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Ordinal approximation in matching and social choice

Ordinal approximation in matching and social choice Ordinal Approximation in Matching and Social Choice ELLIOT ANSHELEVICH Rensselaer Polytechnic Institute In this note, we discuss several settings in which algorithms can provide good outcomes when given only ordinal information. We focus especially on voting mechanisms in settings with spacial preferences, and on the notion of distortion. Categories and Subject Descriptors: J.4 [Computer Applications]: Social and Behavioral Sciences; F.2 [Theory of Computation]: Analysis Of Algorithms General Terms: Algorithms, Theory Additional Key Words and Phrases: Matching, Social Choice, Metric Utility 1. INTRODUCTION Traditional approximation algorithms attempt to find good solutions under the constraint that they are also computable efficiently, as compared with an optimal solution which could be obtained using unbounded resources. There are many other notions of approximation, such as finding good solutions without knowing the future in online algorithms, being able to access the input a limited number of times in streaming algorithms, etc. In this letter we will focus on algorithms which are only given ordinal information, and yet must compete with algorithms which know the "ground truth" numerical information. To illustrate when such constraints can arise, consider the following simple voting scenario. As in classic voting and social choice literature, a set N of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Ordinal approximation in matching and social choice

ACM SIGecom Exchanges , Volume 15 (1) – Sep 6, 2016

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2016 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/2994501.2994504
Publisher site
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Abstract

Ordinal Approximation in Matching and Social Choice ELLIOT ANSHELEVICH Rensselaer Polytechnic Institute In this note, we discuss several settings in which algorithms can provide good outcomes when given only ordinal information. We focus especially on voting mechanisms in settings with spacial preferences, and on the notion of distortion. Categories and Subject Descriptors: J.4 [Computer Applications]: Social and Behavioral Sciences; F.2 [Theory of Computation]: Analysis Of Algorithms General Terms: Algorithms, Theory Additional Key Words and Phrases: Matching, Social Choice, Metric Utility 1. INTRODUCTION Traditional approximation algorithms attempt to find good solutions under the constraint that they are also computable efficiently, as compared with an optimal solution which could be obtained using unbounded resources. There are many other notions of approximation, such as finding good solutions without knowing the future in online algorithms, being able to access the input a limited number of times in streaming algorithms, etc. In this letter we will focus on algorithms which are only given ordinal information, and yet must compete with algorithms which know the "ground truth" numerical information. To illustrate when such constraints can arise, consider the following simple voting scenario. As in classic voting and social choice literature, a set N of

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Sep 6, 2016

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