring rules that have constant expected distortion has a clean characterization [8]. Lowdistortion algorithms for the maximum bipartite matching problem in metric spaces are proposed in [3]. Social choice and facility location problems in the distortion framework are studied in [4].…”

Section: Related Workmentioning

confidence: 99%

Improved Metric Distortion for Deterministic Social Choice Rules

Munagala

Wang

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter has cost equal to her distance to the winning candidate. Ordinal social choice rules only have access to the ordinal preferences of the voters that are assumed to be consistent with the metric distances. Our goal is to design an ordinal social choice rule with minimum distortion, which is the worst-case ratio, over all consistent metrics, between the social cost of the rule and that of the optimal omniscient rule with knowledge of the underlying metric space.The distortion of the best deterministic social choice rule was known to be between 3 and 5. It had been conjectured that any rule that only looks at the weighted tournament graph on the candidates cannot have distortion better than 5. In our paper, we disprove it by presenting a weighted tournament rule with distortion of 4.236. We design this rule by generalizing the classic notion of uncovered sets, and further show that this class of rules cannot have distortion better than 4.236. We then propose a new voting rule, via an alternative generalization of uncovered sets. We show that if a candidate satisfying the criterion of this voting rule exists, then choosing such a candidate yields a distortion bound of 3, matching the lower bound. We present a combinatorial conjecture that implies distortion of 3, and verify it for small numbers of candidates and voters by computer experiments. Using our framework, we also show that selecting any candidate guarantees distortion of at most 3 when the weighted tournament graph is cyclically symmetric.

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Section: Related Workmentioning

confidence: 99%

Improved Metric Distortion for Deterministic Social Choice Rules

Munagala

Wang

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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“…The distortion of matching in a metric space has received far less attention than social choice questions. [5][6][7] analyzed maximum-weight metric matching; the maximization objective makes this problem far easier, and even choosing a uniformly random matching yields a distortion of a small constant. This is very different from our goal of computing a minimum-cost matching, for which no ordinal approximations better than O(n) are known.…”

Section: Discussion and Related Workmentioning

confidence: 99%

“…These observations have recently led to a large body of work using the utilitarian approach, in which we assume that some latent numerical costs or utilities exist, but we only know the ordinal preferences of the agents, not their underlying numerical costs. See for example [3,4,11,16,21,23,29] for the social choice setting, [1,[5][6][7] for matching and other graph problems, and [13] for facility location. These works focus on measuring the distortion of various algorithms: a measure of how well an algorithm behaves when using only ordinal information, as compared to the optimum algorithm which has access to the true underlying numerical information.…”

Section: Introductionmentioning

confidence: 99%

Ordinal Approximation for Social Choice, Matching, and Facility Location Problems Given Candidate Positions

Anshelevich

Zhu

2018

Web and Internet Economics

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In this work we consider general facility location and social choice problems, in which sets of agents A and facilities F are located in a metric space, and our goal is to assign agents to facilities (as well as choose which facilities to open) in order to optimize the social cost. We form new algorithms to do this in the presence of only ordinal information, i.e., when the true costs or distances from the agents to the facilities are unknown, and only the ordinal preferences of the agents for the facilities are available. The main difference between our work and previous work in this area is that while we assume that only ordinal information about agent preferences in known, we know the exact locations of the possible facilities F. Due to this extra information about the facilities, we are able to form powerful algorithms which have small distortion, i.e., perform almost as well as omniscient algorithms but use only ordinal information about agent preferences. For example, we present natural social choice mechanisms for choosing a single facility to open with distortion of at most 3 for minimizing both the total and the median social cost; this factor is provably the best possible. We analyze many general problems including matching, k-center, and k-median, and present black-box reductions from omniscient approximation algorithms with approximation factor β to ordinal algorithms with approximation factor 1 + 2β; doing this gives new ordinal algorithms for many important problems, and establishes a toolkit for analyzing such problems in the future.

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“…The distortion of matching in a metric space has received far less attention than social choice questions. References [7][8][9] analyzed maximum-weight metric matching; the maximization objective makes this problem far easier, and even choosing a uniformly random matching yields a distortion of a small constant. This is very different from our goal of computing a minimum-cost matching, for which no ordinal approximations better than Ω(n) are known.…”

Section: While Only Ordinal Information About Agent Preferences Is Kn...mentioning

confidence: 99%

“…These observations have recently led to a large body of work using the utilitarian approach, in which we assume that some latent numerical costs or utilities exist, but we only know the ordinal preferences of the agents, not their underlying numerical costs. See, for example, References [4,6,16,21,28,33,45] for the social choice setting, References [1,[7][8][9] for matching and other graph problems, and Reference [18] for facility location. These works focus on measuring the distortion of various algorithms: a measure of how well an algorithm behaves when using only ordinal information, as compared to the optimal algorithm that has access to the true underlying numerical information.…”

Section: Introductionmentioning

confidence: 99%

Ordinal Approximation for Social Choice, Matching, and Facility Location Problems Given Candidate Positions

Anshelevich

Zhu

2021

ACM Trans. Econ. Comput.

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In this work, we consider general facility location and social choice problems, in which sets of agents A and facilities F are located in a metric space, and our goal is to assign agents to facilities (as well as choose which facilities to open) to optimize the social cost. We form new algorithms to do this in the presence of only ordinal information , i.e., when the true costs or distances of the agents from the facilities are unknown , and only the ordinal preferences of the agents for the facilities are available. The main difference between our work and previous work in this area is that, while we assume that only ordinal information about agent preferences is known, we also know the exact locations of the possible facilities F. Due to this extra information about the facilities, we are able to form powerful algorithms that have small distortion , i.e., perform almost as well as omniscient algorithms (which know the true numerical distances between agents and facilities) but use only ordinal information about agent preferences. For example, we present natural social choice mechanisms for choosing a single facility to open with distortion of at most 3 for minimizing both the total and the median social cost; this factor is provably the best possible. We analyze many general problems including matching, k -center, and k -median, and we present black-box reductions from omniscient approximation algorithms with approximation factor β to ordinal algorithms with approximation factor 1+2β doing this gives new ordinal algorithms for many important problems and establishes a toolkit for analyzing such problems in the future.

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Tradeoffs Between Information and Ordinal Approximation for Bipartite Matching

Cited by 12 publications

References 18 publications

Improved Metric Distortion for Deterministic Social Choice Rules

Improved Metric Distortion for Deterministic Social Choice Rules

Ordinal Approximation for Social Choice, Matching, and Facility Location Problems Given Candidate Positions

Ordinal Approximation for Social Choice, Matching, and Facility Location Problems Given Candidate Positions

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